id
stringlengths 14
117
| description
stringlengths 29
13k
| code
stringlengths 10
49.8k
| test_samples
dict | source
class label 3
classes | prompt
stringlengths 391
104k
|
|---|---|---|---|---|---|
p03289 AtCoder Beginner Contest 104 - AcCepted_10387
|
You are given a string S. Each character of S is uppercase or lowercase English letter. Determine if S satisfies all of the following conditions:
* The initial character of S is an uppercase `A`.
* There is exactly one occurrence of `C` between the third character from the beginning and the second to last character (inclusive).
* All letters except the `A` and `C` mentioned above are lowercase.
Constraints
* 4 ≤ |S| ≤ 10 (|S| is the length of the string S.)
* Each character of S is uppercase or lowercase English letter.
Input
Input is given from Standard Input in the following format:
S
Output
If S satisfies all of the conditions in the problem statement, print `AC`; otherwise, print `WA`.
Examples
Input
AtCoder
Output
AC
Input
ACoder
Output
WA
Input
AcycliC
Output
WA
Input
AtCoCo
Output
WA
Input
Atcoder
Output
WA
|
S = input()
if S[0]=='A' and S[2:-1].count('C')==1 and (S[1:S.find('C')]+S[S.find('C')+1:]).islower():
print('AC')
else:
print('WA')
|
{
"input": [
"AtCoCo",
"Atcoder",
"ACoder",
"AcycliC",
"AtCoder",
"AtBoCo",
"AtCoddr",
"redoctA",
"ACodes",
"BcycliC",
"etCodAr",
"AtBnCo",
"redpctA",
"ACodds",
"CilcycB",
"@tBnCo",
"retpcdA",
"sddoCA",
"BcyclhC",
"AtCodds",
"oCnBt@",
"Adcpter",
"sAdoCd",
"BycclhC",
"AtCoddt",
"nCnBt@",
"Accpter",
"sAdpCd",
"CycclhC",
"AtBoddt",
"nCoBt@",
"retpccA",
"sAdpdC",
"CzcclhC",
"@tBoddt",
"CnoBt@",
"reptccA",
"sACpdd",
"ChlcczC",
"@tBoddu",
"CooBt@",
"reotccA",
"ddpCAs",
"CzclchC",
"@sBoddu",
"@tBooC",
"teorccA",
"ddACps",
"CzclbhC",
"@uBoddu",
"@tBooD",
"oetrccA",
"ddCAps",
"CzblbhC",
"@dBoudu",
"@oBotD",
"Accrteo",
"edCAps",
"CzbhblC",
"AdBoudu",
"@oBtoD",
"Accqteo",
"edCApt",
"czClbhC",
"odBAudu",
"@ootBD",
"Abcqteo",
"epCAds",
"hzClbcC",
"odBAduu",
"DBtoo@",
"Abcpteo",
"epCBds",
"hzCkbcC",
"odB@duu",
"DBtoo?",
"oetpcbA",
"fpCBds",
"hzBlbcC",
"odB@dut",
"DBtpo?",
"oetpcb@",
"fpCBcs",
"hcBlbzC",
"odBAdut",
"DCtoo?",
"obtpce@",
"fpCBcr",
"bcBlhzC",
"odBdAuu",
"DDtoo?",
"obtpde@",
"rcBCpf",
"bcBlgzC",
"odBdAvu",
"tDDoo?",
"obtpd@e",
"fqCBcr",
"bcBlgyC",
"pdBdAvu",
"tDDop?",
"e@dptbo",
"fqCBdr",
"ccBlgyC",
"uvAdBdp"
],
"output": [
"WA",
"WA",
"WA",
"WA",
"AC",
"WA\n",
"AC\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"AC\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"AC\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n",
"WA\n"
]
}
| 5ATCODER
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You are given a string S. Each character of S is uppercase or lowercase English letter. Determine if S satisfies all of the following conditions:
* The initial character of S is an uppercase `A`.
* There is exactly one occurrence of `C` between the third character from the beginning and the second to last character (inclusive).
* All letters except the `A` and `C` mentioned above are lowercase.
Constraints
* 4 ≤ |S| ≤ 10 (|S| is the length of the string S.)
* Each character of S is uppercase or lowercase English letter.
Input
Input is given from Standard Input in the following format:
S
Output
If S satisfies all of the conditions in the problem statement, print `AC`; otherwise, print `WA`.
Examples
Input
AtCoder
Output
AC
Input
ACoder
Output
WA
Input
AcycliC
Output
WA
Input
AtCoCo
Output
WA
Input
Atcoder
Output
WA
### Input:
AtCoCo
### Output:
WA
### Input:
Atcoder
### Output:
WA
### Code:
S = input()
if S[0]=='A' and S[2:-1].count('C')==1 and (S[1:S.find('C')]+S[S.find('C')+1:]).islower():
print('AC')
else:
print('WA')
|
p03445 AtCoder Petrozavodsk Contest 001 - Simple APSP Problem_10390
|
You are given an H \times W grid. The square at the top-left corner will be represented by (0, 0), and the square at the bottom-right corner will be represented by (H-1, W-1).
Of those squares, N squares (x_1, y_1), (x_2, y_2), ..., (x_N, y_N) are painted black, and the other squares are painted white.
Let the shortest distance between white squares A and B be the minimum number of moves required to reach B from A visiting only white squares, where one can travel to an adjacent square sharing a side (up, down, left or right) in one move.
Since there are H × W - N white squares in total, there are _{(H×W-N)}C_2 ways to choose two of the white squares.
For each of these _{(H×W-N)}C_2 ways, find the shortest distance between the chosen squares, then find the sum of all those distances, modulo 1 000 000 007=10^9+7.
Constraints
* 1 \leq H, W \leq 10^6
* 1 \leq N \leq 30
* 0 \leq x_i \leq H-1
* 0 \leq y_i \leq W-1
* If i \neq j, then either x_i \neq x_j or y_i \neq y_j.
* There is at least one white square.
* For every pair of white squares A and B, it is possible to reach B from A visiting only white squares.
Input
Input is given from Standard Input in the following format:
H W
N
x_1 y_1
x_2 y_2
:
x_N y_N
Output
Print the sum of the shortest distances, modulo 10^9+7.
Examples
Input
2 3
1
1 1
Output
20
Input
2 3
1
1 2
Output
16
Input
3 3
1
1 1
Output
64
Input
4 4
4
0 1
1 1
2 1
2 2
Output
268
Input
1000000 1000000
1
0 0
Output
333211937
|
from collections import deque, Counter
import sys
sys.setrecursionlimit(10 ** 7)
input = sys.stdin.readline
mod = 10**9 + 7
h, w = map(int, input().split())
n = int(input())
ans = 0
black = []
row = Counter()
column = Counter()
for _ in range(n):
x, y = map(int, input().split())
row[x] += 1
column[y] += 1
black.append((x, y))
row[h] += 1
column[w] += 1
def sqsum(x):
return x*(x+1)*(2*x+1)//6
pre = -1
top = 0
bottom = h*w - n
area = []
for i in sorted(row.keys()):
if i == pre+2:
top += w
bottom -= w
area.append([-1, 1])
elif i > pre+2:
ans += (i-pre-2)*top*bottom + ((i-pre-2)*(i-pre-1)//2) * \
w*(bottom-top) - sqsum(i-pre-2)*(w**2)
ans %= mod
top += (i-pre-1)*w
bottom -= (i-pre-1)*w
area.append([-1, i-pre-1])
if i != h:
top += w-row[i]
bottom -= w-row[i]
area.append([i])
pre = i
R = len(area)
pre = -1
left = 0
right = h*w-n
area2 = []
for j in sorted(column.keys()):
if j == pre+2:
left += h
right -= h
area2.append([area[i][1] if area[i][0] == -1 else 1 for i in range(R)])
elif j > pre+2:
ans += (j-pre-2)*left*right + ((j-pre-2)*(j-pre-1)//2) * \
h*(right-left) - sqsum(j-pre-2)*(h**2)
ans %= mod
left += (j-pre-1)*h
right -= (j-pre-1)*h
area2.append([(j-pre-1)*area[i][1] if area[i][0]
== -1 else (j-pre-1) for i in range(R)])
if j != w:
left += h-column[j]
right -= h-column[j]
tmp = []
for i in range(R):
if area[i][0] == -1:
tmp.append(area[i][1])
else:
if (area[i][0], j) in black:
tmp.append(0)
else:
tmp.append(1)
area2.append(tmp)
pre = j
C = len(area2)
area2 = [[area2[j][i] for j in range(C)] for i in range(R)]
vec = [[1, 0], [0, 1], [-1, 0], [0, -1]]
def bfs(p, q):
dist = [[10**5 for _ in range(C)] for __ in range(R)]
visited = [[False for _ in range(C)] for __ in range(R)]
dist[p][q] = 0
visited[p][q] = True
q = deque([(p, q)])
while q:
x, y = q.popleft()
for dx, dy in vec:
if 0 <= x+dx < R and 0 <= y+dy < C and area2[x+dx][y+dy] != 0:
if not visited[x+dx][y+dy]:
dist[x+dx][y+dy] = dist[x][y] + 1
visited[x+dx][y+dy] = True
q.append((x+dx, y+dy))
return dist
ans2 = 0
for x in range(R*C):
i = x//C
j = x % C
if area2[i][j] == 0:
continue
d = bfs(i, j)
for y in range(R*C):
k = y//C
l = y % C
if area2[k][l] == 0:
continue
ans2 += area2[i][j]*area2[k][l]*d[k][l]
ans2 %= mod
ans2 *= pow(2, mod-2, mod)
print((ans+ans2) % mod)
|
{
"input": [
"2 3\n1\n1 2",
"3 3\n1\n1 1",
"1000000 1000000\n1\n0 0",
"4 4\n4\n0 1\n1 1\n2 1\n2 2",
"2 3\n1\n1 1",
"2 3\n1\n0 1",
"2 3\n1\n0 2",
"1000000 1000000\n0\n0 0",
"2 4\n1\n0 1",
"2 4\n0\n0 1",
"1000001 1000000\n0\n0 1",
"4 4\n0\n0 1",
"6 4\n0\n0 1",
"11 4\n0\n0 1",
"12 4\n0\n0 1",
"21 4\n0\n0 2",
"21 8\n0\n-1 2",
"14 8\n0\n-1 2",
"3 3\n1\n0 1",
"4 3\n1\n0 1",
"2 7\n0\n0 1",
"7 4\n0\n0 1",
"12 8\n0\n0 1",
"12 7\n0\n0 2",
"21 1\n0\n0 2",
"14 5\n0\n-1 2",
"14 13\n0\n-1 -2",
"3 6\n1\n1 1",
"2 6\n0\n0 1",
"2 0\n0\n0 1",
"9 4\n0\n0 1",
"8 4\n0\n0 0",
"21 2\n0\n0 2",
"14 14\n0\n0 -1",
"3 6\n0\n1 1",
"16 4\n0\n0 0",
"14 1\n0\n0 2",
"3 6\n1\n1 0",
"13 4\n0\n0 0",
"8 1\n0\n0 2",
"13 8\n0\n0 0",
"25 4\n0\n0 1",
"8 39\n0\n0 -1",
"8 2\n0\n1 2",
"5 39\n0\n0 -1",
"25 6\n0\n0 0",
"25 6\n1\n0 0",
"7 39\n0\n0 -2",
"3 4\n0\n-2 0",
"2 3\n0\n0 1",
"3 3\n1\n0 2",
"3 4\n1\n1 1",
"11 5\n0\n0 1",
"21 6\n0\n0 2",
"6 8\n0\n-1 2",
"10 8\n0\n-1 0",
"14 2\n0\n-1 -1",
"5 8\n0\n0 1",
"21 7\n0\n0 2",
"3 6\n1\n2 0",
"22 4\n0\n0 0",
"17 5\n0\n1 2",
"7 13\n0\n-1 0",
"7 14\n0\n0 -1",
"16 5\n0\n0 0",
"11 3\n0\n1 0",
"10 14\n0\n0 -1",
"3 11\n1\n1 0",
"13 10\n0\n0 0",
"25 4\n1\n0 1",
"13 4\n1\n0 1",
"5 9\n0\n0 -1",
"43 6\n1\n0 0",
"25 6\n1\n0 1",
"9 1\n0\n1 2",
"1 4\n0\n-2 0",
"7 23\n0\n-1 -1",
"5 6\n0\n-3 0",
"3 7\n0\n-5 0",
"3 4\n1\n2 1",
"1 10\n0\n0 1",
"12 1\n0\n0 1",
"21 6\n1\n0 2",
"9 8\n0\n-1 2",
"22 8\n0\n-2 -2",
"2 13\n0\n0 0",
"8 8\n0\n0 1",
"24 7\n0\n0 2",
"3 6\n1\n2 1",
"15 4\n0\n-1 1",
"1 2\n0\n0 0",
"22 1\n0\n0 0",
"16 3\n0\n0 0",
"2 2\n0\n0 4",
"15 3\n0\n1 0",
"3 11\n1\n1 1",
"13 10\n1\n0 0",
"13 4\n1\n0 0",
"43 6\n0\n0 0",
"25 3\n1\n0 1",
"5 3\n0\n-2 0",
"5 7\n0\n-3 0",
"11 4\n1\n0 2",
"11 2\n0\n-1 0",
"22 7\n0\n-2 -2"
],
"output": [
"16",
"64",
"333211937",
"268",
"20",
"20",
"16",
"333218986",
"48",
"56",
"40554683",
"320",
"920",
"4730",
"6016",
"29050",
"135604",
"45584",
"59",
"130",
"273",
"1386",
"30400",
"22078",
"1540",
"15295",
"148239",
"424",
"176",
"0",
"2730",
"1984",
"6601",
"178360",
"459",
"13440",
"455",
"404",
"7514",
"84",
"37492",
"47850",
"760084",
"400",
"277420",
"115475",
"113300",
"569296",
"154",
"25",
"54",
"140",
"7920",
"70875",
"5264",
"18960",
"2016",
"3380",
"100156",
"396",
"33176",
"26180",
"27300",
"33271",
"22120",
"2464",
"77840",
"2279",
"64285",
"46554",
"7154",
"4620",
"535436",
"113408",
"120",
"10",
"128800",
"1595",
"700",
"134",
"165",
"286",
"69438",
"14484",
"154000",
"1625",
"10752",
"144956",
"416",
"11210",
"1",
"1771",
"7144",
"8",
"5940",
"2324",
"62920",
"7124",
"541499",
"24952",
"280",
"2380",
"4470",
"1001",
"113883"
]
}
| 5ATCODER
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You are given an H \times W grid. The square at the top-left corner will be represented by (0, 0), and the square at the bottom-right corner will be represented by (H-1, W-1).
Of those squares, N squares (x_1, y_1), (x_2, y_2), ..., (x_N, y_N) are painted black, and the other squares are painted white.
Let the shortest distance between white squares A and B be the minimum number of moves required to reach B from A visiting only white squares, where one can travel to an adjacent square sharing a side (up, down, left or right) in one move.
Since there are H × W - N white squares in total, there are _{(H×W-N)}C_2 ways to choose two of the white squares.
For each of these _{(H×W-N)}C_2 ways, find the shortest distance between the chosen squares, then find the sum of all those distances, modulo 1 000 000 007=10^9+7.
Constraints
* 1 \leq H, W \leq 10^6
* 1 \leq N \leq 30
* 0 \leq x_i \leq H-1
* 0 \leq y_i \leq W-1
* If i \neq j, then either x_i \neq x_j or y_i \neq y_j.
* There is at least one white square.
* For every pair of white squares A and B, it is possible to reach B from A visiting only white squares.
Input
Input is given from Standard Input in the following format:
H W
N
x_1 y_1
x_2 y_2
:
x_N y_N
Output
Print the sum of the shortest distances, modulo 10^9+7.
Examples
Input
2 3
1
1 1
Output
20
Input
2 3
1
1 2
Output
16
Input
3 3
1
1 1
Output
64
Input
4 4
4
0 1
1 1
2 1
2 2
Output
268
Input
1000000 1000000
1
0 0
Output
333211937
### Input:
2 3
1
1 2
### Output:
16
### Input:
3 3
1
1 1
### Output:
64
### Code:
from collections import deque, Counter
import sys
sys.setrecursionlimit(10 ** 7)
input = sys.stdin.readline
mod = 10**9 + 7
h, w = map(int, input().split())
n = int(input())
ans = 0
black = []
row = Counter()
column = Counter()
for _ in range(n):
x, y = map(int, input().split())
row[x] += 1
column[y] += 1
black.append((x, y))
row[h] += 1
column[w] += 1
def sqsum(x):
return x*(x+1)*(2*x+1)//6
pre = -1
top = 0
bottom = h*w - n
area = []
for i in sorted(row.keys()):
if i == pre+2:
top += w
bottom -= w
area.append([-1, 1])
elif i > pre+2:
ans += (i-pre-2)*top*bottom + ((i-pre-2)*(i-pre-1)//2) * \
w*(bottom-top) - sqsum(i-pre-2)*(w**2)
ans %= mod
top += (i-pre-1)*w
bottom -= (i-pre-1)*w
area.append([-1, i-pre-1])
if i != h:
top += w-row[i]
bottom -= w-row[i]
area.append([i])
pre = i
R = len(area)
pre = -1
left = 0
right = h*w-n
area2 = []
for j in sorted(column.keys()):
if j == pre+2:
left += h
right -= h
area2.append([area[i][1] if area[i][0] == -1 else 1 for i in range(R)])
elif j > pre+2:
ans += (j-pre-2)*left*right + ((j-pre-2)*(j-pre-1)//2) * \
h*(right-left) - sqsum(j-pre-2)*(h**2)
ans %= mod
left += (j-pre-1)*h
right -= (j-pre-1)*h
area2.append([(j-pre-1)*area[i][1] if area[i][0]
== -1 else (j-pre-1) for i in range(R)])
if j != w:
left += h-column[j]
right -= h-column[j]
tmp = []
for i in range(R):
if area[i][0] == -1:
tmp.append(area[i][1])
else:
if (area[i][0], j) in black:
tmp.append(0)
else:
tmp.append(1)
area2.append(tmp)
pre = j
C = len(area2)
area2 = [[area2[j][i] for j in range(C)] for i in range(R)]
vec = [[1, 0], [0, 1], [-1, 0], [0, -1]]
def bfs(p, q):
dist = [[10**5 for _ in range(C)] for __ in range(R)]
visited = [[False for _ in range(C)] for __ in range(R)]
dist[p][q] = 0
visited[p][q] = True
q = deque([(p, q)])
while q:
x, y = q.popleft()
for dx, dy in vec:
if 0 <= x+dx < R and 0 <= y+dy < C and area2[x+dx][y+dy] != 0:
if not visited[x+dx][y+dy]:
dist[x+dx][y+dy] = dist[x][y] + 1
visited[x+dx][y+dy] = True
q.append((x+dx, y+dy))
return dist
ans2 = 0
for x in range(R*C):
i = x//C
j = x % C
if area2[i][j] == 0:
continue
d = bfs(i, j)
for y in range(R*C):
k = y//C
l = y % C
if area2[k][l] == 0:
continue
ans2 += area2[i][j]*area2[k][l]*d[k][l]
ans2 %= mod
ans2 *= pow(2, mod-2, mod)
print((ans+ans2) % mod)
|
p03605 AtCoder Beginner Contest 073 - September 9_10394
|
It is September 9 in Japan now.
You are given a two-digit integer N. Answer the question: Is 9 contained in the decimal notation of N?
Constraints
* 10≤N≤99
Input
Input is given from Standard Input in the following format:
N
Output
If 9 is contained in the decimal notation of N, print `Yes`; if not, print `No`.
Examples
Input
29
Output
Yes
Input
72
Output
No
Input
91
Output
Yes
|
n = input()
ans = 'Yes' if '9' in n else 'No'
print(ans)
|
{
"input": [
"29",
"91",
"72",
"1",
"69",
"115",
"84",
"0",
"181",
"168",
"174",
"304",
"143",
"465",
"929",
"109",
"820",
"147",
"112",
"19",
"215",
"34",
"161",
"8",
"189",
"15",
"361",
"17",
"485",
"16",
"348",
"3",
"49",
"2",
"41",
"4",
"23",
"-2",
"7",
"6",
"9",
"5",
"-3",
"10",
"-4",
"20",
"-8",
"13",
"-10",
"-13",
"-15",
"-6",
"-12",
"-14",
"11",
"108",
"33",
"12",
"54",
"42",
"-7",
"123",
"285",
"274",
"40",
"121",
"272",
"127",
"92",
"89",
"1223",
"18",
"14",
"-5",
"352",
"21",
"53",
"-20",
"146",
"-25",
"-26",
"48",
"252",
"-18",
"-32",
"25",
"82",
"-16",
"45",
"-24",
"28",
"24",
"43",
"22",
"46",
"-33",
"-37",
"-28",
"30",
"-23",
"32",
"-17",
"56"
],
"output": [
"Yes",
"Yes",
"No",
"No\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"Yes\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"Yes\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n"
]
}
| 5ATCODER
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
It is September 9 in Japan now.
You are given a two-digit integer N. Answer the question: Is 9 contained in the decimal notation of N?
Constraints
* 10≤N≤99
Input
Input is given from Standard Input in the following format:
N
Output
If 9 is contained in the decimal notation of N, print `Yes`; if not, print `No`.
Examples
Input
29
Output
Yes
Input
72
Output
No
Input
91
Output
Yes
### Input:
29
### Output:
Yes
### Input:
91
### Output:
Yes
### Code:
n = input()
ans = 'Yes' if '9' in n else 'No'
print(ans)
|
p03766 AtCoder Regular Contest 071 - Infinite Sequence_10398
|
How many infinite sequences a_1, a_2, ... consisting of {{1, ... ,n}} satisfy the following conditions?
* The n-th and subsequent elements are all equal. That is, if n \leq i,j, a_i = a_j.
* For every integer i, the a_i elements immediately following the i-th element are all equal. That is, if i < j < k\leq i+a_i, a_j = a_k.
Find the count modulo 10^9+7.
Constraints
* 1 \leq n \leq 10^6
Input
Input is given from Standard Input in the following format:
n
Output
Print how many sequences satisfy the conditions, modulo 10^9+7.
Examples
Input
2
Output
4
Input
654321
Output
968545283
|
n = int(input())
dp = [0] * (n+1)
mod = 10**9+7
dp[0] = n
dp[1] = n*n
SUM = n+n*n
for i in range(2,n):
dp[i] = (n-1)*(n-1) + n-i+1+SUM-dp[i-2]
dp[i] %= mod
SUM += dp[i]
SUM %= mod
print(dp[n-1])
|
{
"input": [
"654321",
"2",
"53707",
"3",
"42179",
"1",
"69890",
"4",
"68941",
"126548",
"138065",
"132361",
"219101",
"412635",
"147547",
"226036",
"401978",
"462799",
"563821",
"507124",
"417069",
"235764",
"221196",
"335918",
"316839",
"186455",
"47732",
"28011",
"3156",
"4191",
"3206",
"2224",
"866",
"1606",
"2090",
"3411",
"4580",
"2546",
"710",
"519",
"937",
"768",
"1349",
"802",
"1471",
"473",
"61",
"111",
"110",
"100",
"101",
"5",
"82011",
"6",
"67624",
"8",
"48601",
"109858",
"34690",
"95277",
"103569",
"395899",
"261908",
"64563",
"305852",
"347238",
"577994",
"605811",
"829578",
"328962",
"31334",
"430632",
"292532",
"261658",
"354451",
"73454",
"36745",
"2557",
"5883",
"5015",
"281",
"820",
"2327",
"2065",
"2514",
"1779",
"3143",
"1018",
"994",
"1012",
"746",
"711",
"1493",
"2729",
"402",
"54",
"9",
"130264",
"7",
"41430",
"76818",
"144905"
],
"output": [
"968545283",
"4",
"700929608\n",
"15\n",
"477829788\n",
"1\n",
"39294826\n",
"43\n",
"825040611\n",
"41353562\n",
"144629245\n",
"413027178\n",
"267179376\n",
"541957737\n",
"938741083\n",
"64496379\n",
"866680855\n",
"785854092\n",
"627002130\n",
"334593821\n",
"479470907\n",
"999901458\n",
"652869023\n",
"449135902\n",
"32285099\n",
"499701590\n",
"680298744\n",
"516582732\n",
"80976406\n",
"897049493\n",
"629828668\n",
"331667916\n",
"684581999\n",
"613312485\n",
"356070120\n",
"307833923\n",
"197670641\n",
"720737128\n",
"811482250\n",
"416360304\n",
"360611018\n",
"664694733\n",
"997283928\n",
"405954614\n",
"965633400\n",
"820363580\n",
"292753530\n",
"518926683\n",
"780059581\n",
"347832232\n",
"790312799\n",
"117\n",
"298031070\n",
"306\n",
"140016323\n",
"1716\n",
"953396301\n",
"437472929\n",
"146955423\n",
"286193232\n",
"564791687\n",
"310829317\n",
"332153765\n",
"257155273\n",
"372821929\n",
"726907316\n",
"894110072\n",
"560821878\n",
"341930999\n",
"315733764\n",
"355059235\n",
"383672035\n",
"61406479\n",
"264782653\n",
"777054356\n",
"927646567\n",
"367630690\n",
"941452342\n",
"629003532\n",
"185880627\n",
"952635266\n",
"473737027\n",
"47113757\n",
"918014281\n",
"388891861\n",
"758526822\n",
"758164617\n",
"82374915\n",
"667917793\n",
"39796799\n",
"784922482\n",
"613202152\n",
"176879424\n",
"185180836\n",
"423118060\n",
"460539956\n",
"3825\n",
"780631695\n",
"745\n",
"917687471\n",
"870982938\n",
"826751925\n"
]
}
| 5ATCODER
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
How many infinite sequences a_1, a_2, ... consisting of {{1, ... ,n}} satisfy the following conditions?
* The n-th and subsequent elements are all equal. That is, if n \leq i,j, a_i = a_j.
* For every integer i, the a_i elements immediately following the i-th element are all equal. That is, if i < j < k\leq i+a_i, a_j = a_k.
Find the count modulo 10^9+7.
Constraints
* 1 \leq n \leq 10^6
Input
Input is given from Standard Input in the following format:
n
Output
Print how many sequences satisfy the conditions, modulo 10^9+7.
Examples
Input
2
Output
4
Input
654321
Output
968545283
### Input:
654321
### Output:
968545283
### Input:
2
### Output:
4
### Code:
n = int(input())
dp = [0] * (n+1)
mod = 10**9+7
dp[0] = n
dp[1] = n*n
SUM = n+n*n
for i in range(2,n):
dp[i] = (n-1)*(n-1) + n-i+1+SUM-dp[i-2]
dp[i] %= mod
SUM += dp[i]
SUM %= mod
print(dp[n-1])
|
p00027 What day is today?_10404
|
Your task is to write a program which reads a date (from 2004/1/1 to 2004/12/31) and prints the day of the date. Jan. 1, 2004, is Thursday. Note that 2004 is a leap year and we have Feb. 29.
Input
The input is a sequence of datasets. The end of the input is indicated by a line containing one zero. Each dataset consists of two integers m and d separated by a single space in a line. These integers respectively represent the month and the day.
The number of datasets is less than or equal to 50.
Output
For each dataset, print the day (please see the following words) in a line.
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday
Example
Input
1 1
2 29
0 0
Output
Thursday
Sunday
|
days = [31,29,31,30,31,30,31,31,30,31,30,31]
ans = ["Monday","Tuesday","Wednesday","Thursday","Friday","Saturday","Sunday"]
while True:
idx = 3
m,d = map(int, input().split())
if m==0: break
print(ans[(idx+sum(days[:m-1])+d-1)%7])
|
{
"input": [
"1 1\n2 29\n0 0",
"1 1\n2 26\n0 0",
"2 1\n2 26\n0 0",
"1 1\n3 26\n0 0",
"2 1\n2 17\n0 0",
"2 1\n2 18\n0 0",
"2 1\n1 19\n0 0",
"2 2\n2 17\n0 0",
"2 2\n3 17\n0 0",
"2 1\n1 17\n0 0",
"2 1\n1 18\n0 0",
"4 2\n3 17\n0 0",
"2 2\n1 17\n0 0",
"4 2\n6 17\n0 0",
"4 1\n2 17\n0 0",
"4 1\n2 18\n0 0",
"2 2\n2 8\n0 0",
"4 1\n2 7\n0 0",
"4 2\n2 24\n0 0",
"2 2\n6 17\n0 0",
"4 2\n2 16\n0 0",
"4 2\n7 17\n0 0",
"1 1\n2 15\n0 0",
"6 2\n7 17\n0 0",
"6 2\n7 8\n0 0",
"4 2\n3 14\n0 0",
"1 2\n4 16\n0 0",
"3 2\n3 14\n0 0",
"1 3\n4 16\n0 0",
"3 2\n1 14\n0 0",
"3 2\n2 14\n0 0",
"3 3\n2 1\n0 0",
"5 1\n2 17\n0 0",
"5 1\n2 7\n0 0",
"4 3\n2 16\n0 0",
"4 4\n6 4\n0 0",
"4 1\n3 8\n0 0",
"5 1\n2 12\n0 0",
"5 1\n1 7\n0 0",
"3 2\n4 1\n0 0",
"4 7\n3 16\n0 0",
"6 2\n12 8\n0 0",
"4 3\n3 14\n0 0",
"6 2\n1 12\n0 0",
"4 7\n3 19\n0 0",
"2 2\n12 17\n0 0",
"5 4\n6 11\n0 0",
"5 4\n6 7\n0 0",
"6 7\n6 7\n0 0",
"5 4\n2 17\n0 0",
"2 1\n2 19\n0 0",
"1 1\n3 19\n0 0",
"2 1\n2 11\n0 0",
"2 1\n2 7\n0 0",
"2 1\n2 29\n0 0",
"1 1\n5 19\n0 0",
"2 1\n3 17\n0 0",
"2 2\n2 11\n0 0",
"2 1\n1 11\n0 0",
"4 4\n3 17\n0 0",
"2 2\n2 24\n0 0",
"5 2\n6 17\n0 0",
"2 1\n1 15\n0 0",
"4 4\n3 16\n0 0",
"4 1\n4 7\n0 0",
"2 1\n2 15\n0 0",
"4 4\n3 3\n0 0",
"4 1\n4 8\n0 0",
"4 4\n3 4\n0 0",
"4 2\n4 8\n0 0",
"1 2\n2 16\n0 0",
"1 4\n3 4\n0 0",
"4 2\n3 8\n0 0",
"1 2\n3 16\n0 0",
"1 4\n1 4\n0 0",
"3 3\n2 14\n0 0",
"2 1\n4 18\n0 0",
"2 2\n4 24\n0 0",
"1 1\n2 11\n0 0",
"4 1\n3 17\n0 0",
"4 2\n2 18\n0 0",
"2 1\n2 8\n0 0",
"2 1\n1 7\n0 0",
"1 2\n4 24\n0 0",
"5 2\n6 2\n0 0",
"4 4\n3 23\n0 0",
"1 1\n4 7\n0 0",
"4 1\n2 24\n0 0",
"2 1\n2 24\n0 0",
"8 1\n4 8\n0 0",
"1 1\n4 15\n0 0",
"4 2\n4 4\n0 0",
"1 2\n7 17\n0 0",
"1 4\n3 16\n0 0",
"6 2\n1 8\n0 0",
"1 2\n3 14\n0 0",
"1 2\n4 23\n0 0",
"4 2\n1 14\n0 0",
"1 2\n2 14\n0 0",
"3 3\n3 14\n0 0",
"1 2\n2 11\n0 0"
],
"output": [
"Thursday\nSunday",
"Thursday\nThursday\n",
"Sunday\nThursday\n",
"Thursday\nFriday\n",
"Sunday\nTuesday\n",
"Sunday\nWednesday\n",
"Sunday\nMonday\n",
"Monday\nTuesday\n",
"Monday\nWednesday\n",
"Sunday\nSaturday\n",
"Sunday\nSunday\n",
"Friday\nWednesday\n",
"Monday\nSaturday\n",
"Friday\nThursday\n",
"Thursday\nTuesday\n",
"Thursday\nWednesday\n",
"Monday\nSunday\n",
"Thursday\nSaturday\n",
"Friday\nTuesday\n",
"Monday\nThursday\n",
"Friday\nMonday\n",
"Friday\nSaturday\n",
"Thursday\nSunday\n",
"Wednesday\nSaturday\n",
"Wednesday\nThursday\n",
"Friday\nSunday\n",
"Friday\nFriday\n",
"Tuesday\nSunday\n",
"Saturday\nFriday\n",
"Tuesday\nWednesday\n",
"Tuesday\nSaturday\n",
"Wednesday\nSunday\n",
"Saturday\nTuesday\n",
"Saturday\nSaturday\n",
"Saturday\nMonday\n",
"Sunday\nFriday\n",
"Thursday\nMonday\n",
"Saturday\nThursday\n",
"Saturday\nWednesday\n",
"Tuesday\nThursday\n",
"Wednesday\nTuesday\n",
"Wednesday\nWednesday\n",
"Saturday\nSunday\n",
"Wednesday\nMonday\n",
"Wednesday\nFriday\n",
"Monday\nFriday\n",
"Tuesday\nFriday\n",
"Tuesday\nMonday\n",
"Monday\nMonday\n",
"Tuesday\nTuesday\n",
"Sunday\nThursday\n",
"Thursday\nFriday\n",
"Sunday\nWednesday\n",
"Sunday\nSaturday\n",
"Sunday\nSunday\n",
"Thursday\nWednesday\n",
"Sunday\nWednesday\n",
"Monday\nWednesday\n",
"Sunday\nSunday\n",
"Sunday\nWednesday\n",
"Monday\nTuesday\n",
"Sunday\nThursday\n",
"Sunday\nThursday\n",
"Sunday\nTuesday\n",
"Thursday\nWednesday\n",
"Sunday\nSunday\n",
"Sunday\nWednesday\n",
"Thursday\nThursday\n",
"Sunday\nThursday\n",
"Friday\nThursday\n",
"Friday\nMonday\n",
"Sunday\nThursday\n",
"Friday\nMonday\n",
"Friday\nTuesday\n",
"Sunday\nSunday\n",
"Wednesday\nSaturday\n",
"Sunday\nSunday\n",
"Monday\nSaturday\n",
"Thursday\nWednesday\n",
"Thursday\nWednesday\n",
"Friday\nWednesday\n",
"Sunday\nSunday\n",
"Sunday\nWednesday\n",
"Friday\nSaturday\n",
"Sunday\nWednesday\n",
"Sunday\nTuesday\n",
"Thursday\nWednesday\n",
"Thursday\nTuesday\n",
"Sunday\nTuesday\n",
"Sunday\nThursday\n",
"Thursday\nThursday\n",
"Friday\nSunday\n",
"Friday\nSaturday\n",
"Sunday\nTuesday\n",
"Wednesday\nThursday\n",
"Friday\nSunday\n",
"Friday\nFriday\n",
"Friday\nWednesday\n",
"Friday\nSaturday\n",
"Wednesday\nSunday\n",
"Friday\nWednesday\n"
]
}
| 6AIZU
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Your task is to write a program which reads a date (from 2004/1/1 to 2004/12/31) and prints the day of the date. Jan. 1, 2004, is Thursday. Note that 2004 is a leap year and we have Feb. 29.
Input
The input is a sequence of datasets. The end of the input is indicated by a line containing one zero. Each dataset consists of two integers m and d separated by a single space in a line. These integers respectively represent the month and the day.
The number of datasets is less than or equal to 50.
Output
For each dataset, print the day (please see the following words) in a line.
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday
Example
Input
1 1
2 29
0 0
Output
Thursday
Sunday
### Input:
1 1
2 29
0 0
### Output:
Thursday
Sunday
### Input:
1 1
2 26
0 0
### Output:
Thursday
Thursday
### Code:
days = [31,29,31,30,31,30,31,31,30,31,30,31]
ans = ["Monday","Tuesday","Wednesday","Thursday","Friday","Saturday","Sunday"]
while True:
idx = 3
m,d = map(int, input().split())
if m==0: break
print(ans[(idx+sum(days[:m-1])+d-1)%7])
|
p00158 Collatz's Problem_10408
|
For a positive integer n
* If n is even, divide by 2.
* If n is odd, multiply by 3 and add 1.
If you repeat the above operation, the result will be 1. A problem called "Colatz conjecture" is that repeating this operation for any positive integer n will always result in 1. This problem is an unsolved problem, also known as the "Kakutani problem" in Japan. It is known that there is no counterexample for a very large number 3 × 253 = 27,021,597,764,222,976 using a computer, but it has not been mathematically proven.
Create a program that takes the integer n as an input and outputs the number of operations that are repeated until the result is 1. The integer n should be an integer that is 1 or more and the value in the middle of repeating the above calculation is 1000000 or less. For example, if you receive 3 as input, the operation column will be
3 → 10 → 5 → 16 → 8 → 4 → 2 → 1
Therefore, 7 is output, which is the number of operations (the number of arrows above).
Input
A sequence of multiple datasets is given as input. The end of the input is indicated by a single line of zeros. One integer n (n ≤ 1000000) is given on one row for each dataset.
The number of datasets does not exceed 50.
Output
Outputs the number of operations for each dataset on one line.
Example
Input
3
10
0
Output
7
6
|
while 1:
n = int(input())
if n == 0:
break
cnt = 0
while n != 1:
if n % 2 == 0:
n //= 2
else:
n = n * 3 + 1
cnt += 1
print(cnt)
|
{
"input": [
"3\n10\n0",
"3\n15\n0",
"3\n3\n0",
"3\n11\n0",
"3\n2\n0",
"3\n9\n0",
"3\n6\n0",
"3\n1\n0",
"3\n0\n0",
"3\n18\n0",
"3\n16\n0",
"3\n4\n0",
"3\n5\n0",
"3\n17\n0",
"3\n30\n0",
"3\n22\n0",
"3\n41\n0",
"3\n59\n0",
"3\n24\n0",
"3\n7\n0",
"3\n53\n0",
"3\n55\n0",
"3\n27\n0",
"3\n13\n0",
"3\n31\n0",
"3\n8\n0",
"3\n25\n0",
"3\n66\n0",
"3\n47\n0",
"3\n109\n0",
"3\n77\n0",
"3\n33\n0",
"3\n37\n0",
"3\n115\n0",
"3\n121\n0",
"3\n51\n0",
"3\n98\n0",
"3\n172\n0",
"3\n87\n0",
"3\n239\n0",
"3\n39\n0",
"3\n251\n0",
"3\n123\n0",
"3\n34\n0",
"3\n130\n0",
"3\n62\n0",
"3\n182\n0",
"3\n78\n0",
"3\n207\n0",
"3\n161\n0",
"3\n157\n0",
"3\n64\n0",
"3\n350\n0",
"3\n338\n0",
"3\n413\n0",
"3\n175\n0",
"3\n440\n0",
"3\n43\n0",
"3\n105\n0",
"3\n135\n0",
"3\n249\n0",
"3\n125\n0",
"3\n590\n0",
"3\n621\n0",
"3\n279\n0",
"3\n221\n0",
"3\n211\n0",
"3\n167\n0",
"3\n259\n0",
"3\n82\n0",
"3\n147\n0",
"3\n361\n0",
"3\n111\n0",
"3\n107\n0",
"3\n315\n0",
"3\n343\n0",
"3\n191\n0",
"3\n142\n0",
"3\n319\n0",
"3\n193\n0",
"3\n2190\n0",
"3\n94\n0",
"3\n292\n0",
"3\n1043\n0",
"3\n365\n0",
"3\n3340\n0",
"3\n97\n0",
"3\n91\n0",
"3\n391\n0",
"3\n521\n0",
"3\n503\n0",
"3\n823\n0",
"3\n451\n0",
"3\n594\n0",
"3\n684\n0",
"3\n0\n1",
"3\n0\n2",
"3\n0\n-1",
"3\n28\n0",
"3\n0\n-2",
"3\n58\n0"
],
"output": [
"7\n6",
"7\n17\n",
"7\n7\n",
"7\n14\n",
"7\n1\n",
"7\n19\n",
"7\n8\n",
"7\n0\n",
"7\n",
"7\n20\n",
"7\n4\n",
"7\n2\n",
"7\n5\n",
"7\n12\n",
"7\n18\n",
"7\n15\n",
"7\n109\n",
"7\n32\n",
"7\n10\n",
"7\n16\n",
"7\n11\n",
"7\n112\n",
"7\n111\n",
"7\n9\n",
"7\n106\n",
"7\n3\n",
"7\n23\n",
"7\n27\n",
"7\n104\n",
"7\n113\n",
"7\n22\n",
"7\n26\n",
"7\n21\n",
"7\n33\n",
"7\n95\n",
"7\n24\n",
"7\n25\n",
"7\n31\n",
"7\n30\n",
"7\n52\n",
"7\n34\n",
"7\n65\n",
"7\n46\n",
"7\n13\n",
"7\n28\n",
"7\n107\n",
"7\n93\n",
"7\n35\n",
"7\n88\n",
"7\n98\n",
"7\n36\n",
"7\n6\n",
"7\n81\n",
"7\n50\n",
"7\n89\n",
"7\n80\n",
"7\n115\n",
"7\n29\n",
"7\n38\n",
"7\n41\n",
"7\n47\n",
"7\n108\n",
"7\n56\n",
"7\n87\n",
"7\n42\n",
"7\n114\n",
"7\n39\n",
"7\n67\n",
"7\n122\n",
"7\n110\n",
"7\n116\n",
"7\n45\n",
"7\n69\n",
"7\n100\n",
"7\n37\n",
"7\n125\n",
"7\n44\n",
"7\n103\n",
"7\n55\n",
"7\n119\n",
"7\n76\n",
"7\n105\n",
"7\n117\n",
"7\n124\n",
"7\n94\n",
"7\n136\n",
"7\n118\n",
"7\n92\n",
"7\n120\n",
"7\n123\n",
"7\n66\n",
"7\n134\n",
"7\n53\n",
"7\n74\n",
"7\n126\n",
"7\n",
"7\n",
"7\n",
"7\n18\n",
"7\n",
"7\n19\n"
]
}
| 6AIZU
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
For a positive integer n
* If n is even, divide by 2.
* If n is odd, multiply by 3 and add 1.
If you repeat the above operation, the result will be 1. A problem called "Colatz conjecture" is that repeating this operation for any positive integer n will always result in 1. This problem is an unsolved problem, also known as the "Kakutani problem" in Japan. It is known that there is no counterexample for a very large number 3 × 253 = 27,021,597,764,222,976 using a computer, but it has not been mathematically proven.
Create a program that takes the integer n as an input and outputs the number of operations that are repeated until the result is 1. The integer n should be an integer that is 1 or more and the value in the middle of repeating the above calculation is 1000000 or less. For example, if you receive 3 as input, the operation column will be
3 → 10 → 5 → 16 → 8 → 4 → 2 → 1
Therefore, 7 is output, which is the number of operations (the number of arrows above).
Input
A sequence of multiple datasets is given as input. The end of the input is indicated by a single line of zeros. One integer n (n ≤ 1000000) is given on one row for each dataset.
The number of datasets does not exceed 50.
Output
Outputs the number of operations for each dataset on one line.
Example
Input
3
10
0
Output
7
6
### Input:
3
10
0
### Output:
7
6
### Input:
3
15
0
### Output:
7
17
### Code:
while 1:
n = int(input())
if n == 0:
break
cnt = 0
while n != 1:
if n % 2 == 0:
n //= 2
else:
n = n * 3 + 1
cnt += 1
print(cnt)
|
p00315 Quality Management_10411
|
The cloth coasters produced and sold by Aizu Takada City are known for their symmetrical design and great beauty. As part of quality control, Aizu Takada City has installed cameras on the production line to automatically verify that the images obtained by shooting each coaster are symmetrical. Each coaster is represented as a square black and white image of N x N pixels. Each pixel has a value of 0 or 1 corresponding to a white or black image.
This time, the software of the image analysis system will be updated along with the equipment update of the production line. The new system has been devised to reduce the amount of communication data, and data is sent from the camera to the analysis system by the following method.
* The information of the first coaster flowing on the line is sent to the system as an N × N pixel image.
* For the coaster information on the second and subsequent images, only the difference from the previous image is sent. The difference is given as a set of pixel positions that change from "0 to 1" or "1 to 0".
For C coasters, enter the pixel information of the first image and the difference information of the following C-1 image, and create a program that reports the number of coasters that are vertically symmetrical and symmetrical.
Input
The input is given in the following format.
C N
p11p12 ... p1N
p21p22 ... p2N
::
pN1pN2 ... pNN
diff1
diff2
::
diffC-1
The first line gives the number of coasters C (1 ≤ C ≤ 10000) and the number of pixels N (2 ≤ N ≤ 1000 and N is even) in the vertical and horizontal directions of the image. Lines 2 to N + 1 are given the number pij (pij is 0 or 1) in rows N x columns N representing the pixels of the image of the first coaster.
After the N + 2nd line, the difference diffi representing the information of the 2nd and subsequent coasters is given in the following format.
D
r1 c1
r2 c2
::
rD cD
The number of changed pixels D (0 ≤ D ≤ 100) is given in the first line. The following D rows are given ri and ci (1 ≤ ri, ci ≤ N), which represent the row and column numbers of the changed pixels, respectively. The same position cannot be given more than once in diffi.
Output
The number of coasters that are vertically symmetrical and symmetrical is output on one line.
Examples
Input
7 8
00100000
00011000
10111101
01100110
01000110
10111101
00011000
00100100
2
5 3
1 6
1
6 8
3
6 8
3 3
3 6
2
6 3
6 6
0
2
3 8
6 8
Output
3
Input
1 6
000000
000000
010010
010010
000000
000000
Output
1
Input
2 2
00
00
4
1 1
1 2
2 1
2 2
Output
2
|
def next(N, i):
return ((N-i-1)+N)%N
def getState(N, G, i, j):
return G[i][j] == G[i][next(N, j)] and G[i][j] == G[next(N, i)][j] and G[i][j] == G[next(N, i)][next(N, j)]
def getInit(N, G):
dcnt = 0
for i in range(N//2):
for j in range(N//2):
if not getState(N, G, i, j): dcnt += 1
return dcnt
C, N = map(int, input().split())
#G = [[0]*N]*N
G = [['N' for _ in range(N)] for _ in range(N)]
for i in range(N):
str = input()
for j in range(N):
G[i][j] = int(str[j])
ans = 0
dcnt = getInit(N, G)
if dcnt == 0: ans += 1
for i in range(C-1):
k = int(input())
for j in range(k):
r, c = map(int, input().split())
r -= 1
c -= 1
pre = getState(N, G, r, c)
G[r][c] = 0 if G[r][c]== 1 else 1
post = getState(N, G, r, c)
if not pre and post: dcnt -= 1
elif pre and not post: dcnt += 1
if dcnt == 0: ans += 1
print(ans)
|
{
"input": [
"1 6\n000000\n000000\n010010\n010010\n000000\n000000",
"7 8\n00100000\n00011000\n10111101\n01100110\n01000110\n10111101\n00011000\n00100100\n2\n5 3\n1 6\n1\n6 8\n3\n6 8\n3 3\n3 6\n2\n6 3\n6 6\n0\n2\n3 8\n6 8",
"2 2\n00\n00\n4\n1 1\n1 2\n2 1\n2 2",
"1 6\n000000\n000000\n010010\n011010\n000000\n000000",
"1 2\n00\n00\n4\n1 1\n1 2\n2 1\n2 2",
"2 0\n00\n00\n4\n1 1\n2 2\n2 1\n2 2",
"7 8\n00100000\n00011000\n10111101\n01100110\n01000110\n10111101\n00011000\n00100100\n2\n5 3\n0 6\n1\n6 8\n3\n6 8\n3 3\n3 6\n2\n6 3\n6 6\n0\n2\n3 8\n6 8",
"1 6\n000000\n000000\n010010\n011010\n000000\n100000",
"7 8\n00100000\n00011000\n10111101\n01100110\n01000110\n10111101\n00011000\n00100100\n2\n5 3\n0 6\n1\n6 16\n3\n6 8\n3 3\n3 6\n2\n6 3\n6 6\n0\n2\n3 8\n6 8",
"1 2\n00\n00\n4\n1 1\n1 2\n2 1\n3 2",
"1 6\n000000\n010000\n010010\n011010\n000000\n100000",
"7 8\n00100000\n00011000\n10111101\n01100110\n01000110\n10111101\n00011000\n00100100\n2\n5 3\n0 6\n1\n6 16\n3\n6 8\n3 3\n3 6\n2\n6 3\n6 6\n0\n2\n1 8\n6 8",
"1 2\n00\n00\n4\n1 1\n1 2\n2 2\n3 2",
"1 6\n000000\n010000\n010000\n011010\n000000\n100000",
"7 8\n00100000\n00011000\n10111101\n01100110\n01000110\n10111101\n00011000\n00100100\n2\n5 3\n0 6\n1\n6 16\n3\n6 8\n3 3\n3 6\n2\n6 3\n6 6\n0\n3\n1 8\n6 8",
"1 2\n00\n00\n4\n1 2\n1 2\n2 2\n3 2",
"1 6\n000001\n010000\n010000\n011010\n000000\n100000",
"7 8\n00100000\n00011000\n10111101\n01100110\n01000110\n10111101\n00011000\n00100100\n2\n2 3\n0 6\n1\n6 16\n3\n6 8\n3 3\n3 6\n2\n6 3\n6 6\n0\n3\n1 8\n6 8",
"1 2\n00\n00\n4\n1 2\n1 2\n2 4\n3 2",
"7 8\n00100000\n00011000\n10111101\n01100110\n01000110\n10111101\n00011000\n00100100\n2\n2 3\n0 6\n1\n6 16\n3\n6 8\n3 2\n3 6\n2\n6 3\n6 6\n0\n3\n1 8\n6 8",
"1 2\n00\n00\n4\n1 2\n1 1\n2 4\n3 2",
"7 8\n00000000\n00011000\n10111101\n01100110\n01000110\n10111101\n00011000\n00100100\n2\n2 3\n0 6\n1\n6 16\n3\n6 8\n3 2\n3 6\n2\n6 3\n6 6\n0\n3\n1 8\n6 8",
"1 2\n00\n00\n4\n1 2\n1 1\n2 4\n3 0",
"7 8\n00000000\n00011000\n10111101\n01100110\n01000110\n10111101\n00011000\n00100100\n2\n2 3\n0 6\n1\n6 16\n3\n6 8\n3 2\n3 6\n2\n6 3\n6 6\n0\n0\n1 8\n6 8",
"1 2\n00\n1\n4\n1 2\n1 1\n2 4\n3 0",
"7 8\n00000000\n00011000\n10111101\n01100110\n01000110\n10111101\n00011000\n00100100\n2\n2 3\n0 6\n1\n6 16\n3\n6 8\n3 2\n3 6\n2\n6 5\n6 6\n0\n0\n1 8\n6 8",
"1 2\n00\n1\n4\n1 2\n1 2\n2 4\n3 0",
"7 8\n00000000\n00011000\n10111101\n01100110\n01000110\n10111101\n00011000\n00110100\n2\n2 3\n0 6\n1\n6 16\n3\n6 8\n3 2\n3 6\n2\n6 5\n6 6\n0\n0\n1 8\n6 8",
"1 2\n00\n1\n4\n1 2\n1 2\n0 4\n3 0",
"1 2\n00\n1\n4\n1 1\n1 2\n0 4\n3 0",
"1 3\n00\n1\n4\n1 1\n1 2\n0 4\n3 0",
"1 3\n-1\n1\n4\n1 1\n1 2\n0 4\n3 0",
"2 3\n-1\n1\n4\n1 1\n1 2\n0 4\n3 0",
"2 3\n-1\n1\n4\n1 0\n1 2\n0 4\n3 0",
"2 3\n-1\n1\n4\n1 0\n0 2\n0 4\n3 0",
"1 6\n000000\n000000\n010000\n010010\n000000\n000000",
"7 8\n00100000\n00011000\n10111101\n01100110\n01000110\n10111101\n00011000\n00100100\n2\n5 6\n1 6\n1\n6 8\n3\n6 8\n3 3\n3 6\n2\n6 3\n6 6\n0\n2\n3 8\n6 8",
"2 2\n00\n00\n4\n1 1\n2 2\n2 1\n2 2",
"1 6\n000000\n000001\n010010\n011010\n000000\n000000",
"7 8\n00100000\n00011000\n10011101\n01100110\n01000110\n10111101\n00011000\n00100100\n2\n5 3\n0 6\n1\n6 8\n3\n6 8\n3 3\n3 6\n2\n6 3\n6 6\n0\n2\n3 8\n6 8",
"1 6\n000100\n000000\n010010\n011010\n000000\n100000",
"7 8\n00100000\n00011000\n10111100\n01100110\n01000110\n10111101\n00011000\n00100100\n2\n5 3\n0 6\n1\n6 16\n3\n6 8\n3 3\n3 6\n2\n6 3\n6 6\n0\n2\n3 8\n6 8",
"1 6\n000000\n010000\n010010\n011010\n000000\n000000",
"7 8\n00100000\n00011000\n10111101\n01100110\n01000110\n10111101\n00011000\n00100100\n2\n5 3\n0 6\n1\n6 16\n3\n6 8\n3 3\n3 1\n2\n6 3\n6 6\n0\n2\n1 8\n6 8",
"1 4\n00\n00\n4\n1 1\n1 2\n2 2\n3 2",
"1 6\n000000\n010000\n010000\n011010\n001000\n100000",
"7 8\n00100010\n00011000\n10111101\n01100110\n01000110\n10111101\n00011000\n00100100\n2\n5 3\n0 6\n1\n6 16\n3\n6 8\n3 3\n3 6\n2\n6 3\n6 6\n0\n3\n1 8\n6 8",
"1 2\n00\n00\n4\n2 2\n1 2\n2 2\n3 2",
"1 6\n000001\n010000\n010000\n011010\n000000\n100010",
"1 2\n00\n00\n4\n1 2\n1 2\n2 4\n3 3",
"7 8\n00100000\n00011000\n10111101\n01100110\n01000110\n10111101\n00011000\n00100100\n2\n2 3\n0 6\n1\n6 16\n3\n6 8\n3 2\n3 6\n2\n5 3\n6 6\n0\n3\n1 8\n6 8",
"1 2\n00\n00\n4\n1 2\n1 1\n1 4\n3 2",
"7 8\n00000000\n00011000\n10111101\n01100110\n01000110\n10111101\n00011000\n00100100\n2\n2 3\n0 6\n1\n8 16\n3\n6 8\n3 2\n3 6\n2\n6 3\n6 6\n0\n3\n1 8\n6 8",
"7 8\n00000000\n00011000\n10111101\n01100110\n01000111\n10111101\n00011000\n00100100\n2\n2 3\n0 6\n1\n6 16\n3\n6 8\n3 2\n3 6\n2\n6 3\n6 6\n0\n0\n1 8\n6 8",
"1 2\n00\n1\n4\n1 2\n1 1\n2 4\n3 1",
"7 8\n00000000\n00011000\n10111101\n01100110\n01000110\n10111101\n00011000\n00010100\n2\n2 3\n0 6\n1\n6 16\n3\n6 8\n3 2\n3 6\n2\n6 5\n6 6\n0\n0\n1 8\n6 8",
"1 2\n00\n1\n4\n1 2\n2 2\n2 4\n3 0",
"1 2\n00\n1\n4\n2 2\n1 2\n0 4\n3 0",
"1 2\n00\n1\n6\n1 1\n1 2\n0 4\n3 0",
"1 3\n0\n1\n4\n1 1\n1 2\n0 4\n3 0",
"1 3\n-1\n1\n4\n1 1\n1 2\n0 0\n3 0",
"2 3\n-1\n0\n4\n1 1\n1 2\n0 4\n3 0",
"2 3\n-1\n2\n4\n1 0\n1 2\n0 4\n3 0",
"2 3\n-1\n1\n4\n0 0\n1 2\n0 4\n3 0",
"1 6\n000000\n000000\n011000\n010010\n000000\n000000",
"7 8\n00100000\n00011000\n10111101\n01100110\n01000110\n10111101\n00011000\n00100100\n2\n5 6\n1 6\n1\n6 8\n3\n6 8\n2 3\n3 6\n2\n6 3\n6 6\n0\n2\n3 8\n6 8",
"1 4\n000000\n000001\n010010\n011010\n000000\n000000",
"7 8\n00100000\n00011000\n10011101\n01101110\n01000110\n10111101\n00011000\n00100100\n2\n5 3\n0 6\n1\n6 8\n3\n6 8\n3 3\n3 6\n2\n6 3\n6 6\n0\n2\n3 8\n6 8",
"1 0\n000100\n000000\n010010\n011010\n000000\n100000",
"7 8\n00100000\n00011000\n10111100\n01100110\n01000110\n10111101\n00011000\n00100100\n2\n5 3\n0 6\n1\n6 16\n3\n6 8\n3 3\n3 6\n2\n6 4\n6 6\n0\n2\n3 8\n6 8",
"7 8\n00100000\n00011000\n10111101\n01100110\n01000110\n10111101\n00011000\n00100100\n2\n5 3\n0 6\n1\n6 16\n3\n4 8\n3 3\n3 1\n2\n6 3\n6 6\n0\n2\n1 8\n6 8",
"1 0\n00\n00\n4\n1 1\n1 2\n2 2\n3 2",
"1 7\n000000\n010000\n010000\n011010\n001000\n100000",
"7 8\n00100010\n00011000\n10111101\n01100110\n01000110\n10111101\n00011000\n00100100\n2\n5 3\n0 6\n1\n6 16\n3\n6 10\n3 3\n3 6\n2\n6 3\n6 6\n0\n3\n1 8\n6 8",
"1 2\n00\n00\n4\n2 2\n1 0\n2 2\n3 2",
"1 6\n000001\n010010\n010000\n011010\n000000\n100010",
"7 8\n00100000\n00011000\n10111101\n11100110\n01000110\n10111101\n00011000\n00100100\n2\n2 3\n0 6\n1\n6 16\n3\n6 8\n3 2\n3 6\n2\n5 3\n6 6\n0\n3\n1 8\n6 8",
"1 2\n00\n00\n4\n1 2\n1 1\n1 4\n1 2",
"7 8\n00000000\n00011000\n10111101\n01100110\n01000110\n10111101\n00011000\n00100100\n2\n2 3\n0 6\n1\n8 16\n3\n6 1\n3 2\n3 6\n2\n6 3\n6 6\n0\n3\n1 8\n6 8",
"7 8\n00000000\n00011000\n10111101\n01100110\n01000111\n10111101\n00011000\n00100100\n2\n2 3\n0 6\n1\n6 16\n3\n6 8\n3 2\n0 6\n2\n6 3\n6 6\n0\n0\n1 8\n6 8",
"1 2\n00\n1\n4\n1 3\n1 1\n2 4\n3 1",
"7 8\n00000000\n00010000\n10111101\n01100110\n01000110\n10111101\n00011000\n00010100\n2\n2 3\n0 6\n1\n6 16\n3\n6 8\n3 2\n3 6\n2\n6 5\n6 6\n0\n0\n1 8\n6 8",
"1 2\n00\n1\n4\n1 2\n2 2\n2 8\n3 0",
"1 0\n00\n1\n4\n2 2\n1 2\n0 4\n3 0",
"1 2\n00\n1\n6\n1 1\n1 2\n0 4\n2 0",
"1 3\n0\n1\n4\n1 1\n1 2\n0 4\n3 -1",
"1 3\n-1\n1\n4\n0 1\n1 2\n0 0\n3 0",
"2 3\n-1\n0\n4\n1 1\n1 0\n0 4\n3 0",
"3 3\n-1\n1\n4\n0 0\n1 2\n0 4\n3 0",
"1 6\n000000\n000000\n011000\n010010\n000000\n000100",
"7 8\n00100000\n00011000\n10111101\n01101110\n01000110\n10111101\n00011000\n00100100\n2\n5 6\n1 6\n1\n6 8\n3\n6 8\n2 3\n3 6\n2\n6 3\n6 6\n0\n2\n3 8\n6 8",
"2 0\n00\n00\n4\n1 1\n2 2\n0 1\n2 2",
"1 4\n000000\n000001\n010010\n011010\n000100\n000000",
"1 0\n000100\n000000\n010010\n111010\n000000\n100000",
"7 8\n00100000\n00011000\n10111100\n01100110\n01000110\n10111101\n00011000\n00100100\n2\n5 3\n0 6\n1\n6 22\n3\n6 8\n3 3\n3 6\n2\n6 4\n6 6\n0\n2\n3 8\n6 8",
"1 0\n00\n00\n2\n1 1\n1 2\n2 2\n3 2",
"1 6\n000001\n010010\n010010\n011010\n000000\n100010",
"7 8\n00100000\n00011000\n10111101\n11100110\n01000110\n10111101\n00011000\n00100100\n2\n2 3\n0 6\n1\n6 31\n3\n6 8\n3 2\n3 6\n2\n5 3\n6 6\n0\n3\n1 8\n6 8",
"1 2\n-1\n00\n4\n1 2\n1 1\n1 4\n1 2",
"7 8\n00000000\n00011000\n10111101\n01100110\n01000110\n10111101\n00011000\n00100100\n2\n2 3\n1 6\n1\n8 16\n3\n6 1\n3 2\n3 6\n2\n6 3\n6 6\n0\n3\n1 8\n6 8",
"7 8\n00000000\n00011000\n10111101\n01100110\n01000111\n10111101\n00011000\n00100100\n2\n2 3\n0 6\n1\n6 16\n3\n0 8\n3 2\n0 6\n2\n6 3\n6 6\n0\n0\n1 8\n6 8",
"1 2\n00\n1\n4\n1 3\n1 1\n0 4\n3 1",
"1 0\n00\n1\n4\n1 2\n1 2\n0 4\n3 0"
],
"output": [
"1",
"3",
"2",
"0\n",
"1\n",
"2\n",
"0\n",
"0\n",
"0\n",
"1\n",
"0\n",
"0\n",
"1\n",
"0\n",
"0\n",
"1\n",
"0\n",
"0\n",
"1\n",
"0\n",
"1\n",
"0\n",
"1\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"1\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"1\n",
"0\n",
"1\n",
"0\n",
"1\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"1\n",
"0\n",
"0\n",
"1\n",
"0\n",
"0\n",
"1\n",
"0\n",
"0\n",
"1\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"1\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"2\n",
"0\n",
"1\n",
"0\n",
"1\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"1\n"
]
}
| 6AIZU
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
The cloth coasters produced and sold by Aizu Takada City are known for their symmetrical design and great beauty. As part of quality control, Aizu Takada City has installed cameras on the production line to automatically verify that the images obtained by shooting each coaster are symmetrical. Each coaster is represented as a square black and white image of N x N pixels. Each pixel has a value of 0 or 1 corresponding to a white or black image.
This time, the software of the image analysis system will be updated along with the equipment update of the production line. The new system has been devised to reduce the amount of communication data, and data is sent from the camera to the analysis system by the following method.
* The information of the first coaster flowing on the line is sent to the system as an N × N pixel image.
* For the coaster information on the second and subsequent images, only the difference from the previous image is sent. The difference is given as a set of pixel positions that change from "0 to 1" or "1 to 0".
For C coasters, enter the pixel information of the first image and the difference information of the following C-1 image, and create a program that reports the number of coasters that are vertically symmetrical and symmetrical.
Input
The input is given in the following format.
C N
p11p12 ... p1N
p21p22 ... p2N
::
pN1pN2 ... pNN
diff1
diff2
::
diffC-1
The first line gives the number of coasters C (1 ≤ C ≤ 10000) and the number of pixels N (2 ≤ N ≤ 1000 and N is even) in the vertical and horizontal directions of the image. Lines 2 to N + 1 are given the number pij (pij is 0 or 1) in rows N x columns N representing the pixels of the image of the first coaster.
After the N + 2nd line, the difference diffi representing the information of the 2nd and subsequent coasters is given in the following format.
D
r1 c1
r2 c2
::
rD cD
The number of changed pixels D (0 ≤ D ≤ 100) is given in the first line. The following D rows are given ri and ci (1 ≤ ri, ci ≤ N), which represent the row and column numbers of the changed pixels, respectively. The same position cannot be given more than once in diffi.
Output
The number of coasters that are vertically symmetrical and symmetrical is output on one line.
Examples
Input
7 8
00100000
00011000
10111101
01100110
01000110
10111101
00011000
00100100
2
5 3
1 6
1
6 8
3
6 8
3 3
3 6
2
6 3
6 6
0
2
3 8
6 8
Output
3
Input
1 6
000000
000000
010010
010010
000000
000000
Output
1
Input
2 2
00
00
4
1 1
1 2
2 1
2 2
Output
2
### Input:
1 6
000000
000000
010010
010010
000000
000000
### Output:
1
### Input:
7 8
00100000
00011000
10111101
01100110
01000110
10111101
00011000
00100100
2
5 3
1 6
1
6 8
3
6 8
3 3
3 6
2
6 3
6 6
0
2
3 8
6 8
### Output:
3
### Code:
def next(N, i):
return ((N-i-1)+N)%N
def getState(N, G, i, j):
return G[i][j] == G[i][next(N, j)] and G[i][j] == G[next(N, i)][j] and G[i][j] == G[next(N, i)][next(N, j)]
def getInit(N, G):
dcnt = 0
for i in range(N//2):
for j in range(N//2):
if not getState(N, G, i, j): dcnt += 1
return dcnt
C, N = map(int, input().split())
#G = [[0]*N]*N
G = [['N' for _ in range(N)] for _ in range(N)]
for i in range(N):
str = input()
for j in range(N):
G[i][j] = int(str[j])
ans = 0
dcnt = getInit(N, G)
if dcnt == 0: ans += 1
for i in range(C-1):
k = int(input())
for j in range(k):
r, c = map(int, input().split())
r -= 1
c -= 1
pre = getState(N, G, r, c)
G[r][c] = 0 if G[r][c]== 1 else 1
post = getState(N, G, r, c)
if not pre and post: dcnt -= 1
elif pre and not post: dcnt += 1
if dcnt == 0: ans += 1
print(ans)
|
p00485 Shopping in JOI Kingdom_10415
|
There are N towns in JOI, which are connected by M bidirectional roads. There are shopping malls in K towns, and the people go to one of those towns through the road to shop.
Depending on the location of your home, you may have to travel long distances to go shopping, which is very inconvenient. To understand this situation, the King decided to investigate how the shortest distance to the town where the shopping mall is located can be longer depending on the location of the house. This survey is very difficult because the house may be built in the middle of the road (see the explanation in Input Example 1). So the King asked you, a good programmer, to create a program to do the research.
input
Read the following input from standard input.
* The integers N, M, and K are written on the first line, separated by blanks. N represents the number of towns in JOI country, M represents the number of roads in JOI country, and i> K represents the number of towns with shopping malls. The towns are numbered 1, 2, ..., N.
* The following M line represents road information. The integers ai, bi, li (1 ≤ ai ≤ N, 1 ≤ bi ≤ N, 1 ≤ li ≤ 1000) are written on the first line (1 ≤ i ≤ M), separated by blanks. This means that the i-th road connects the town ai and the town bi and is li in length. Both ends of the road are never the same town. Also, for any two towns p and q, there are no more than two roads connecting p and q. You can follow several roads from any town to any town.
* The following K line represents shopping mall information. One integer si (1 ≤ si ≤ N) is written on the i + M + 1 line (1 ≤ i ≤ K). This means that there is a shopping mall in the town si. The same value does not appear more than once in s1, ..., sK.
output
To the standard output, output one integer rounded to the nearest whole number of the shortest distance to the town where the shopping mall is located.
Example
Input
3 3 1
1 2 1
2 3 1
3 1 1
1
Output
2
|
from heapq import heappop as pop
from heapq import heappush as push
INF = 10 ** 18
class edge:
def __init__(self, to, cost):
self.to = to
self.cost = cost
#V, E, r = map(int,input().split())
N, M, K = map(int,input().split())
G = [[] for i in range(N)]
#G[i]...頂点iからの辺list、(行き先、コスト)
d = [INF for i in range(N)]
#d[i]...スタートからみた頂点iまでの最短距離
def dijkstra(lst):
que = []
for s in lst:
d[s] = 0
push(que, (0,s))
while len(que):
p = pop(que)
v = p[1]
if (d[v] < p[0]):
continue
for i in range(len(G[v])):
e = G[v][i]
if d[e.to] > d[v] + e.cost:
d[e.to] = d[v] + e.cost
push(que, (d[e.to], e.to))
for i in range(M):
s, t, c = map(int,input().split())
s -= 1
t -= 1
G[s].append(edge(t,c))
G[t].append(edge(s,c))
lst = [int(input()) - 1 for i in range(K)]
dijkstra(lst)
anss = []
append = anss.append
for i in range(N):
for e in G[i]:
x = d[i] + d[e.to] + e.cost
if x % 2:
append(x // 2 + 1)
else:
append(x // 2)
print(max(anss))
|
{
"input": [
"3 3 1\n1 2 1\n2 3 1\n3 1 1\n1",
"4 3 1\n1 2 1\n2 3 1\n3 1 1\n1",
"4 3 1\n1 2 1\n2 3 2\n1 1 1\n1",
"4 3 1\n1 2 1\n2 3 1\n1 2 1\n2",
"4 3 1\n1 2 1\n2 3 4\n1 1 1\n1",
"8 3 1\n1 1 2\n2 3 4\n3 1 0\n1",
"4 3 1\n1 2 2\n2 4 4\n1 1 1\n1",
"4 3 1\n1 1 0\n1 3 0\n3 2 0\n1",
"10 3 1\n1 2 5\n3 3 2\n3 1 1\n2",
"4 3 1\n1 2 1\n2 3 1\n1 1 1\n1",
"4 3 1\n1 2 1\n2 3 1\n1 2 1\n1",
"6 3 1\n1 2 1\n2 3 1\n3 1 1\n1",
"4 3 1\n1 2 1\n2 3 1\n3 1 2\n1",
"6 3 1\n1 2 1\n2 3 0\n3 1 1\n1",
"4 3 1\n1 2 1\n2 3 2\n2 1 1\n1",
"6 3 1\n1 1 1\n2 3 1\n3 1 1\n1",
"6 3 1\n1 1 2\n2 3 1\n3 1 1\n1",
"3 3 1\n1 2 1\n2 3 1\n2 1 1\n1",
"4 3 1\n1 2 1\n2 1 1\n3 1 1\n1",
"6 3 1\n2 2 1\n2 3 1\n3 1 1\n1",
"4 3 1\n1 2 1\n1 3 1\n3 1 2\n1",
"4 3 1\n1 2 1\n2 3 1\n1 1 1\n2",
"6 3 1\n1 1 1\n2 3 0\n3 1 1\n1",
"9 3 1\n1 1 2\n2 3 1\n3 1 1\n1",
"8 3 1\n1 2 1\n2 1 1\n3 1 1\n1",
"4 3 1\n1 2 1\n1 3 1\n3 2 2\n1",
"4 3 1\n1 2 1\n2 3 0\n1 1 1\n2",
"6 3 1\n1 1 1\n2 3 0\n3 1 1\n2",
"9 3 1\n1 1 4\n2 3 1\n3 1 1\n1",
"4 3 1\n1 2 1\n1 3 1\n3 2 0\n1",
"4 3 1\n1 2 1\n1 4 1\n3 2 0\n1",
"4 3 1\n1 2 0\n1 4 1\n3 2 0\n1",
"5 3 1\n1 2 1\n2 3 1\n1 2 1\n1",
"4 3 1\n1 2 1\n2 3 0\n3 1 2\n1",
"4 3 1\n1 2 1\n2 3 2\n1 1 2\n1",
"4 3 1\n1 2 1\n2 4 2\n2 1 1\n1",
"6 3 1\n1 2 2\n2 3 1\n3 1 1\n1",
"11 3 1\n1 1 1\n2 3 0\n3 1 1\n1",
"8 3 1\n1 1 2\n2 3 1\n3 1 1\n1",
"8 3 1\n1 2 1\n2 1 1\n3 1 0\n1",
"4 3 1\n1 2 0\n1 3 1\n3 2 2\n1",
"6 3 1\n1 1 1\n2 3 0\n3 1 1\n3",
"9 3 1\n1 1 4\n2 3 2\n3 1 1\n1",
"4 3 1\n2 2 1\n1 3 1\n3 2 0\n1",
"5 3 1\n1 2 1\n2 3 1\n1 2 0\n1",
"3 3 1\n1 2 1\n2 3 0\n3 1 2\n1",
"6 3 1\n1 2 2\n2 3 2\n3 1 1\n1",
"8 3 1\n1 1 2\n2 3 1\n3 1 0\n1",
"6 3 1\n1 1 0\n2 3 0\n3 1 1\n3",
"4 3 1\n2 4 1\n1 3 1\n3 2 0\n1",
"3 3 1\n1 2 1\n2 3 0\n3 1 3\n1",
"10 3 1\n1 2 2\n2 3 2\n3 1 1\n1",
"8 3 1\n1 1 2\n2 3 2\n3 1 0\n1",
"6 3 1\n1 2 0\n2 3 0\n3 1 1\n3",
"4 3 1\n2 4 0\n1 3 1\n3 2 0\n1",
"6 3 1\n1 2 0\n2 3 0\n3 1 1\n2",
"6 3 1\n1 2 0\n2 5 0\n3 1 1\n2",
"5 3 1\n1 2 1\n2 3 1\n3 1 1\n1",
"4 3 1\n1 2 0\n2 3 1\n3 1 1\n1",
"4 3 1\n1 2 1\n2 3 1\n1 1 2\n1",
"4 3 1\n1 2 2\n2 3 1\n1 2 1\n1",
"3 3 1\n1 2 2\n2 3 1\n3 1 1\n1",
"4 3 1\n1 1 1\n2 3 1\n3 1 2\n1",
"6 3 1\n1 2 1\n2 3 0\n3 1 0\n1",
"4 3 1\n1 4 1\n2 3 2\n2 1 1\n1",
"4 3 1\n2 2 1\n2 1 1\n3 1 1\n1",
"6 3 1\n2 2 1\n2 3 1\n3 1 2\n1",
"4 3 1\n1 2 1\n2 4 4\n1 1 1\n1",
"9 3 1\n1 1 2\n2 3 0\n3 1 1\n1",
"4 3 1\n1 2 1\n1 3 1\n3 2 2\n2",
"9 3 1\n1 1 4\n2 3 1\n3 1 0\n1",
"4 3 1\n1 2 1\n1 3 0\n3 2 0\n1",
"5 3 1\n1 2 2\n2 3 1\n1 2 1\n1",
"5 3 1\n1 2 1\n2 3 2\n1 1 2\n1",
"4 3 1\n1 2 1\n1 4 2\n2 1 1\n1",
"6 3 1\n1 2 2\n2 3 0\n3 1 1\n1",
"9 3 1\n1 2 4\n2 3 2\n3 1 1\n1",
"8 3 1\n1 1 2\n4 3 1\n3 1 0\n1",
"4 3 1\n1 1 0\n2 3 0\n3 1 1\n3",
"3 3 1\n2 2 1\n2 3 0\n3 1 3\n1",
"10 3 1\n1 2 2\n2 3 2\n2 1 1\n1",
"6 3 1\n1 2 0\n2 3 0\n3 2 1\n3",
"9 3 1\n1 1 2\n2 3 4\n3 1 0\n1",
"4 3 1\n1 2 0\n2 3 1\n1 1 1\n1",
"4 3 1\n1 3 1\n2 3 1\n1 1 2\n1",
"4 3 1\n1 2 2\n2 2 1\n1 2 1\n1",
"4 3 1\n1 1 2\n2 3 1\n3 1 2\n1",
"4 3 1\n1 4 1\n2 3 0\n2 1 1\n1",
"4 3 1\n2 2 1\n2 1 1\n1 1 1\n1",
"4 3 1\n1 2 0\n1 3 1\n3 2 2\n2",
"4 3 1\n1 1 4\n2 3 1\n3 1 0\n1",
"4 3 1\n1 1 1\n1 3 0\n3 2 0\n1",
"5 3 1\n2 2 1\n2 3 1\n1 2 1\n1",
"4 3 1\n1 1 0\n2 3 1\n3 1 1\n3",
"10 3 1\n1 2 3\n2 3 2\n3 1 1\n1",
"4 3 1\n2 2 2\n2 2 1\n1 2 1\n1",
"4 3 1\n1 1 2\n3 3 1\n3 1 2\n1",
"4 3 1\n1 4 1\n2 3 1\n2 1 1\n1",
"4 3 1\n1 2 2\n2 4 4\n1 2 1\n1",
"10 3 1\n1 2 3\n3 3 2\n3 1 1\n1",
"2 3 1\n2 2 2\n2 2 1\n1 2 1\n1"
],
"output": [
"2",
"2\n",
"3\n",
"1\n",
"5\n",
"4\n",
"6\n",
"0\n",
"7\n",
"2\n",
"2\n",
"2\n",
"2\n",
"1\n",
"3\n",
"2\n",
"2\n",
"2\n",
"1\n",
"3\n",
"2\n",
"2\n",
"1\n",
"2\n",
"1\n",
"2\n",
"2\n",
"2\n",
"2\n",
"1\n",
"1\n",
"1\n",
"2\n",
"2\n",
"3\n",
"3\n",
"2\n",
"1\n",
"2\n",
"1\n",
"2\n",
"2\n",
"3\n",
"2\n",
"1\n",
"2\n",
"3\n",
"1\n",
"1\n",
"2\n",
"2\n",
"3\n",
"2\n",
"1\n",
"1\n",
"1\n",
"1\n",
"2\n",
"1\n",
"2\n",
"2\n",
"2\n",
"3\n",
"1\n",
"3\n",
"2\n",
"4\n",
"5\n",
"1\n",
"2\n",
"2\n",
"1\n",
"2\n",
"3\n",
"2\n",
"2\n",
"4\n",
"1\n",
"1\n",
"4\n",
"3\n",
"1\n",
"4\n",
"1\n",
"2\n",
"2\n",
"3\n",
"1\n",
"2\n",
"2\n",
"2\n",
"1\n",
"2\n",
"1\n",
"3\n",
"2\n",
"3\n",
"2\n",
"5\n",
"3\n",
"2\n"
]
}
| 6AIZU
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
There are N towns in JOI, which are connected by M bidirectional roads. There are shopping malls in K towns, and the people go to one of those towns through the road to shop.
Depending on the location of your home, you may have to travel long distances to go shopping, which is very inconvenient. To understand this situation, the King decided to investigate how the shortest distance to the town where the shopping mall is located can be longer depending on the location of the house. This survey is very difficult because the house may be built in the middle of the road (see the explanation in Input Example 1). So the King asked you, a good programmer, to create a program to do the research.
input
Read the following input from standard input.
* The integers N, M, and K are written on the first line, separated by blanks. N represents the number of towns in JOI country, M represents the number of roads in JOI country, and i> K represents the number of towns with shopping malls. The towns are numbered 1, 2, ..., N.
* The following M line represents road information. The integers ai, bi, li (1 ≤ ai ≤ N, 1 ≤ bi ≤ N, 1 ≤ li ≤ 1000) are written on the first line (1 ≤ i ≤ M), separated by blanks. This means that the i-th road connects the town ai and the town bi and is li in length. Both ends of the road are never the same town. Also, for any two towns p and q, there are no more than two roads connecting p and q. You can follow several roads from any town to any town.
* The following K line represents shopping mall information. One integer si (1 ≤ si ≤ N) is written on the i + M + 1 line (1 ≤ i ≤ K). This means that there is a shopping mall in the town si. The same value does not appear more than once in s1, ..., sK.
output
To the standard output, output one integer rounded to the nearest whole number of the shortest distance to the town where the shopping mall is located.
Example
Input
3 3 1
1 2 1
2 3 1
3 1 1
1
Output
2
### Input:
3 3 1
1 2 1
2 3 1
3 1 1
1
### Output:
2
### Input:
4 3 1
1 2 1
2 3 1
3 1 1
1
### Output:
2
### Code:
from heapq import heappop as pop
from heapq import heappush as push
INF = 10 ** 18
class edge:
def __init__(self, to, cost):
self.to = to
self.cost = cost
#V, E, r = map(int,input().split())
N, M, K = map(int,input().split())
G = [[] for i in range(N)]
#G[i]...頂点iからの辺list、(行き先、コスト)
d = [INF for i in range(N)]
#d[i]...スタートからみた頂点iまでの最短距離
def dijkstra(lst):
que = []
for s in lst:
d[s] = 0
push(que, (0,s))
while len(que):
p = pop(que)
v = p[1]
if (d[v] < p[0]):
continue
for i in range(len(G[v])):
e = G[v][i]
if d[e.to] > d[v] + e.cost:
d[e.to] = d[v] + e.cost
push(que, (d[e.to], e.to))
for i in range(M):
s, t, c = map(int,input().split())
s -= 1
t -= 1
G[s].append(edge(t,c))
G[t].append(edge(s,c))
lst = [int(input()) - 1 for i in range(K)]
dijkstra(lst)
anss = []
append = anss.append
for i in range(N):
for e in G[i]:
x = d[i] + d[e.to] + e.cost
if x % 2:
append(x // 2 + 1)
else:
append(x // 2)
print(max(anss))
|
p00671 Live Schedule_10418
|
YOKARI TAMURA is a nationally famous artist. This month YOKARI will be touring live for D days. Divide this country into C different regions when deciding on a tour schedule. YOKARI benefits from performing live in an area, which is represented by a positive integer. As a general rule, YOKARI will perform up to one live concert per day. However, if you can perform live in a certain area and then live in an adjacent area, you can perform the live again in that area on the same day. As long as this condition is met, you can perform live many times while moving around the area. Also, you cannot have more than one live concert in the same area on the same day. In addition, the total number of days with more than one live concert on the same day must be less than or equal to X during the tour.
You are a YOKARI official and have to tentatively schedule her live tour. Which area would be most beneficial to perform on which day? However, YOKARI has a burden represented by a non-negative integer for each live, and the total burden during the tour period must be within W. Your job is to read the burden and expected profits on YOKARI at each live, tentatively decide the schedule, and output the maximum value of the total profits.
Constraints
* All inputs are integers
* 1 ≤ C ≤ 15
* 1 ≤ D ≤ 30
* 0 ≤ W ≤ 50
* 0 ≤ X ≤ 5
* 0 ≤ Ei, j ≤ 1,000
* 0 ≤ Fi, j ≤ 10
* The number of test cases does not exceed 100.
Input
The input consists of multiple test cases. One test case follows the format below.
C D W X
E1,1 E1,1… E1, D
E2,1 E2,1… E2, D
...
EC, 1 EC, 2… EC, D
F1,1 F1,1… F1, D
F2,1 F2,1… F2, D
...
FC, 1 FC, 2… FC, D
C is the number of region types, D is the length of the tour period, W is the maximum total amount of burden YOKARI can tolerate for this tour, and X is the total number of days that a live can be performed more than once on the same day during the tour It is the upper limit. Ei, j (1 ≤ i ≤ C and 1 ≤ j ≤ D) are the expected benefits of performing live on day j in region i. When Ei, j is 0, it indicates that the live cannot be performed in the region i on the jth day. Fi, j (1 ≤ i ≤ C and 1 ≤ j ≤ D) is the burden on YOKARI to perform live on day j in region i. This value is 0 when Ei, j is 0. Region i is adjacent to regions i + 1 and i -1 respectively. However, region 1 and region C (C> 2) are not adjacent. The end of the input is indicated by a line where each of the four 0s is separated by a single character space.
Output
For each case, tentatively schedule and output the maximum expected total profit on one line.
Example
Input
5 5 10 2
1 1 0 1 1
0 9 1 0 1
1 1 1 9 1
1 1 9 0 1
1 1 1 1 0
1 1 0 1 1
0 9 1 0 1
1 1 1 9 1
1 1 1 0 1
1 1 1 1 0
1 1 10 0
3
7
1 1 5 0
3
6
1 2 10 1
6 7
5 6
2 1 10 1
4
8
3
7
2 1 10 0
4
8
3
7
2 1 5 0
4
8
3
6
0 0 0 0
Output
18
3
0
7
12
8
4
|
from itertools import accumulate
def main():
while True:
c, d, w, x = map(int, input().split())
if c == 0:
break
es = [[] for _ in range(d)]
for _ in range(c):
lst = list(map(int, input().split()))
for i in range(d):
es[i].append(lst[i])
fs = [[] for _ in range(d)]
for _ in range(c):
lst = list(map(int, input().split()))
for i in range(d):
fs[i].append(lst[i])
for day in range(d):
for i in range(c):
if es[day][i] == 0:
fs[day][i] = 100
es = list(map(lambda lst:[0] + list(accumulate(lst)), es))
fs = list(map(lambda lst:[0] + list(accumulate(lst)), fs))
ef1 = [[] for _ in range(d)]
ef2 = [[] for _ in range(d)]
for day in range(d):
ef1[day].append((0, 0))
for i in range(c):
for j in range(i + 1, c + 1):
if fs[day][j] - fs[day][i] <= w:
if j - i == 1:
ef1[day].append((fs[day][j] - fs[day][i], es[day][j] - es[day][i]))
else:
ef2[day].append((fs[day][j] - fs[day][i], es[day][j] - es[day][i]))
for day in range(d):
used = {}
for f, e in ef1[day]:
if f not in used or used[f] < e:
used[f] = e
ef1[day] = sorted([(f, e) for f, e in used.items()])
for day in range(d):
used = {}
for f, e in ef2[day]:
if f not in used or used[f] < e:
used[f] = e
ef2[day] = sorted([(f, e) for f, e in used.items()])
dp = [[[None] * (x + 1) for _ in range(w + 1)] for _ in range(d + 1)]
dp[0][0][0] = 0
for day in range(d):
for weight in range(w + 1):
for use in range(x + 1):
score = dp[day][weight][use]
if score == None:continue
for f, e in ef1[day]:
if weight + f > w:break
if dp[day + 1][weight + f][use] == None or dp[day + 1][weight + f][use] < score + e:
dp[day + 1][weight + f][use] = score + e
if use >= x:continue
for f, e in ef2[day]:
if weight + f > w:break
if dp[day + 1][weight + f][use + 1] == None or dp[day + 1][weight + f][use + 1] < score + e:
dp[day + 1][weight + f][use + 1] = score + e
print(max([dp[d][weight][rest] if dp[d][weight][rest] != None else 0 for weight in range(w + 1) for rest in range(x + 1)]))
main()
|
{
"input": [
"5 5 10 2\n1 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 1 1 0\n1 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n6\n1 2 10 1\n6 7\n5 6\n2 1 10 1\n4\n8\n3\n7\n2 1 10 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 10 2\n1 1 0 1 0\n0 9 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 1 1 0\n1 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n6\n1 2 10 1\n6 7\n5 6\n2 1 10 1\n4\n8\n3\n7\n2 1 10 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 9 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 1 1 0\n1 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n6\n1 2 10 1\n6 7\n5 10\n2 1 10 1\n4\n8\n3\n7\n2 1 10 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 5 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 1 1 0\n2 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 10 1\n4\n8\n4\n7\n2 1 20 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 5 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 2 1 0\n2 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 13 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 11 1\n4\n8\n4\n7\n2 1 20 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 10 2\n1 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 1 1 0\n1 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n6\n1 2 10 1\n6 7\n5 6\n2 1 10 1\n4\n8\n3\n7\n2 1 10 0\n4\n8\n3\n7\n2 1 5 0\n7\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 5 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 1 1 0\n1 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 10 1\n4\n8\n3\n7\n2 1 20 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n0\n0 0 0 0",
"5 5 10 2\n1 1 0 1 0\n0 9 1 0 1\n1 1 1 9 2\n1 1 9 0 1\n1 1 1 1 0\n1 2 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n6\n1 2 10 1\n6 7\n5 6\n2 1 10 1\n4\n8\n3\n7\n2 1 10 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 2 2\n1 1 0 1 0\n0 9 1 0 1\n1 1 1 6 1\n1 1 9 0 1\n1 1 1 1 0\n1 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n6\n1 2 10 1\n6 7\n5 10\n2 1 10 1\n4\n8\n3\n7\n2 1 10 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 5 1 0 1\n1 1 1 9 1\n1 1 8 0 1\n1 1 1 1 0\n2 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 12 1\n4\n8\n4\n7\n2 1 20 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 5 1 0 1\n1 2 1 9 1\n1 1 9 0 1\n1 1 1 1 0\n2 1 0 1 1\n0 9 1 0 1\n1 1 1 15 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 13 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 10 1\n4\n8\n4\n7\n2 1 20 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 5 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 2 1 0\n2 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 13 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 11 1\n6\n8\n4\n7\n2 1 20 0\n4\n8\n3\n11\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 2 2\n1 1 0 1 0\n0 9 1 0 1\n1 1 1 6 1\n1 1 9 0 1\n1 1 1 1 0\n1 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n6\n1 2 10 1\n6 3\n5 10\n2 1 10 1\n4\n8\n3\n7\n2 1 10 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 5 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 1 1 0\n2 1 0 1 1\n0 9 1 0 1\n1 2 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 13 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 1 1\n4\n8\n4\n7\n2 1 20 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 5 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 2 1 0\n2 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 13 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 11 1\n6\n8\n4\n7\n2 1 20 0\n4\n13\n3\n11\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 10 2\n1 1 0 1 1\n0 7 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 1 1 0\n1 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n6\n1 2 10 1\n6 7\n5 6\n2 1 10 1\n4\n8\n1\n7\n2 1 10 1\n4\n8\n3\n7\n2 1 5 0\n7\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 5 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 2 1 0\n2 1 0 1 1\n0 9 1 0 1\n1 2 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 13 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 1 1\n4\n8\n4\n7\n2 1 20 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 10 2\n1 1 0 1 0\n0 9 1 0 1\n1 1 1 9 2\n1 1 9 0 1\n1 1 1 1 0\n1 2 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 0 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n6\n1 2 10 1\n1 7\n5 6\n2 1 10 1\n4\n8\n3\n7\n2 1 10 0\n4\n8\n3\n7\n2 1 5 0\n4\n0\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 5 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 2 1 0\n2 1 0 1 1\n0 9 2 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 13 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n10 7\n5 10\n2 1 11 1\n6\n8\n4\n7\n2 1 20 0\n4\n13\n3\n11\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"7 5 10 2\n1 1 0 1 1\n0 7 1 0 1\n1 1 1 9 1\n0 1 9 0 1\n1 1 1 1 0\n1 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n6\n1 2 10 1\n6 7\n5 6\n2 1 10 1\n4\n8\n1\n7\n2 1 10 1\n4\n8\n3\n7\n2 1 5 0\n7\n8\n3\n6\n0 0 0 0",
"5 5 2 2\n1 1 0 1 0\n0 9 1 0 1\n1 1 1 6 1\n1 1 9 0 1\n1 1 1 1 0\n2 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n6\n1 2 16 1\n6 3\n5 10\n2 1 10 1\n4\n8\n3\n7\n2 1 10 0\n4\n8\n3\n7\n2 1 5 0\n4\n11\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 5 1 0 1\n1 1 1 9 1\n1 0 9 0 1\n1 1 2 1 0\n2 1 0 1 1\n0 9 1 0 1\n1 2 0 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 13 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 1 1\n4\n8\n4\n7\n2 1 20 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 10 2\n1 1 0 1 0\n0 9 1 0 1\n1 1 1 9 2\n1 1 9 0 1\n1 1 1 1 0\n1 2 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 0 0 1\n1 1 1 1 0\n1 1 15 0\n3\n7\n1 1 5 0\n3\n6\n1 2 10 1\n1 7\n5 6\n2 1 10 1\n4\n8\n5\n7\n2 1 10 0\n4\n8\n3\n7\n2 1 5 0\n4\n0\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 9 1 0 1\n1 1 0 9 1\n1 1 9 0 1\n1 1 1 1 0\n1 1 0 1 1\n0 9 1 0 0\n1 1 1 9 1\n0 1 0 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n9\n1 2 18 1\n6 7\n5 10\n2 1 10 1\n4\n8\n0\n2\n2 1 10 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 9 1 0 1\n1 1 0 9 1\n1 1 9 0 1\n1 1 1 1 0\n1 1 0 1 1\n0 9 1 0 0\n1 1 1 9 1\n0 1 0 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n9\n1 2 18 1\n6 7\n5 10\n2 1 10 1\n4\n8\n0\n2\n2 1 10 0\n4\n8\n3\n7\n2 1 5 0\n7\n7\n3\n6\n0 0 0 0",
"5 5 10 2\n2 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 1 1 0\n1 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n6\n1 2 10 1\n6 7\n5 6\n2 1 10 1\n4\n8\n3\n7\n2 1 10 0\n4\n8\n3\n7\n2 1 5 0\n7\n8\n3\n6\n0 0 0 0",
"5 5 10 2\n1 1 0 1 0\n0 9 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 1 1 0\n1 2 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n6\n1 2 20 1\n6 7\n5 6\n2 1 10 1\n4\n8\n3\n7\n2 1 10 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 5 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 1 1 -1\n2 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 10 1\n4\n8\n3\n7\n2 1 20 0\n4\n8\n3\n7\n2 1 5 0\n5\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 5 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 1 1 0\n2 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 12 1\n4\n8\n4\n7\n2 1 20 1\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 5 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 1 1 -1\n2 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 10 1\n4\n15\n3\n7\n2 1 20 0\n4\n8\n3\n0\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 5 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 1 1 0\n2 1 0 1 1\n0 9 1 0 1\n1 2 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 13 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 18 1\n4\n8\n4\n7\n2 1 20 0\n4\n8\n3\n7\n2 1 5 0\n7\n8\n3\n6\n0 0 0 0",
"5 5 10 2\n1 1 0 1 0\n0 9 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 1 1 0\n1 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n6\n1 2 10 1\n6 7\n5 10\n2 1 10 1\n4\n8\n3\n7\n2 1 10 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 9 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 1 1 0\n1 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 10 1\n4\n8\n3\n7\n2 1 10 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 5 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 1 1 0\n1 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 10 1\n4\n8\n3\n7\n2 1 10 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 5 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 1 1 0\n1 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 10 1\n4\n8\n3\n7\n2 1 20 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 5 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 1 1 0\n2 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 10 1\n4\n8\n3\n7\n2 1 20 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 5 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 1 1 0\n2 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 13 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 10 1\n4\n8\n4\n7\n2 1 20 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 5 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 1 1 0\n2 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 13 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 11 1\n4\n8\n4\n7\n2 1 20 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 10 2\n1 1 0 1 0\n0 9 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 1 1 0\n1 2 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n6\n1 2 10 1\n6 7\n5 6\n2 1 10 1\n4\n8\n3\n7\n2 1 10 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 10 2\n1 1 0 1 0\n0 9 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 1 1 0\n1 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n6\n1 2 10 1\n6 7\n5 10\n2 1 10 2\n4\n8\n3\n7\n2 1 10 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 9 1 0 1\n1 1 1 6 1\n1 1 9 0 1\n1 1 1 1 0\n1 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n6\n1 2 10 1\n6 7\n5 10\n2 1 10 1\n4\n8\n3\n7\n2 1 10 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 9 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 1 1 0\n1 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 10 1\n4\n8\n3\n2\n2 1 10 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 5 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 1 1 -1\n2 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 10 1\n4\n8\n3\n7\n2 1 20 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 5 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 1 1 0\n2 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 12 1\n4\n8\n4\n7\n2 1 20 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 5 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 1 1 0\n2 1 0 1 1\n0 9 1 0 1\n1 1 1 15 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 13 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 10 1\n4\n8\n4\n7\n2 1 20 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 5 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 1 1 0\n2 1 0 1 1\n0 9 1 0 1\n1 2 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 13 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 11 1\n4\n8\n4\n7\n2 1 20 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 5 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 2 1 0\n2 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 13 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 11 1\n4\n8\n4\n7\n2 1 20 0\n4\n8\n3\n11\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 10 2\n1 1 0 1 1\n0 7 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 1 1 0\n1 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n6\n1 2 10 1\n6 7\n5 6\n2 1 10 1\n4\n8\n3\n7\n2 1 10 0\n4\n8\n3\n7\n2 1 5 0\n7\n8\n3\n6\n0 0 0 0",
"5 5 10 2\n1 1 0 1 0\n0 9 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 1 1 0\n1 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n6\n1 2 10 1\n6 7\n5 10\n2 1 10 2\n4\n8\n3\n7\n2 1 10 0\n4\n8\n3\n6\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 9 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 1 1 0\n1 1 0 1 1\n0 9 1 0 0\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 10 1\n4\n8\n3\n2\n2 1 10 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 5 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 1 1 0\n1 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 10 1\n4\n8\n3\n7\n2 1 20 0\n1\n8\n3\n7\n2 1 5 0\n4\n8\n3\n0\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 5 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 1 1 -1\n2 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 10 1\n4\n8\n3\n7\n2 1 20 0\n4\n8\n3\n0\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 5 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 1 1 0\n2 1 0 1 1\n0 9 1 0 1\n1 2 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 13 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 18 1\n4\n8\n4\n7\n2 1 20 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 10 2\n1 1 0 1 1\n0 7 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 1 1 0\n1 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n6\n1 2 10 1\n6 7\n5 6\n2 1 10 1\n4\n8\n1\n7\n2 1 10 0\n4\n8\n3\n7\n2 1 5 0\n7\n8\n3\n6\n0 0 0 0",
"5 5 10 2\n1 1 0 1 0\n0 9 1 0 1\n1 1 1 9 2\n1 1 9 0 1\n1 1 1 1 0\n1 2 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n6\n1 2 10 1\n6 7\n5 6\n2 1 10 1\n4\n8\n3\n7\n2 1 10 0\n4\n8\n3\n7\n2 1 5 0\n4\n0\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 9 1 0 1\n1 1 0 9 1\n1 1 9 0 1\n1 1 1 1 0\n1 1 0 1 1\n0 9 1 0 0\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 10 1\n4\n8\n3\n2\n2 1 10 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 5 1 0 1\n1 1 0 9 1\n1 1 9 0 1\n1 1 1 1 -1\n2 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 10 1\n4\n8\n3\n7\n2 1 20 0\n4\n8\n3\n0\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 5 1 0 1\n1 1 1 9 1\n1 1 8 0 1\n1 1 1 1 0\n2 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n9 10\n2 1 12 1\n4\n8\n4\n7\n2 1 20 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 5 1 0 1\n1 2 1 9 1\n1 1 9 0 1\n1 1 1 1 0\n2 1 0 1 1\n0 9 1 0 1\n1 1 1 15 1\n2 1 1 0 1\n1 1 1 1 0\n1 1 13 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 10 1\n4\n8\n4\n7\n2 1 20 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 10 2\n1 1 0 1 0\n0 9 1 0 1\n1 1 1 9 2\n1 1 9 0 1\n1 1 1 1 0\n1 2 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n6\n1 2 10 1\n1 7\n5 6\n2 1 10 1\n4\n8\n3\n7\n2 1 10 0\n4\n8\n3\n7\n2 1 5 0\n4\n0\n3\n6\n0 0 0 0",
"5 5 2 2\n1 1 0 1 0\n0 9 1 0 1\n1 1 1 6 1\n1 1 9 0 1\n1 1 1 1 0\n2 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n6\n1 2 10 1\n6 3\n5 10\n2 1 10 1\n4\n8\n3\n7\n2 1 10 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 9 1 0 1\n1 1 0 9 1\n1 1 9 0 1\n1 1 1 1 0\n1 1 0 1 1\n0 9 1 0 0\n1 1 1 9 1\n1 1 0 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 10 1\n4\n8\n3\n2\n2 1 10 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 5 1 0 1\n1 1 0 9 1\n1 1 9 0 1\n1 1 1 1 -1\n2 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 10 1\n4\n8\n3\n7\n2 1 20 0\n6\n8\n3\n0\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 6 1 0 1\n1 2 1 9 1\n1 1 9 0 1\n1 1 1 1 0\n2 1 0 1 1\n0 9 1 0 1\n1 1 1 15 1\n2 1 1 0 1\n1 1 1 1 0\n1 1 13 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 10 1\n4\n8\n4\n7\n2 1 20 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 5 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 2 1 0\n2 1 0 1 1\n0 9 2 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 13 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 11 1\n6\n8\n4\n7\n2 1 20 0\n4\n13\n3\n11\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 10 2\n1 1 0 1 1\n0 7 1 0 1\n1 1 1 9 1\n0 1 9 0 1\n1 1 1 1 0\n1 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n6\n1 2 10 1\n6 7\n5 6\n2 1 10 1\n4\n8\n1\n7\n2 1 10 1\n4\n8\n3\n7\n2 1 5 0\n7\n8\n3\n6\n0 0 0 0",
"5 5 2 2\n1 1 0 1 0\n0 9 1 0 1\n1 1 1 6 1\n1 1 9 0 1\n1 1 1 1 0\n2 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n6\n1 2 10 1\n6 3\n5 10\n2 1 10 1\n4\n8\n3\n7\n2 1 10 0\n4\n8\n3\n7\n2 1 5 0\n4\n11\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 9 1 0 1\n1 1 0 9 1\n1 1 9 0 1\n1 1 1 1 0\n1 1 0 1 1\n0 9 1 0 0\n1 1 1 9 1\n0 1 0 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 10 1\n4\n8\n3\n2\n2 1 10 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 5 1 0 1\n1 1 1 9 1\n1 0 9 0 1\n1 1 2 1 0\n2 1 0 1 1\n0 9 1 0 1\n1 2 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 13 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 1 1\n4\n8\n4\n7\n2 1 20 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 10 2\n1 1 0 1 0\n0 9 1 0 1\n1 1 1 9 2\n1 1 9 0 1\n1 1 1 1 0\n1 2 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 0 0 1\n1 1 1 1 0\n1 1 15 0\n3\n7\n1 1 5 0\n3\n6\n1 2 10 1\n1 7\n5 6\n2 1 10 1\n4\n8\n3\n7\n2 1 10 0\n4\n8\n3\n7\n2 1 5 0\n4\n0\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 9 1 0 1\n1 1 0 9 1\n1 1 9 0 1\n1 1 1 1 0\n1 1 0 1 1\n0 9 1 0 0\n1 1 1 9 1\n0 1 0 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 10 1\n4\n8\n0\n2\n2 1 10 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"7 5 10 2\n1 1 -1 1 1\n0 7 1 0 1\n1 1 1 9 1\n0 1 9 0 1\n1 1 1 1 0\n1 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n6\n1 2 10 1\n6 7\n5 6\n2 1 10 1\n4\n8\n1\n7\n2 1 10 1\n4\n8\n3\n7\n2 1 5 0\n7\n8\n3\n6\n0 0 0 0",
"7 5 10 2\n1 1 -1 1 1\n0 7 1 0 1\n1 1 1 9 1\n0 1 9 0 1\n1 1 1 1 0\n1 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n13\n1 1 5 0\n3\n6\n1 2 10 1\n6 7\n5 6\n2 1 10 1\n4\n8\n1\n7\n2 1 10 1\n4\n8\n3\n7\n2 1 5 0\n7\n8\n3\n6\n0 0 0 0",
"5 5 10 2\n1 1 0 1 0\n0 9 1 0 1\n1 1 1 5 2\n1 1 9 0 1\n1 1 1 1 0\n1 2 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 0 0 1\n1 1 1 1 0\n1 1 15 0\n3\n7\n1 1 5 0\n3\n6\n1 2 10 1\n1 7\n5 6\n2 1 10 1\n4\n8\n5\n7\n2 1 10 0\n4\n8\n3\n7\n2 1 5 0\n4\n0\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 9 1 0 1\n1 1 0 9 1\n1 1 9 0 1\n1 1 1 1 0\n1 1 0 1 1\n0 9 1 0 0\n1 1 1 9 1\n0 1 0 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n9\n1 2 18 1\n6 7\n5 10\n2 1 10 1\n4\n8\n0\n2\n2 1 10 0\n4\n8\n3\n7\n2 1 5 0\n4\n7\n3\n6\n0 0 0 0",
"7 5 10 2\n1 1 -1 1 1\n0 7 1 0 1\n1 1 1 9 1\n0 1 3 0 1\n1 1 1 1 0\n1 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n13\n1 1 5 0\n3\n6\n1 2 10 1\n6 7\n5 6\n2 1 10 1\n4\n8\n1\n7\n2 1 10 1\n4\n8\n3\n7\n2 1 5 0\n7\n8\n3\n6\n0 0 0 0",
"5 5 10 2\n1 1 0 1 0\n0 9 1 0 1\n1 1 1 5 2\n1 1 9 0 1\n1 1 1 1 0\n1 2 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 0 0 1\n1 1 1 1 0\n1 1 15 0\n3\n7\n1 1 5 0\n2\n6\n1 2 10 1\n1 7\n5 6\n2 1 10 1\n4\n8\n5\n7\n2 1 10 0\n4\n8\n3\n7\n2 1 5 0\n4\n0\n3\n6\n0 0 0 0",
"7 5 10 2\n1 1 -1 1 1\n0 7 1 0 1\n1 1 1 9 1\n0 1 3 0 1\n1 1 1 1 0\n1 1 0 1 1\n-1 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n13\n1 1 5 0\n3\n6\n1 2 10 1\n6 7\n5 6\n2 1 10 1\n4\n8\n1\n7\n2 1 10 1\n4\n8\n3\n7\n2 1 5 0\n7\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 9 1 0 1\n1 1 0 9 1\n1 1 9 0 1\n1 1 1 1 0\n1 1 0 1 1\n0 9 1 0 0\n1 1 1 9 1\n0 1 0 0 1\n1 1 1 1 0\n1 1 10 0\n3\n10\n1 1 5 0\n3\n9\n1 2 18 1\n6 7\n5 10\n2 1 10 1\n4\n8\n0\n2\n2 1 10 0\n4\n8\n3\n7\n2 1 5 0\n7\n7\n3\n6\n0 0 0 0",
"5 5 10 2\n1 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 0 1 0\n1 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n6\n1 2 10 1\n6 7\n5 6\n2 1 10 1\n4\n8\n3\n7\n2 1 10 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 9 1 0 1\n1 1 1 9 1\n1 0 9 0 1\n1 1 1 1 0\n1 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n6\n1 2 10 1\n6 7\n5 10\n2 1 10 1\n4\n8\n3\n7\n2 1 10 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 2 0\n0 9 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 1 1 0\n1 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 10 1\n4\n8\n3\n7\n2 1 10 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 5 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 1 1 0\n1 1 -1 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 10 1\n4\n8\n3\n7\n2 1 10 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n2 1 0 1 0\n0 5 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 1 1 0\n2 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 10 1\n4\n8\n3\n7\n2 1 20 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 5 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 1 1 0\n2 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n7 7\n5 10\n2 1 10 1\n4\n8\n4\n7\n2 1 20 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 5 1 0 1\n1 1 0 9 1\n1 1 9 0 1\n1 1 1 1 0\n2 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 13 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 10 1\n4\n8\n4\n7\n2 1 20 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 5 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 1 1 0\n2 1 0 1 1\n-1 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 13 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 11 1\n4\n8\n4\n7\n2 1 20 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 5 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 2 1 0\n2 1 0 1 1\n0 7 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 13 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 11 1\n4\n8\n4\n7\n2 1 20 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 9 1 0 2\n1 1 1 6 1\n1 1 9 0 1\n1 1 1 1 0\n1 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n6\n1 2 10 1\n6 7\n5 10\n2 1 10 1\n4\n8\n3\n7\n2 1 10 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 9 1 0 1\n1 1 1 9 1\n1 1 9 0 0\n1 1 1 1 0\n1 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 10 1\n4\n8\n3\n2\n2 1 10 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 5 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 1 1 0\n1 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 10 1\n4\n8\n3\n7\n2 1 20 0\n4\n8\n4\n7\n2 1 5 0\n4\n8\n3\n0\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 5 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 1 1 0\n2 1 0 1 1\n0 9 1 0 0\n1 1 1 15 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 13 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 10 1\n4\n8\n4\n7\n2 1 20 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 5 1 0 1\n1 1 1 9 1\n1 1 9 0 1\n1 1 1 1 0\n2 1 0 1 1\n0 9 1 0 1\n1 2 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 13 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 11 1\n4\n8\n4\n7\n2 1 20 1\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 10 2\n1 1 0 1 1\n0 7 1 0 1\n1 1 1 4 1\n1 1 9 0 1\n1 1 1 1 0\n1 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n6\n1 2 10 1\n6 7\n5 6\n2 1 10 1\n4\n8\n3\n7\n2 1 10 0\n4\n8\n3\n7\n2 1 5 0\n7\n8\n3\n6\n0 0 0 0",
"5 5 10 2\n1 1 0 1 0\n0 9 1 0 1\n1 1 1 9 2\n1 1 9 0 1\n1 1 1 1 0\n1 2 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n6\n1 2 10 1\n6 7\n5 6\n2 1 10 1\n4\n8\n3\n7\n2 1 10 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n7\n0 0 0 0",
"5 5 10 2\n1 1 0 1 0\n0 9 1 0 1\n1 1 2 9 1\n1 1 9 0 1\n1 1 1 1 0\n1 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n6\n1 2 10 1\n6 7\n5 10\n2 1 10 2\n4\n8\n3\n7\n2 1 10 0\n4\n8\n3\n6\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 2 2\n1 1 0 1 0\n0 9 1 0 1\n1 1 1 6 1\n1 0 9 0 1\n1 1 1 1 0\n1 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n6\n1 2 10 1\n6 7\n5 10\n2 1 10 1\n4\n8\n3\n7\n2 1 10 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 5 1 0 1\n1 1 1 9 1\n1 1 8 0 1\n1 2 1 1 0\n2 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 12 1\n4\n8\n4\n7\n2 1 20 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 8 2\n1 1 0 1 0\n0 5 0 0 1\n1 2 1 9 1\n1 1 9 0 1\n1 1 1 1 0\n2 1 0 1 1\n0 9 1 0 1\n1 1 1 15 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 13 0\n3\n7\n1 1 5 0\n3\n9\n1 2 10 1\n6 7\n5 10\n2 1 10 1\n4\n8\n4\n7\n2 1 20 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0",
"5 5 10 2\n1 1 0 1 0\n0 9 1 0 1\n1 1 1 9 2\n1 1 9 0 1\n1 1 1 1 0\n1 2 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n6\n1 2 10 1\n6 7\n5 6\n2 1 10 1\n4\n8\n3\n7\n2 1 10 0\n5\n8\n3\n7\n2 1 5 0\n4\n0\n3\n6\n0 0 0 0",
"5 5 2 2\n1 1 0 1 0\n0 9 1 0 1\n1 1 1 6 1\n1 1 9 0 1\n1 1 1 1 0\n1 1 0 1 1\n0 9 1 0 1\n1 1 1 9 1\n1 1 1 0 1\n1 1 1 1 0\n1 1 10 0\n3\n7\n1 1 5 0\n3\n6\n1 2 10 1\n6 3\n5 17\n2 1 10 1\n4\n8\n3\n7\n2 1 10 0\n4\n8\n3\n7\n2 1 5 0\n4\n8\n3\n6\n0 0 0 0"
],
"output": [
"18\n3\n0\n7\n12\n8\n4",
"18\n3\n0\n7\n12\n8\n4\n",
"16\n3\n0\n7\n12\n8\n4\n",
"16\n3\n0\n7\n8\n8\n4\n",
"17\n3\n0\n7\n12\n8\n4\n",
"18\n3\n0\n7\n12\n8\n7\n",
"16\n3\n0\n7\n12\n8\n8\n",
"19\n3\n0\n7\n12\n8\n4\n",
"10\n3\n0\n7\n12\n8\n4\n",
"15\n3\n0\n7\n12\n8\n4\n",
"17\n3\n0\n7\n8\n8\n4\n",
"17\n3\n0\n7\n14\n8\n4\n",
"10\n3\n0\n6\n12\n8\n4\n",
"16\n3\n0\n7\n0\n8\n4\n",
"17\n3\n0\n7\n14\n13\n4\n",
"18\n3\n0\n7\n12\n12\n7\n",
"17\n3\n0\n7\n0\n8\n4\n",
"20\n3\n0\n7\n12\n8\n4\n",
"17\n3\n0\n10\n14\n13\n4\n",
"25\n12\n12\n7\n",
"10\n3\n0\n9\n12\n8\n4\n",
"18\n3\n0\n7\n0\n8\n4\n",
"20\n3\n0\n7\n8\n8\n4\n",
"17\n3\n0\n13\n12\n8\n4\n",
"17\n3\n0\n13\n12\n8\n7\n",
"19\n3\n0\n7\n12\n8\n7\n",
"18\n3\n0\n13\n12\n8\n4\n",
"16\n3\n0\n7\n12\n8\n5\n",
"16\n3\n0\n7\n12\n12\n4\n",
"16\n3\n0\n7\n19\n8\n4\n",
"16\n3\n0\n7\n12\n8\n7\n",
"18\n3\n0\n7\n12\n8\n4\n",
"16\n3\n0\n7\n12\n8\n4\n",
"16\n3\n0\n7\n12\n8\n4\n",
"16\n3\n0\n7\n12\n8\n4\n",
"16\n3\n0\n7\n12\n8\n4\n",
"16\n3\n0\n7\n8\n8\n4\n",
"16\n3\n0\n7\n12\n8\n4\n",
"18\n3\n0\n7\n12\n8\n4\n",
"18\n3\n0\n7\n12\n8\n4\n",
"16\n3\n0\n7\n12\n8\n4\n",
"16\n3\n0\n7\n12\n8\n4\n",
"16\n3\n0\n7\n12\n8\n4\n",
"16\n3\n0\n7\n12\n8\n4\n",
"16\n3\n0\n7\n8\n8\n4\n",
"16\n3\n0\n7\n12\n8\n4\n",
"17\n3\n0\n7\n12\n8\n4\n",
"18\n3\n0\n7\n12\n8\n7\n",
"18\n3\n0\n7\n12\n8\n4\n",
"17\n3\n0\n7\n12\n8\n4\n",
"16\n3\n0\n7\n12\n8\n8\n",
"16\n3\n0\n7\n12\n8\n4\n",
"16\n3\n0\n7\n12\n8\n4\n",
"18\n3\n0\n7\n12\n8\n7\n",
"19\n3\n0\n7\n12\n8\n4\n",
"17\n3\n0\n7\n12\n8\n4\n",
"16\n3\n0\n7\n12\n8\n4\n",
"15\n3\n0\n7\n12\n8\n4\n",
"17\n3\n0\n7\n8\n8\n4\n",
"19\n3\n0\n7\n12\n8\n4\n",
"10\n3\n0\n6\n12\n8\n4\n",
"17\n3\n0\n7\n12\n8\n4\n",
"16\n3\n0\n7\n12\n8\n4\n",
"17\n3\n0\n7\n8\n8\n4\n",
"17\n3\n0\n7\n14\n13\n4\n",
"18\n3\n0\n7\n12\n12\n7\n",
"10\n3\n0\n6\n12\n8\n4\n",
"17\n3\n0\n7\n12\n8\n4\n",
"17\n3\n0\n7\n0\n8\n4\n",
"20\n3\n0\n7\n12\n8\n4\n",
"17\n3\n0\n7\n12\n8\n4\n",
"25\n12\n12\n7\n",
"25\n12\n12\n7\n",
"20\n3\n0\n7\n8\n8\n4\n",
"17\n3\n0\n13\n12\n8\n4\n",
"25\n12\n12\n7\n",
"20\n3\n0\n7\n8\n8\n4\n",
"25\n12\n12\n7\n",
"17\n3\n0\n13\n12\n8\n7\n",
"18\n3\n0\n7\n12\n8\n4\n",
"16\n3\n0\n7\n12\n8\n4\n",
"17\n3\n0\n7\n12\n8\n4\n",
"16\n3\n0\n7\n12\n8\n4\n",
"16\n3\n0\n7\n12\n8\n4\n",
"16\n3\n0\n7\n8\n8\n4\n",
"16\n3\n0\n7\n8\n8\n4\n",
"16\n3\n0\n7\n12\n8\n4\n",
"17\n3\n0\n7\n12\n8\n4\n",
"17\n3\n0\n7\n12\n8\n4\n",
"16\n3\n0\n7\n12\n8\n4\n",
"16\n3\n0\n7\n12\n8\n8\n",
"17\n3\n0\n7\n8\n8\n4\n",
"16\n3\n0\n7\n12\n12\n4\n",
"18\n3\n0\n7\n12\n8\n7\n",
"19\n3\n0\n7\n12\n8\n4\n",
"19\n3\n0\n7\n12\n8\n4\n",
"10\n3\n0\n7\n12\n8\n4\n",
"16\n3\n0\n7\n12\n8\n4\n",
"17\n3\n0\n7\n8\n8\n4\n",
"19\n3\n0\n7\n12\n8\n4\n",
"10\n3\n0\n6\n12\n8\n4\n"
]
}
| 6AIZU
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
YOKARI TAMURA is a nationally famous artist. This month YOKARI will be touring live for D days. Divide this country into C different regions when deciding on a tour schedule. YOKARI benefits from performing live in an area, which is represented by a positive integer. As a general rule, YOKARI will perform up to one live concert per day. However, if you can perform live in a certain area and then live in an adjacent area, you can perform the live again in that area on the same day. As long as this condition is met, you can perform live many times while moving around the area. Also, you cannot have more than one live concert in the same area on the same day. In addition, the total number of days with more than one live concert on the same day must be less than or equal to X during the tour.
You are a YOKARI official and have to tentatively schedule her live tour. Which area would be most beneficial to perform on which day? However, YOKARI has a burden represented by a non-negative integer for each live, and the total burden during the tour period must be within W. Your job is to read the burden and expected profits on YOKARI at each live, tentatively decide the schedule, and output the maximum value of the total profits.
Constraints
* All inputs are integers
* 1 ≤ C ≤ 15
* 1 ≤ D ≤ 30
* 0 ≤ W ≤ 50
* 0 ≤ X ≤ 5
* 0 ≤ Ei, j ≤ 1,000
* 0 ≤ Fi, j ≤ 10
* The number of test cases does not exceed 100.
Input
The input consists of multiple test cases. One test case follows the format below.
C D W X
E1,1 E1,1… E1, D
E2,1 E2,1… E2, D
...
EC, 1 EC, 2… EC, D
F1,1 F1,1… F1, D
F2,1 F2,1… F2, D
...
FC, 1 FC, 2… FC, D
C is the number of region types, D is the length of the tour period, W is the maximum total amount of burden YOKARI can tolerate for this tour, and X is the total number of days that a live can be performed more than once on the same day during the tour It is the upper limit. Ei, j (1 ≤ i ≤ C and 1 ≤ j ≤ D) are the expected benefits of performing live on day j in region i. When Ei, j is 0, it indicates that the live cannot be performed in the region i on the jth day. Fi, j (1 ≤ i ≤ C and 1 ≤ j ≤ D) is the burden on YOKARI to perform live on day j in region i. This value is 0 when Ei, j is 0. Region i is adjacent to regions i + 1 and i -1 respectively. However, region 1 and region C (C> 2) are not adjacent. The end of the input is indicated by a line where each of the four 0s is separated by a single character space.
Output
For each case, tentatively schedule and output the maximum expected total profit on one line.
Example
Input
5 5 10 2
1 1 0 1 1
0 9 1 0 1
1 1 1 9 1
1 1 9 0 1
1 1 1 1 0
1 1 0 1 1
0 9 1 0 1
1 1 1 9 1
1 1 1 0 1
1 1 1 1 0
1 1 10 0
3
7
1 1 5 0
3
6
1 2 10 1
6 7
5 6
2 1 10 1
4
8
3
7
2 1 10 0
4
8
3
7
2 1 5 0
4
8
3
6
0 0 0 0
Output
18
3
0
7
12
8
4
### Input:
5 5 10 2
1 1 0 1 1
0 9 1 0 1
1 1 1 9 1
1 1 9 0 1
1 1 1 1 0
1 1 0 1 1
0 9 1 0 1
1 1 1 9 1
1 1 1 0 1
1 1 1 1 0
1 1 10 0
3
7
1 1 5 0
3
6
1 2 10 1
6 7
5 6
2 1 10 1
4
8
3
7
2 1 10 0
4
8
3
7
2 1 5 0
4
8
3
6
0 0 0 0
### Output:
18
3
0
7
12
8
4
### Input:
5 5 10 2
1 1 0 1 0
0 9 1 0 1
1 1 1 9 1
1 1 9 0 1
1 1 1 1 0
1 1 0 1 1
0 9 1 0 1
1 1 1 9 1
1 1 1 0 1
1 1 1 1 0
1 1 10 0
3
7
1 1 5 0
3
6
1 2 10 1
6 7
5 6
2 1 10 1
4
8
3
7
2 1 10 0
4
8
3
7
2 1 5 0
4
8
3
6
0 0 0 0
### Output:
18
3
0
7
12
8
4
### Code:
from itertools import accumulate
def main():
while True:
c, d, w, x = map(int, input().split())
if c == 0:
break
es = [[] for _ in range(d)]
for _ in range(c):
lst = list(map(int, input().split()))
for i in range(d):
es[i].append(lst[i])
fs = [[] for _ in range(d)]
for _ in range(c):
lst = list(map(int, input().split()))
for i in range(d):
fs[i].append(lst[i])
for day in range(d):
for i in range(c):
if es[day][i] == 0:
fs[day][i] = 100
es = list(map(lambda lst:[0] + list(accumulate(lst)), es))
fs = list(map(lambda lst:[0] + list(accumulate(lst)), fs))
ef1 = [[] for _ in range(d)]
ef2 = [[] for _ in range(d)]
for day in range(d):
ef1[day].append((0, 0))
for i in range(c):
for j in range(i + 1, c + 1):
if fs[day][j] - fs[day][i] <= w:
if j - i == 1:
ef1[day].append((fs[day][j] - fs[day][i], es[day][j] - es[day][i]))
else:
ef2[day].append((fs[day][j] - fs[day][i], es[day][j] - es[day][i]))
for day in range(d):
used = {}
for f, e in ef1[day]:
if f not in used or used[f] < e:
used[f] = e
ef1[day] = sorted([(f, e) for f, e in used.items()])
for day in range(d):
used = {}
for f, e in ef2[day]:
if f not in used or used[f] < e:
used[f] = e
ef2[day] = sorted([(f, e) for f, e in used.items()])
dp = [[[None] * (x + 1) for _ in range(w + 1)] for _ in range(d + 1)]
dp[0][0][0] = 0
for day in range(d):
for weight in range(w + 1):
for use in range(x + 1):
score = dp[day][weight][use]
if score == None:continue
for f, e in ef1[day]:
if weight + f > w:break
if dp[day + 1][weight + f][use] == None or dp[day + 1][weight + f][use] < score + e:
dp[day + 1][weight + f][use] = score + e
if use >= x:continue
for f, e in ef2[day]:
if weight + f > w:break
if dp[day + 1][weight + f][use + 1] == None or dp[day + 1][weight + f][use + 1] < score + e:
dp[day + 1][weight + f][use + 1] = score + e
print(max([dp[d][weight][rest] if dp[d][weight][rest] != None else 0 for weight in range(w + 1) for rest in range(x + 1)]))
main()
|
p00814 Life Line_10422
|
Let's play a new board game ``Life Line''.
The number of the players is greater than 1 and less than 10.
In this game, the board is a regular triangle in which many small regular triangles are arranged (See Figure l). The edges of each small triangle are of the same length.
<image>
Figure 1: The board
The size of the board is expressed by the number of vertices on the bottom edge of the outer triangle. For example, the size of the board in Figure 1 is 4.
At the beginning of the game, each player is assigned his own identification number between 1 and 9, and is given some stones on which his identification number is written.
Each player puts his stone in turn on one of the ``empty'' vertices. An ``empty vertex'' is a vertex that has no stone on it.
When one player puts his stone on one of the vertices during his turn, some stones might be removed from the board. The player gains points which is equal to the number of the removed stones of others, but loses points which is equal to the number of the removed stones of himself. The points of a player for a single turn is the points he gained minus the points he lost in that turn.
The conditions for removing stones are as follows:
* The stones on the board are divided into groups. Each group contains a set of stones whose numbers are the same and placed adjacently. That is, if the same numbered stones are placed adjacently, they belong to the same group.
* If none of the stones in a group is adjacent to at least one ``empty'' vertex, all the stones in that group are removed from the board.
<image>
Figure 2: The groups of stones
Figure 2 shows an example of the groups of stones.
Suppose that the turn of the player `4' comes now. If he puts his stone on the vertex shown in Figure 3a, the conditions will be satisfied to remove some groups of stones (shadowed in Figure 3b). The player gains 6 points, because the 6 stones of others are removed from the board (See Figure 3c).
<image>
Figure 3a
|
Figure 3b
|
Figure 3c
---|---|---
As another example, suppose that the turn of the player `2' comes in Figure 2. If the player puts his stone on the vertex shown in Figure 4a, the conditions will be satisfied to remove some groups of stones (shadowed in Figure 4b). The player gains 4 points, because the 4 stones of others are removed. But, at the same time, he loses 3 points, because his 3 stones are removed. As the result, the player's points of this turn is 4 - 3 = 1 (See Figure 4c).
<image>
Figure 4a
|
Figure 4b
|
Figure 4c
---|---|---
When each player puts all of his stones on the board, the game is over. The total score of a player is the summation of the points of all of his turns.
Your job is to write a program that tells you the maximum points a player can get (i.e., the points he gains - the points he loses) in his current turn.
Input
The input consists of multiple data. Each data represents the state of the board of the game still in progress.
The format of each data is as follows.
N C
S1,1
S2,1 S2,2
S3,1 S3,2 S3,3
...
SN,1 ... SN,N
N is the size of the board (3 ≤ N ≤ 10).
C is the identification number of the player whose turn comes now (1 ≤ C ≤ 9) . That is, your program must calculate his points in this turn.
Si,j is the state of the vertex on the board (0 ≤ Si,j ≤ 9) . If the value of Si,j is positive, it means that there is the stone numbered by Si,j there. If the value of Si,j is 0, it means that the vertex is ``empty''.
Two zeros in a line, i.e., 0 0, represents the end of the input.
Output
For each data, the maximum points the player can get in the turn should be output, each in a separate line.
Examples
Input
4 4
2
2 3
1 0 4
1 1 4 0
4 5
2
2 3
3 0 4
1 1 4 0
4 1
2
2 3
3 0 4
1 1 4 0
4 1
1
1 1
1 1 1
1 1 1 0
4 2
1
1 1
1 1 1
1 1 1 0
4 1
0
2 2
5 0 7
0 5 7 0
4 2
0
0 3
1 0 4
0 1 0 4
4 3
0
3 3
3 2 3
0 3 0 3
4 2
0
3 3
3 2 3
0 3 0 3
6 1
1
1 2
1 1 0
6 7 6 8
0 7 6 8 2
6 6 7 2 2 0
5 9
0
0 0
0 0 0
0 0 0 0
0 0 0 0 0
5 3
3
3 2
4 3 2
4 4 0 3
3 3 3 0 3
0 0
Output
6
5
1
-10
8
-1
0
1
-1
5
0
5
Input
4 4
2
2 3
1 0 4
1 1 4 0
4 5
2
2 3
3 0 4
1 1 4 0
4 1
2
2 3
3 0 4
1 1 4 0
4 1
1
1 1
1 1 1
1 1 1 0
4 2
1
1 1
1 1 1
1 1 1 0
4 1
0
2 2
5 0 7
0 5 7 0
4 2
0
0 3
1 0 4
0 1 0 4
4 3
0
3 3
3 2 3
0 3 0 3
4 2
0
3 3
3 2 3
0 3 0 3
6 1
1
1 2
1 1 0
6 7 6 8
0 7 6 8 2
6 6 7 2 2 0
5 9
0
0 0
0 0 0
0 0 0 0
0 0 0 0 0
5 3
3
3 2
4 3 2
4 4 0 3
3 3 3 0 3
0 0
Output
6
5
1
-10
8
-1
0
1
-1
5
0
5
|
import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools
sys.setrecursionlimit(10**7)
inf = 10**20
eps = 1.0 / 10**13
mod = 10**9+7
dd = [(-1,0),(0,1),(1,0),(0,-1)]
ddn = [(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()
def pf(s): return print(s, flush=True)
def main():
rr = []
def f(n,m):
a = [[-1]*(n+3)] + [[-1] + LI() + [-1]*2 for _ in range(n)] + [[-1]*(n+3)]
aa = [c[:] for c in a]
d = collections.defaultdict(int)
def _f(i,j,c):
if a[i][j] == 0:
return (0, set([(i,j)]))
if a[i][j] != c:
return (0,set())
a[i][j] = -1
r = [1, set()]
for di,dj in [(-1,-1),(-1,0),(0,-1),(0,1),(1,0),(1,1)]:
t = _f(i+di,j+dj,c)
r[0] += t[0]
r[1] |= t[1]
# print('_f',i,j,c,r)
return tuple(r)
for i in range(1,n+1):
for j in range(1,i+1):
if a[i][j] != m:
continue
c,s = _f(i,j,a[i][j])
if len(s) == 1:
d[list(s)[0]] = -1
a = aa
aa = [c[:] for c in a]
for i in range(1,n+1):
for j in range(1,i+1):
if a[i][j] != 0:
continue
if (i,j) in d:
continue
tf = True
for di,dj in [(-1,-1),(-1,0),(0,-1),(0,1),(1,0),(1,1)]:
if a[i+di][j+dj] in [0,m]:
tf = False
break
if tf:
d[(i,j)] = -1
else:
d[(i,j)] = 0
ts = collections.defaultdict(set)
for i in range(1,n+1):
for j in range(1,i+1):
if a[i][j] != m:
continue
cc = a[i][j]
sf = -1 if a[i][j] == m else 1
c,s = _f(i,j,a[i][j])
# print('res',i,j,c,s,sf,len(s))
if len(s) > 1:
for sc in s:
ts[sc].add(cc)
d[sc] = 0
a = aa
# print(d)
# print('\n'.join("\t".join(map(str,_)) for _ in a))
for i in range(1,n+1):
for j in range(1,i+1):
if a[i][j] < 1:
continue
cc = a[i][j]
sf = -1 if a[i][j] == m else 1
c,s = _f(i,j,a[i][j])
# print('res',i,j,c,s,sf,len(s))
if len(s) == 1 and cc not in ts[list(s)[0]]:
if sf == 1:
d[list(s)[0]] += c * sf
else:
d[list(s)[0]] += c * sf
# print('\n'.join("\t".join(map(str,_)) for _ in a))
# print('\n'.join("\t".join(map(str,_)) for _ in a))
# print(d)
if len(d) == 0:
return 0
return max(d.values())
while True:
n,m = LI()
if n == 0 and m == 0:
break
rr.append(f(n,m))
return '\n'.join(map(str,rr))
print(main())
|
{
"input": [
"4 4\n 2\n 2 3\n 1 0 4\n1 1 4 0\n4 5\n 2\n 2 3\n 3 0 4\n1 1 4 0\n4 1\n 2\n 2 3\n 3 0 4\n1 1 4 0\n4 1\n 1\n 1 1\n 1 1 1\n1 1 1 0\n4 2\n 1\n 1 1\n 1 1 1\n1 1 1 0\n4 1\n 0\n 2 2\n 5 0 7\n0 5 7 0\n4 2\n 0\n 0 3\n 1 0 4\n0 1 0 4\n4 3\n 0\n 3 3\n 3 2 3\n0 3 0 3\n4 2\n 0\n 3 3\n 3 2 3\n0 3 0 3\n6 1\n 1\n 1 2\n 1 1 0\n 6 7 6 8\n 0 7 6 8 2\n6 6 7 2 2 0\n5 9\n 0\n 0 0\n 0 0 0\n 0 0 0 0\n0 0 0 0 0\n5 3\n 3\n 3 2\n 4 3 2\n 4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 4\n0 1 0 4\n4 3\n0\n3 3\n3 2 3\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n1 2\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n0 0 0 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 4\n0 1 0 4\n4 3\n0\n3 3\n3 2 3\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n0 0 0 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 1\n0 1 0 4\n4 3\n0\n3 3\n3 2 3\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n1 2\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n0 0 0 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 4\n0 1 0 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n0 0 0 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 0 7 0\n4 2\n0\n0 3\n1 0 4\n0 1 0 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n-1 0 -1 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 4\n0 1 0 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n0 0 0 0 0\n5 5\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n0 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 1\n0 1 0 4\n4 3\n0\n3 3\n3 2 3\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n1 2\n1 1 0\n6 7 6 8\n0 7 6 8 1\n6 5 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n0 0 0 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 -1 4\n0 1 0 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n-1 0 -1 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 0\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 4\n0 1 0 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n-1 0 -1 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n 2\n 2 3\n 1 0 4\n1 1 4 0\n4 5\n 2\n 2 3\n 3 0 4\n1 1 4 0\n4 1\n 2\n 2 3\n 3 0 4\n1 1 4 0\n4 1\n 1\n 1 1\n 1 1 1\n1 1 1 0\n4 2\n 1\n 1 1\n 1 1 1\n1 1 1 0\n4 1\n 0\n 2 2\n 5 0 7\n0 5 7 0\n4 2\n 0\n 0 3\n 1 0 4\n0 1 0 4\n4 3\n 0\n 3 3\n 3 2 3\n0 3 0 3\n4 2\n 0\n 3 3\n 3 2 3\n0 3 0 3\n6 1\n 1\n 1 2\n 1 1 0\n 6 7 6 8\n 0 7 6 8 2\n6 6 7 2 2 0\n5 9\n 0\n 0 0\n 0 0 -1\n 0 0 0 0\n0 0 0 0 0\n5 3\n 3\n 0 2\n 4 3 2\n 4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 4\n0 1 0 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 2\n0\n2 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n0 0 0 0 0\n5 5\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n0 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 0\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 1\n0 1 0 4\n4 3\n0\n3 3\n3 2 3\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n1 2\n1 1 0\n6 7 6 8\n0 7 6 8 1\n6 5 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n0 0 0 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 6\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n0\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 4\n0 1 0 4\n4 3\n0\n3 3\n3 2 3\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n0 0 0 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 4\n0 1 0 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n0 -1 0 0 0\n5 3\n3\n3 2\n0 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n0 1 4 0\n4 1\n2\n2 3\n5 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 0\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 1\n0 1 0 4\n4 3\n0\n3 6\n3 2 3\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n1 2\n1 1 0\n6 7 6 8\n0 7 6 8 1\n6 5 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n0 0 0 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 7\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 4\n0 1 1 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 2\n0\n2 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n0 0 0 0 0\n5 5\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n0 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n0 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 0\n5 0 7\n0 5 11 0\n4 2\n0\n0 3\n1 0 1\n0 1 0 4\n4 3\n0\n3 3\n3 2 3\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n1 2\n1 1 0\n6 7 6 8\n0 7 6 8 1\n6 5 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n0 0 0 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 4\n0 2 0 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 6 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 7\n0\n0 0\n0 0 0\n0 0 0 0\n1 0 -1 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 1\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n0 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n0 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 0\n5 0 7\n0 5 11 0\n4 2\n0\n0 3\n1 0 1\n0 1 0 4\n4 3\n0\n3 3\n3 2 3\n0 3 0 3\n4 2\n0\n2 3\n3 2 3\n0 3 0 3\n6 1\n1\n1 2\n1 1 0\n6 7 6 8\n0 7 6 8 1\n6 5 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n0 0 0 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n0 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 4\n0 2 0 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 6 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 7\n0\n0 0\n0 0 0\n0 0 0 0\n1 0 -1 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 1\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 4\n0 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 4\n0 2 0 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 6 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 7\n0\n0 0\n0 0 0\n0 0 0 0\n1 0 -1 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 1\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 4\n0 1 0 4\n4 3\n0\n3 3\n3 2 3\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n0 0 0 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 1 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 2\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 4\n0 1 0 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n0 0 0 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 0 7 0\n4 2\n0\n0 3\n1 0 4\n0 1 0 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n-1 0 -1 0 0\n5 3\n3\n3 3\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 0\n3 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 -1 4\n0 1 0 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n-1 0 -1 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 1 2 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 0 7 0\n4 2\n0\n0 3\n1 0 4\n0 1 0 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 4\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n-1 0 -1 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 2\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 4\n0 1 0 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 2\n0\n2 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n0 0 0 0 0\n5 5\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 4\n0 1 0 8\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n0 -1 0 0 0\n5 3\n3\n3 2\n0 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 6\n0 1 4 0\n4 1\n2\n2 3\n5 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 0\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 1\n0 1 0 4\n4 3\n0\n3 6\n2 2 3\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n1 2\n1 1 0\n6 7 6 8\n0 7 6 8 1\n6 5 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n0 0 0 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 4\n0 2 0 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 6 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 7\n0\n0 0\n0 0 0\n0 0 0 0\n1 -1 -1 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 1\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 7\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 4\n0 1 1 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 2\n0\n2 3\n3 2 3\n0 1 0 3\n6 1\n1\n0 2\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 1 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n0 0 0 0 0\n5 1\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n0 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 4\n0 2 0 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 6 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 7\n0\n0 0\n0 0 0\n0 0 0 0\n1 0 -1 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 0 3 0 1\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 4\n0 0 4\n1 1 4 0\n4 1\n2\n2 1\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 4\n0 2 0 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 6 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 7\n0\n0 0\n0 0 1\n0 0 0 0\n1 0 -1 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 1\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 1\n0 1 0 4\n4 3\n0\n3 3\n3 2 3\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n1 2\n1 1 0\n6 6 6 8\n0 7 6 8 1\n6 5 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 1 0 0\n0 0 0 0 1\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 3\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 4\n0 1 0 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 3\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n0 0 0 0 0\n5 5\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 4\n0 1 0 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 4\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 1\n0\n0 0\n0 0 0\n0 0 0 0\n0 -1 0 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n 2\n 2 3\n 1 0 4\n1 1 4 0\n4 5\n 2\n 2 3\n 3 0 4\n1 1 4 0\n4 1\n 2\n 2 3\n 3 0 4\n1 1 4 0\n4 1\n 1\n 1 1\n 1 1 1\n1 1 1 0\n4 2\n 1\n 1 1\n 1 1 1\n1 1 1 0\n4 1\n 0\n 2 2\n 5 0 7\n0 5 7 0\n4 2\n 0\n 0 3\n 1 0 4\n0 1 0 4\n4 3\n 0\n 3 3\n 3 2 3\n0 3 0 3\n4 1\n 0\n 3 3\n 3 2 3\n0 3 0 3\n6 1\n 1\n 1 2\n 1 1 0\n 6 7 6 8\n 0 7 6 8 2\n6 6 7 2 2 0\n5 9\n 0\n 0 0\n 0 0 -1\n 0 0 0 0\n0 0 0 1 0\n5 3\n 3\n 0 2\n 4 3 2\n 4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 7\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 1\n0 5 7 0\n4 2\n0\n0 3\n1 0 4\n0 1 0 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 2\n0\n2 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 -1 0\n0 0 0 0 0\n5 5\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 6\n0 1 4 0\n4 1\n2\n2 3\n5 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 1\n0 1 0 4\n4 3\n0\n3 6\n2 2 3\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n1 2\n1 1 0\n6 7 6 8\n0 7 6 8 1\n6 5 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n0 0 0 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 1\n0 1 0 4\n4 3\n0\n3 3\n3 2 3\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n1 2\n1 1 0\n8 6 6 8\n0 7 6 8 1\n6 5 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 1 0 0\n0 0 0 0 1\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 3\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 0 7 0\n4 2\n0\n0 3\n1 0 4\n0 1 0 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 1\n-1 0 -1 0 0\n5 3\n3\n3 3\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 3\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 4\n0 1 0 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 2\n0\n3 3\n3 1 3\n0 3 0 3\n6 1\n1\n0 3\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n0 0 0 0 0\n5 5\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 1 2 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 0 7 0\n4 2\n0\n0 3\n1 0 4\n0 1 0 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 4\n0\n1 3\n3 2 4\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n-1 0 -1 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n0 1 4 0\n4 1\n2\n2 3\n5 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n0 1 1 0\n4 1\n0\n2 4\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 1\n0 1 0 4\n4 3\n0\n3 3\n3 2 3\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n1 2\n1 1 0\n6 7 6 8\n0 7 6 8 1\n6 5 7 2 0 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n0 0 0 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n 2\n 2 3\n 1 0 4\n1 1 4 0\n4 5\n 2\n 2 3\n 3 0 4\n1 0 4 0\n4 1\n 2\n 2 3\n 3 0 4\n1 1 4 0\n4 1\n 1\n 1 1\n 1 1 1\n1 1 1 0\n4 2\n 1\n 1 1\n 1 1 1\n1 1 1 0\n4 1\n 0\n 2 2\n 5 0 7\n0 5 7 0\n4 2\n 0\n 0 3\n 1 0 4\n0 1 0 4\n4 3\n 0\n 3 3\n 3 2 3\n0 3 0 3\n4 1\n 0\n 3 3\n 3 2 3\n0 3 0 3\n6 1\n 1\n 1 2\n 1 1 0\n 6 7 6 8\n 0 7 6 8 2\n6 6 7 2 2 0\n5 9\n 0\n 0 0\n 0 0 -1\n 0 0 0 0\n0 0 0 1 0\n5 3\n 3\n 0 2\n 4 3 2\n 4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 7\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 1\n0 5 7 0\n4 2\n0\n0 3\n1 0 4\n0 1 0 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 -1 0\n0 0 0 0 0\n5 5\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 0 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n10 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 4\n0 1 0 4\n4 3\n0\n3 3\n3 2 3\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n1 2\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 -1 0 0\n0 0 0 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 1 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 1\n0 1 0 4\n4 3\n0\n3 3\n3 2 3\n0 3 0 3\n4 2\n0\n4 3\n3 2 3\n0 3 0 3\n6 1\n1\n1 2\n1 1 0\n8 6 6 8\n0 7 6 8 1\n6 5 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 1 0 0\n0 0 0 0 1\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n 2\n 2 3\n 1 0 4\n1 1 4 0\n4 5\n 2\n 2 3\n 3 0 4\n1 1 4 0\n4 1\n 2\n 2 3\n 3 0 4\n1 1 7 0\n4 1\n 1\n 1 1\n 1 1 1\n1 1 1 0\n4 2\n 1\n 1 0\n 1 1 1\n1 1 1 0\n4 1\n 0\n 2 2\n 5 0 7\n0 5 7 0\n4 2\n 0\n 0 3\n 1 0 4\n0 1 0 4\n4 3\n 0\n 3 3\n 3 2 3\n0 3 0 3\n4 2\n 0\n 3 3\n 3 2 3\n0 3 0 3\n6 1\n 1\n 1 2\n 1 1 0\n 6 7 6 8\n 0 7 6 8 2\n6 6 7 2 2 0\n5 9\n -1\n 0 0\n 0 0 -1\n 0 0 1 0\n0 0 0 0 0\n5 3\n 3\n 3 2\n 4 3 2\n 4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n0 1 4 0\n4 1\n2\n2 3\n5 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n0 1 1 0\n4 2\n1\n1 1\n1 1 1\n0 1 1 0\n4 1\n0\n2 4\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 1\n0 1 0 4\n4 3\n0\n3 3\n3 2 3\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n1 2\n1 1 0\n6 7 6 8\n0 7 6 8 1\n6 5 7 2 0 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n0 0 0 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n 2\n 2 3\n 1 0 4\n1 1 4 0\n4 5\n 2\n 2 3\n 3 0 4\n1 0 4 0\n4 1\n 2\n 2 3\n 3 0 4\n1 1 4 0\n4 1\n 1\n 1 1\n 1 1 1\n1 1 1 0\n4 2\n 1\n 1 1\n 1 1 1\n1 1 1 0\n4 1\n 0\n 2 0\n 5 0 7\n0 5 7 0\n4 2\n 0\n 0 3\n 1 0 4\n0 1 0 4\n4 3\n 0\n 3 3\n 3 2 3\n0 3 0 3\n4 1\n 0\n 3 3\n 3 2 3\n0 3 0 3\n6 1\n 1\n 1 2\n 1 1 0\n 6 7 6 8\n 0 7 6 8 2\n6 6 7 2 2 0\n5 9\n 0\n 0 0\n 0 0 -1\n 0 0 0 0\n0 0 0 1 0\n5 3\n 3\n 0 2\n 4 3 2\n 4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 0 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n10 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 4\n0 1 0 4\n4 3\n0\n3 3\n3 3 3\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n1 2\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 -1 0 0\n0 0 0 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 1 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 0 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n0 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n10 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 4\n0 1 0 4\n4 3\n0\n3 3\n3 3 3\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n1 2\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 -1 0 0\n0 0 0 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 1 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n0 1 4 0\n4 1\n2\n2 3\n5 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n0 1 1 0\n4 2\n1\n1 1\n1 1 1\n0 1 1 0\n4 1\n0\n2 4\n5 0 7\n0 5 7 0\n4 2\n0\n-1 3\n1 0 1\n0 1 0 1\n4 3\n0\n3 3\n3 2 3\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n1 2\n1 1 0\n6 7 6 8\n0 7 6 8 1\n6 5 7 2 0 0\n5 9\n0\n0 0\n1 0 0\n0 0 0 0\n0 0 0 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 0 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n0 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n10 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 4\n0 1 0 4\n4 3\n0\n3 3\n3 3 5\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n1 3\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 -1 0 0\n0 0 0 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 1 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 0 0\n4 1\n0\n2 2\n5 0 7\n0 0 7 0\n4 2\n0\n0 3\n1 0 4\n0 1 0 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n-1 0 -1 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n0\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 4\n0 1 0 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n1 0 -1 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n0 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 1\n0 1 0 4\n4 3\n0\n3 3\n3 2 3\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n1 2\n1 1 0\n6 7 6 8\n0 7 6 8 1\n6 5 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n0 0 0 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 0 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 1 2 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 0 7 0\n4 2\n0\n0 3\n1 0 4\n0 1 0 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 4\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 7 6 8\n0 7 7 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n-1 0 -1 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 6\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 1\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 4\n0 1 0 4\n4 3\n0\n3 3\n3 2 3\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n0 0 0 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 0\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 4\n0 1 0 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 2\n0\n3 6\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n-1 0 -1 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n0 1 4 0\n4 1\n2\n2 3\n5 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 1\n0 1 0 4\n4 3\n0\n3 6\n3 2 3\n0 3 0 3\n4 1\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n1 2\n1 1 0\n6 7 6 8\n0 7 6 8 1\n6 5 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n0 0 0 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n0 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 4\n0 1 0 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n0 -1 0 0 0\n5 3\n3\n3 2\n0 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 7\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n0 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 4\n0 1 0 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 2\n0\n2 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n0 0 0 0 0\n5 5\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n0 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 4\n0 2 0 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n1 0 -1 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 1\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 4\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 -1 4\n0 1 0 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 2 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 1\n-1 0 -1 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 4\n0 2 0 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 1 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 7\n0\n0 0\n0 0 0\n0 0 0 0\n1 0 -1 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 1\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 1 0\n4 5\n2\n2 3\n3 0 4\n0 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n0 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 0\n5 0 7\n0 5 11 0\n4 2\n0\n0 3\n1 0 1\n0 1 0 4\n4 3\n0\n3 3\n3 2 3\n0 3 0 3\n4 2\n0\n2 3\n3 2 3\n0 3 0 3\n6 1\n1\n1 2\n1 1 0\n6 7 6 8\n0 7 6 8 1\n6 5 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n0 0 0 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 4\n0 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 4\n0 2 0 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 6 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n1 7\n0\n0 0\n0 0 0\n0 0 0 0\n1 0 -1 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 1\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 7\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 4\n0 1 1 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 2\n0\n2 3\n4 2 3\n0 1 0 3\n6 1\n1\n0 2\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n0 0 0 0 0\n5 2\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 4\n0 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 4\n0 2 0 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 2\n0\n3 3\n3 2 0\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 6 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 7\n0\n0 0\n0 0 0\n0 0 0 0\n1 0 -1 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 1\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n0 1 4 0\n4 1\n2\n2 3\n5 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 1\n0 2 0 4\n4 3\n0\n3 6\n3 2 3\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n1 2\n1 1 0\n6 7 6 8\n0 7 6 8 1\n6 5 7 0 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n0 0 0 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n0 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 0\n5 0 7\n0 5 11 0\n4 2\n0\n0 3\n1 0 1\n0 1 0 4\n4 3\n0\n3 3\n3 2 3\n0 0 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n1 2\n1 1 0\n6 7 6 8\n0 7 6 8 1\n6 5 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n0 0 0 0 0\n5 4\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n0 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 -1 4\n0 1 0 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 2 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 1\n-1 0 -1 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n0 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 4\n0 0 4\n1 1 4 0\n4 1\n2\n2 1\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 4\n0 2 0 3\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 6 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 7\n0\n0 0\n0 0 1\n0 0 0 0\n1 0 -1 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 1\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 4\n0 1 0 4\n4 3\n0\n3 3\n3 2 3\n0 3 0 3\n4 2\n0\n3 3\n3 2 4\n0 3 0 3\n6 1\n1\n1 2\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 -1 0 0\n0 0 0 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 1 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 0 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 1\n0 1 0 4\n4 3\n0\n3 3\n3 2 3\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n1 2\n1 1 0\n6 6 6 8\n0 7 6 8 1\n6 5 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 1 0 0\n0 0 0 0 1\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 1 2 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 0\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 0 7 0\n4 2\n0\n0 3\n1 0 4\n0 1 0 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 4\n0\n1 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n-1 0 -1 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 6\n0 1 4 0\n4 1\n2\n2 3\n5 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 1\n0 1 0 4\n4 3\n0\n3 6\n2 2 3\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n1 2\n1 1 0\n6 7 6 8\n0 7 6 8 1\n6 5 2 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n0 0 0 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 3\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 -1 7\n0 0 7 0\n4 2\n0\n0 3\n1 0 4\n0 1 0 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 1\n-1 0 -1 0 0\n5 3\n3\n3 3\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 7\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 1 2 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 0 7 0\n4 2\n0\n0 3\n1 0 4\n0 1 0 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 4\n0\n1 3\n3 2 4\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n-1 0 -1 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 5\n 2\n 2 3\n 1 0 4\n1 1 4 0\n4 5\n 2\n 2 3\n 3 0 4\n1 1 4 0\n4 1\n 2\n 2 3\n 3 0 4\n1 1 7 0\n4 1\n 1\n 1 1\n 1 1 1\n1 1 1 0\n4 2\n 1\n 1 0\n 1 1 1\n1 1 1 0\n4 1\n 0\n 2 2\n 5 0 7\n0 5 7 0\n4 2\n 0\n 0 3\n 1 0 4\n0 1 0 4\n4 3\n 0\n 3 3\n 3 2 3\n0 3 0 3\n4 2\n 0\n 3 3\n 3 2 3\n0 3 0 3\n6 1\n 1\n 1 2\n 1 1 0\n 6 7 6 8\n 0 7 6 8 2\n6 6 7 2 2 0\n5 9\n -1\n 0 0\n 0 0 -1\n 0 0 1 0\n0 0 0 0 0\n5 3\n 3\n 3 2\n 4 3 2\n 4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 0 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n0 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n10 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 4\n0 1 0 4\n4 3\n0\n3 3\n3 3 3\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n1 3\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 -1 0 0\n0 0 0 0 0\n5 5\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 1 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n0\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 4\n0 1 0 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n3 9\n0\n0 0\n0 0 0\n0 0 0 0\n1 0 -1 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 4\n0 5 7 0\n4 2\n0\n0 3\n1 0 4\n0 1 0 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 5\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n0 -1 0 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n0 1\n1 1 1\n1 1 1 0\n4 1\n0\n1 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 4\n0 1 0 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n0 -1 0 0 0\n5 3\n3\n3 2\n0 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n0 1 4 0\n4 2\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 0\n5 0 7\n0 5 11 0\n4 2\n0\n0 3\n1 0 1\n0 1 0 4\n4 3\n0\n3 3\n3 2 3\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 2 0 3\n6 1\n1\n1 2\n1 1 0\n6 7 6 8\n0 7 6 8 1\n6 5 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n0 0 0 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 4\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 4\n0\n0 3\n1 -1 4\n0 1 0 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 2 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 1\n-1 0 -1 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 4\n0 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 3 7 0\n4 2\n0\n0 3\n1 0 4\n0 2 0 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 6 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 7\n0\n0 0\n0 0 1\n0 0 0 0\n1 0 -1 0 0\n5 3\n3\n3 3\n4 3 2\n4 4 0 3\n3 3 3 0 1\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n1\n0 3\n1 0 4\n0 1 0 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 3\n2 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n0 0 0 0 0\n5 5\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n 2\n 2 3\n 1 0 4\n1 1 4 0\n4 5\n 2\n 2 3\n 3 0 4\n1 1 7 0\n4 1\n 2\n 2 3\n 3 0 4\n1 1 4 0\n4 1\n 1\n 1 1\n 1 1 1\n1 1 1 0\n4 2\n 1\n 1 1\n 1 1 1\n1 1 1 0\n4 1\n 0\n 2 2\n 5 0 7\n0 5 7 0\n4 2\n 0\n 0 3\n 1 0 4\n0 1 0 4\n4 3\n 0\n 3 3\n 3 2 3\n0 3 0 3\n4 2\n 0\n 3 3\n 3 2 3\n0 3 0 3\n6 1\n 1\n 1 2\n 1 1 0\n 6 7 6 8\n 0 7 6 8 2\n6 6 7 2 2 0\n5 9\n 0\n 0 0\n 0 0 -1\n 0 0 0 0\n0 0 0 1 0\n5 3\n 3\n 0 2\n 6 3 2\n 4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n0 1 4 0\n4 1\n2\n2 3\n5 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 1\n0 2 0 4\n4 3\n0\n3 6\n3 2 3\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n1 2\n1 1 0\n6 7 6 8\n0 7 6 8 1\n6 5 9 0 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n0 0 0 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n0 1 4 0\n4 1\n2\n2 3\n3 0 4\n0 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 0\n5 0 7\n0 5 11 0\n4 2\n0\n0 3\n1 0 1\n0 1 0 4\n4 3\n0\n3 3\n3 2 3\n0 0 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n1 2\n1 1 0\n6 7 6 8\n0 7 6 8 1\n6 5 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n0 0 0 0 0\n5 4\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n0 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n0 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 2 0\n4 1\n0\n2 0\n5 0 7\n0 5 11 0\n4 2\n0\n0 3\n1 0 1\n0 1 0 4\n4 3\n0\n3 3\n3 2 3\n0 3 0 3\n4 2\n0\n3 3\n6 2 3\n0 3 0 3\n6 1\n1\n1 2\n1 1 0\n6 7 6 8\n0 7 6 8 1\n6 5 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n0 0 0 -1 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n0 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 4\n0 2 0 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 6 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 7\n0\n0 0\n0 0 1\n0 0 0 0\n1 -1 -1 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 1\n0 0",
"4 8\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 4\n0 1 0 4\n4 3\n0\n3 3\n3 2 3\n0 3 0 3\n4 2\n0\n3 3\n3 2 4\n0 3 0 3\n6 1\n1\n1 2\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 -1 0 0\n0 0 0 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 1 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n0 0 4\n1 0 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 1\n0 1 0 4\n4 3\n0\n3 3\n3 2 3\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n1 2\n1 1 0\n6 6 6 8\n0 7 6 8 1\n6 5 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 1 0 0\n0 0 0 0 1\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n0 1 4 0\n4 1\n2\n2 3\n5 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 0 1 0\n4 1\n0\n2 4\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 1\n0 1 0 4\n4 3\n0\n3 3\n3 2 3\n0 3 0 3\n4 2\n0\n3 3\n3 1 3\n0 3 0 3\n6 1\n1\n1 2\n1 1 0\n6 7 6 8\n0 7 6 8 1\n6 5 7 2 0 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n0 0 0 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 4\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n0 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 5 7 0\n4 2\n0\n0 3\n1 0 4\n0 2 0 4\n4 3\n0\n3 3\n2 2 2\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 6 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 7\n0\n0 0\n0 0 0\n0 1 0 0\n1 0 -1 -1 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 0 3 0 1\n0 0",
"4 4\n2\n2 3\n1 0 3\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 -1 7\n0 0 7 0\n4 2\n0\n0 3\n1 0 4\n0 1 0 4\n4 3\n0\n3 3\n3 2 2\n0 3 0 3\n4 2\n0\n3 3\n3 2 3\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n0 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 1\n-1 0 -1 0 0\n5 3\n3\n3 3\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0",
"4 7\n2\n2 3\n1 0 4\n1 1 4 0\n4 5\n2\n2 3\n3 0 4\n1 1 2 0\n4 1\n2\n2 3\n3 0 4\n1 1 4 0\n4 1\n1\n1 1\n1 1 1\n1 1 1 0\n4 2\n1\n1 1\n1 1 1\n1 1 1 0\n4 1\n0\n2 2\n5 0 7\n0 0 7 0\n4 2\n0\n0 3\n1 0 4\n0 1 0 4\n4 3\n0\n3 3\n3 2 2\n0 1 0 3\n4 4\n0\n1 3\n3 2 4\n0 3 0 3\n6 1\n1\n0 2\n1 1 0\n6 7 6 8\n0 7 6 8 2\n6 6 7 2 2 0\n5 9\n0\n0 0\n0 0 0\n0 0 0 0\n-1 0 -1 0 0\n5 3\n3\n3 2\n4 3 2\n4 4 0 3\n3 3 3 0 3\n0 0"
],
"output": [
"6\n5\n1\n-10\n8\n-1\n0\n1\n-1\n5\n0\n5",
"6\n5\n1\n-10\n8\n-1\n0\n1\n-1\n5\n0\n5",
"6\n5\n1\n-10\n8\n-1\n0\n1\n-1\n5\n0\n5\n",
"6\n5\n1\n-10\n8\n-1\n1\n1\n-1\n5\n0\n5\n",
"6\n5\n1\n-10\n8\n-1\n0\n2\n-1\n5\n0\n5\n",
"6\n5\n1\n-10\n8\n0\n0\n2\n-1\n5\n0\n5\n",
"6\n5\n1\n-10\n8\n-1\n0\n2\n-1\n5\n0\n8\n",
"6\n2\n1\n-10\n8\n-1\n1\n1\n-1\n5\n0\n5\n",
"6\n5\n1\n-10\n8\n-1\n1\n2\n-1\n5\n0\n5\n",
"6\n5\n1\n0\n8\n-1\n0\n2\n-1\n5\n0\n5\n",
"6\n5\n1\n-10\n8\n-1\n0\n1\n-1\n5\n0\n0\n",
"6\n5\n1\n-10\n8\n-1\n0\n2\n0\n5\n0\n8\n",
"6\n2\n1\n-10\n8\n0\n1\n1\n-1\n5\n0\n5\n",
"6\n5\n-1\n-10\n8\n-1\n0\n1\n-1\n5\n0\n5\n",
"6\n5\n1\n-10\n8\n-1\n0\n2\n-1\n5\n0\n2\n",
"6\n2\n1\n-10\n0\n-1\n1\n1\n-1\n5\n0\n5\n",
"6\n5\n1\n-10\n8\n-1\n2\n2\n0\n5\n0\n8\n",
"6\n2\n1\n0\n8\n0\n1\n1\n-1\n5\n0\n5\n",
"6\n5\n1\n-10\n8\n-1\n0\n2\n-1\n3\n0\n5\n",
"6\n2\n1\n0\n8\n0\n1\n1\n0\n5\n0\n5\n",
"6\n1\n1\n-10\n8\n-1\n0\n2\n-1\n3\n0\n5\n",
"6\n0\n1\n-10\n8\n-1\n0\n2\n-1\n3\n0\n5\n",
"6\n5\n1\n-10\n8\n-1\n0\n1\n-1\n5\n0\n-3\n",
"6\n5\n1\n-10\n6\n-1\n0\n2\n-1\n5\n0\n5\n",
"6\n5\n1\n-10\n8\n0\n0\n2\n-1\n5\n0\n4\n",
"6\n3\n1\n-10\n8\n-1\n1\n2\n-1\n5\n0\n5\n",
"6\n5\n1\n-10\n8\n0\n0\n2\n0\n5\n0\n5\n",
"6\n5\n1\n-8\n8\n-1\n0\n2\n0\n5\n0\n8\n",
"6\n5\n1\n-10\n8\n-1\n1\n2\n-1\n5\n0\n2\n",
"6\n2\n1\n-10\n0\n-1\n1\n0\n-1\n5\n0\n5\n",
"6\n5\n1\n-10\n8\n-1\n0\n2\n-1\n3\n1\n5\n",
"6\n5\n1\n-10\n8\n-1\n2\n2\n0\n4\n0\n8\n",
"6\n1\n1\n-10\n8\n-1\n0\n2\n-1\n3\n0\n2\n",
"6\n0\n-1\n-10\n8\n-1\n0\n2\n-1\n3\n0\n5\n",
"6\n5\n1\n-10\n8\n-1\n1\n1\n-1\n3\n0\n5\n",
"3\n5\n1\n-10\n8\n-1\n0\n2\n-1\n5\n0\n8\n",
"6\n5\n1\n-10\n8\n-1\n0\n2\n0\n5\n0\n5\n",
"6\n5\n1\n-10\n8\n-1\n0\n1\n0\n5\n0\n0\n",
"6\n5\n1\n-10\n8\n0\n0\n2\n0\n5\n0\n8\n",
"6\n2\n1\n-10\n8\n-1\n1\n0\n-1\n5\n0\n5\n",
"6\n5\n1\n-10\n8\n-1\n1\n1\n-1\n4\n0\n5\n",
"5\n5\n1\n-10\n8\n0\n0\n2\n-1\n5\n0\n4\n",
"3\n5\n1\n-10\n8\n-1\n0\n2\n0\n5\n0\n8\n",
"6\n5\n1\n-10\n8\n0\n0\n2\n1\n5\n0\n5\n",
"6\n2\n1\n-10\n-1\n-1\n1\n1\n-1\n5\n0\n5\n",
"6\n3\n1\n-10\n8\n-1\n0\n1\n0\n5\n0\n0\n",
"6\n5\n1\n-10\n8\n0\n0\n2\n-1\n5\n0\n8\n",
"6\n3\n1\n-10\n8\n-1\n0\n1\n-1\n5\n0\n-3\n",
"6\n5\n1\n-10\n8\n-1\n1\n1\n0\n4\n0\n5\n",
"6\n5\n1\n-10\n-1\n-1\n0\n1\n-1\n5\n0\n5\n",
"6\n2\n1\n0\n-1\n-1\n1\n1\n-1\n5\n0\n5\n",
"6\n3\n1\n-10\n8\n0\n0\n1\n0\n5\n0\n0\n",
"6\n3\n1\n-10\n8\n-1\n0\n0\n-1\n5\n0\n-3\n",
"6\n3\n1\n-10\n-1\n-1\n0\n0\n-1\n5\n0\n-3\n",
"6\n2\n1\n0\n-1\n-1\n0\n1\n-1\n5\n0\n5\n",
"6\n3\n1\n-10\n-1\n-1\n0\n1\n-1\n5\n0\n-3\n",
"6\n5\n1\n-10\n0\n0\n0\n2\n-1\n5\n0\n5\n",
"6\n2\n1\n-10\n8\n-1\n0\n2\n-1\n5\n0\n5\n",
"6\n2\n1\n-10\n8\n-1\n1\n1\n-1\n5\n0\n2\n",
"6\n5\n1\n-10\n8\n0\n0\n2\n0\n6\n0\n5\n",
"6\n5\n1\n-10\n8\n0\n0\n1\n-1\n5\n0\n5\n",
"6\n5\n1\n0\n8\n-1\n0\n2\n0\n5\n0\n5\n",
"6\n2\n1\n-10\n8\n-1\n1\n1\n0\n5\n0\n5\n",
"6\n5\n1\n-10\n-1\n-1\n0\n2\n-1\n5\n0\n2\n",
"6\n5\n1\n-10\n-1\n-1\n0\n2\n0\n5\n0\n8\n",
"6\n5\n1\n-10\n-1\n-1\n0\n2\n-1\n5\n0\n5\n",
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"6\n5\n1\n-10\n8\n-1\n0\n2\n-1\n4\n0\n5\n",
"3\n2\n1\n0\n8\n0\n1\n1\n0\n5\n0\n5\n",
"6\n0\n1\n-10\n8\n-1\n0\n2\n-1\n3\n-1\n",
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"6\n0\n1\n-10\n8\n-1\n0\n2\n0\n3\n0\n5\n",
"6\n2\n1\n-10\n8\n-1\n1\n1\n-1\n2\n0\n5\n",
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"6\n5\n1\n0\n8\n-1\n1\n2\n-1\n5\n0\n2\n",
"6\n0\n-1\n-10\n8\n-1\n1\n2\n-1\n3\n0\n5\n",
"6\n5\n1\n-10\n8\n-1\n0\n1\n0\n5\n0\n-3\n",
"6\n3\n1\n-10\n8\n-1\n1\n1\n-1\n3\n0\n5\n",
"6\n5\n1\n0\n8\n0\n0\n2\n0\n5\n0\n5\n",
"6\n2\n1\n-10\n8\n-1\n1\n0\n-1\n4\n0\n5\n",
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"5\n5\n1\n-10\n-1\n-1\n0\n1\n-1\n5\n0\n5\n",
"6\n3\n1\n-10\n-1\n-1\n0\n0\n-1\n5\n0\n13\n",
"6\n2\n1\n-10\n8\n-1\n0\n2\n-1\n5\n0\n",
"6\n5\n1\n-10\n8\n-1\n0\n3\n-1\n5\n0\n5\n",
"6\n5\n1\n-10\n-1\n0\n0\n2\n-1\n5\n0\n2\n",
"6\n2\n1\n-10\n8\n0\n1\n1\n0\n5\n0\n5\n",
"6\n5\n0\n-10\n8\n-1\n0\n2\n-1\n5\n0\n5\n",
"6\n0\n1\n-10\n8\n-1\n0\n2\n-1\n3\n0\n4\n",
"6\n5\n1\n-10\n8\n-1\n1\n2\n-1\n5\n0\n8\n",
"6\n5\n1\n-10\n8\n-1\n0\n1\n-1\n5\n0\n2\n",
"6\n2\n1\n-10\n8\n-1\n1\n1\n-1\n4\n0\n5\n",
"6\n2\n3\n-10\n8\n0\n1\n0\n-1\n5\n0\n5\n",
"6\n2\n1\n0\n6\n0\n1\n1\n0\n5\n0\n5\n",
"6\n5\n1\n0\n8\n-1\n0\n2\n-1\n3\n1\n5\n",
"5\n5\n1\n-10\n8\n-1\n0\n1\n0\n5\n0\n-3\n",
"6\n1\n1\n-10\n8\n-1\n1\n1\n-1\n3\n0\n5\n",
"6\n2\n1\n-10\n-1\n-1\n1\n1\n0\n5\n0\n5\n",
"6\n1\n1\n-10\n8\n-1\n0\n0\n-1\n3\n0\n2\n",
"5\n5\n1\n-10\n8\n1\n0\n2\n-1\n4\n0\n4\n",
"5\n5\n1\n-10\n8\n0\n0\n0\n1\n5\n0\n5\n"
]
}
| 6AIZU
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Let's play a new board game ``Life Line''.
The number of the players is greater than 1 and less than 10.
In this game, the board is a regular triangle in which many small regular triangles are arranged (See Figure l). The edges of each small triangle are of the same length.
<image>
Figure 1: The board
The size of the board is expressed by the number of vertices on the bottom edge of the outer triangle. For example, the size of the board in Figure 1 is 4.
At the beginning of the game, each player is assigned his own identification number between 1 and 9, and is given some stones on which his identification number is written.
Each player puts his stone in turn on one of the ``empty'' vertices. An ``empty vertex'' is a vertex that has no stone on it.
When one player puts his stone on one of the vertices during his turn, some stones might be removed from the board. The player gains points which is equal to the number of the removed stones of others, but loses points which is equal to the number of the removed stones of himself. The points of a player for a single turn is the points he gained minus the points he lost in that turn.
The conditions for removing stones are as follows:
* The stones on the board are divided into groups. Each group contains a set of stones whose numbers are the same and placed adjacently. That is, if the same numbered stones are placed adjacently, they belong to the same group.
* If none of the stones in a group is adjacent to at least one ``empty'' vertex, all the stones in that group are removed from the board.
<image>
Figure 2: The groups of stones
Figure 2 shows an example of the groups of stones.
Suppose that the turn of the player `4' comes now. If he puts his stone on the vertex shown in Figure 3a, the conditions will be satisfied to remove some groups of stones (shadowed in Figure 3b). The player gains 6 points, because the 6 stones of others are removed from the board (See Figure 3c).
<image>
Figure 3a
|
Figure 3b
|
Figure 3c
---|---|---
As another example, suppose that the turn of the player `2' comes in Figure 2. If the player puts his stone on the vertex shown in Figure 4a, the conditions will be satisfied to remove some groups of stones (shadowed in Figure 4b). The player gains 4 points, because the 4 stones of others are removed. But, at the same time, he loses 3 points, because his 3 stones are removed. As the result, the player's points of this turn is 4 - 3 = 1 (See Figure 4c).
<image>
Figure 4a
|
Figure 4b
|
Figure 4c
---|---|---
When each player puts all of his stones on the board, the game is over. The total score of a player is the summation of the points of all of his turns.
Your job is to write a program that tells you the maximum points a player can get (i.e., the points he gains - the points he loses) in his current turn.
Input
The input consists of multiple data. Each data represents the state of the board of the game still in progress.
The format of each data is as follows.
N C
S1,1
S2,1 S2,2
S3,1 S3,2 S3,3
...
SN,1 ... SN,N
N is the size of the board (3 ≤ N ≤ 10).
C is the identification number of the player whose turn comes now (1 ≤ C ≤ 9) . That is, your program must calculate his points in this turn.
Si,j is the state of the vertex on the board (0 ≤ Si,j ≤ 9) . If the value of Si,j is positive, it means that there is the stone numbered by Si,j there. If the value of Si,j is 0, it means that the vertex is ``empty''.
Two zeros in a line, i.e., 0 0, represents the end of the input.
Output
For each data, the maximum points the player can get in the turn should be output, each in a separate line.
Examples
Input
4 4
2
2 3
1 0 4
1 1 4 0
4 5
2
2 3
3 0 4
1 1 4 0
4 1
2
2 3
3 0 4
1 1 4 0
4 1
1
1 1
1 1 1
1 1 1 0
4 2
1
1 1
1 1 1
1 1 1 0
4 1
0
2 2
5 0 7
0 5 7 0
4 2
0
0 3
1 0 4
0 1 0 4
4 3
0
3 3
3 2 3
0 3 0 3
4 2
0
3 3
3 2 3
0 3 0 3
6 1
1
1 2
1 1 0
6 7 6 8
0 7 6 8 2
6 6 7 2 2 0
5 9
0
0 0
0 0 0
0 0 0 0
0 0 0 0 0
5 3
3
3 2
4 3 2
4 4 0 3
3 3 3 0 3
0 0
Output
6
5
1
-10
8
-1
0
1
-1
5
0
5
Input
4 4
2
2 3
1 0 4
1 1 4 0
4 5
2
2 3
3 0 4
1 1 4 0
4 1
2
2 3
3 0 4
1 1 4 0
4 1
1
1 1
1 1 1
1 1 1 0
4 2
1
1 1
1 1 1
1 1 1 0
4 1
0
2 2
5 0 7
0 5 7 0
4 2
0
0 3
1 0 4
0 1 0 4
4 3
0
3 3
3 2 3
0 3 0 3
4 2
0
3 3
3 2 3
0 3 0 3
6 1
1
1 2
1 1 0
6 7 6 8
0 7 6 8 2
6 6 7 2 2 0
5 9
0
0 0
0 0 0
0 0 0 0
0 0 0 0 0
5 3
3
3 2
4 3 2
4 4 0 3
3 3 3 0 3
0 0
Output
6
5
1
-10
8
-1
0
1
-1
5
0
5
### Input:
4 4
2
2 3
1 0 4
1 1 4 0
4 5
2
2 3
3 0 4
1 1 4 0
4 1
2
2 3
3 0 4
1 1 4 0
4 1
1
1 1
1 1 1
1 1 1 0
4 2
1
1 1
1 1 1
1 1 1 0
4 1
0
2 2
5 0 7
0 5 7 0
4 2
0
0 3
1 0 4
0 1 0 4
4 3
0
3 3
3 2 3
0 3 0 3
4 2
0
3 3
3 2 3
0 3 0 3
6 1
1
1 2
1 1 0
6 7 6 8
0 7 6 8 2
6 6 7 2 2 0
5 9
0
0 0
0 0 0
0 0 0 0
0 0 0 0 0
5 3
3
3 2
4 3 2
4 4 0 3
3 3 3 0 3
0 0
### Output:
6
5
1
-10
8
-1
0
1
-1
5
0
5
### Input:
4 4
2
2 3
1 0 4
1 1 4 0
4 5
2
2 3
3 0 4
1 1 4 0
4 1
2
2 3
3 0 4
1 1 4 0
4 1
1
1 1
1 1 1
1 1 1 0
4 2
1
1 1
1 1 1
1 1 1 0
4 1
0
2 2
5 0 7
0 5 7 0
4 2
0
0 3
1 0 4
0 1 0 4
4 3
0
3 3
3 2 3
0 3 0 3
4 2
0
3 3
3 2 3
0 3 0 3
6 1
1
1 2
1 1 0
6 7 6 8
0 7 6 8 2
6 6 7 2 2 0
5 9
0
0 0
0 0 0
0 0 0 0
0 0 0 0 0
5 3
3
3 2
4 3 2
4 4 0 3
3 3 3 0 3
0 0
### Output:
6
5
1
-10
8
-1
0
1
-1
5
0
5
### Code:
import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools
sys.setrecursionlimit(10**7)
inf = 10**20
eps = 1.0 / 10**13
mod = 10**9+7
dd = [(-1,0),(0,1),(1,0),(0,-1)]
ddn = [(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()
def pf(s): return print(s, flush=True)
def main():
rr = []
def f(n,m):
a = [[-1]*(n+3)] + [[-1] + LI() + [-1]*2 for _ in range(n)] + [[-1]*(n+3)]
aa = [c[:] for c in a]
d = collections.defaultdict(int)
def _f(i,j,c):
if a[i][j] == 0:
return (0, set([(i,j)]))
if a[i][j] != c:
return (0,set())
a[i][j] = -1
r = [1, set()]
for di,dj in [(-1,-1),(-1,0),(0,-1),(0,1),(1,0),(1,1)]:
t = _f(i+di,j+dj,c)
r[0] += t[0]
r[1] |= t[1]
# print('_f',i,j,c,r)
return tuple(r)
for i in range(1,n+1):
for j in range(1,i+1):
if a[i][j] != m:
continue
c,s = _f(i,j,a[i][j])
if len(s) == 1:
d[list(s)[0]] = -1
a = aa
aa = [c[:] for c in a]
for i in range(1,n+1):
for j in range(1,i+1):
if a[i][j] != 0:
continue
if (i,j) in d:
continue
tf = True
for di,dj in [(-1,-1),(-1,0),(0,-1),(0,1),(1,0),(1,1)]:
if a[i+di][j+dj] in [0,m]:
tf = False
break
if tf:
d[(i,j)] = -1
else:
d[(i,j)] = 0
ts = collections.defaultdict(set)
for i in range(1,n+1):
for j in range(1,i+1):
if a[i][j] != m:
continue
cc = a[i][j]
sf = -1 if a[i][j] == m else 1
c,s = _f(i,j,a[i][j])
# print('res',i,j,c,s,sf,len(s))
if len(s) > 1:
for sc in s:
ts[sc].add(cc)
d[sc] = 0
a = aa
# print(d)
# print('\n'.join("\t".join(map(str,_)) for _ in a))
for i in range(1,n+1):
for j in range(1,i+1):
if a[i][j] < 1:
continue
cc = a[i][j]
sf = -1 if a[i][j] == m else 1
c,s = _f(i,j,a[i][j])
# print('res',i,j,c,s,sf,len(s))
if len(s) == 1 and cc not in ts[list(s)[0]]:
if sf == 1:
d[list(s)[0]] += c * sf
else:
d[list(s)[0]] += c * sf
# print('\n'.join("\t".join(map(str,_)) for _ in a))
# print('\n'.join("\t".join(map(str,_)) for _ in a))
# print(d)
if len(d) == 0:
return 0
return max(d.values())
while True:
n,m = LI()
if n == 0 and m == 0:
break
rr.append(f(n,m))
return '\n'.join(map(str,rr))
print(main())
|
p01078 Star_10426
|
Problem
Find the area of a regular N / K polygon inscribed in a circle with a radius of 1.
However, a regular N / K polygon is defined as "the outermost figure that takes N points on the circumference at equal intervals and connects each point every K-1".
For example, a 5/2 polygon can be drawn as follows. First, take five points at equal intervals on the circumference of radius 1.
Sample Input 2 diagram
Next, connect each point every other 2-1 = 1.
Sample Input 2 diagram
The outermost figure is a regular 5/2 square.
Sample Input 2 diagram
Constraints
The input satisfies the following constraints.
* 5 ≤ N ≤ 106
* 1 <K <N / 2
* N and K are integers that are relatively prime
Input
The input is given in the following format.
N K
Two integers N and K are given on one line.
Output
Output the area of a regular N / K polygon inscribed in a circle with a radius of 1 on one line. An error of 10-5 or less is acceptable.
Examples
Input
5 2
Output
1.12256994
Input
20 3
Output
2.93114293
Input
7 3
Output
1.08395920
Input
100000 3
Output
3.14159265
|
# AOJ 1593: Star
# Python3 2018.7.13 bal4u
import math
PI = 3.1415926535897932384626433832795
# area = n*r^2*sin(180/n)*cos(180k/n)*sec(180(k-1)/n), for n/k star
N, K = map(int, input().split())
print(N*math.sin(PI/N)*math.cos(K*PI/N)/math.cos((K-1)*PI/N))
|
{
"input": [
"100000 3",
"20 3",
"7 3",
"5 2",
"100000 2",
"36 3",
"36 2",
"100010 4",
"000010 4",
"001010 4",
"100100 3",
"33 3",
"101000 2",
"36 4",
"001010 2",
"001000 4",
"110000 3",
"6 3",
"101000 3",
"36 8",
"001011 4",
"001000 6",
"36 15",
"010010 3",
"001010 7",
"011000 6",
"110010 4",
"001010 9",
"010000 6",
"101001 4",
"101010 9",
"010000 7",
"110000 7",
"001110 9",
"001100 9",
"110010 9",
"110010 16",
"110010 11",
"110010 18",
"110000 25",
"110000 48",
"110000 86",
"110101 86",
"110111 100",
"010111 100",
"010111 110",
"010011 110",
"010011 111",
"010011 101",
"011011 111",
"011010 111",
"011010 101",
"011000 111",
"011000 110",
"011000 010",
"011000 011",
"111000 111",
"111000 011",
"111000 101",
"111000 110",
"011100 110",
"011000 100",
"010000 100",
"010000 110",
"111000 100",
"110000 100",
"101000 111",
"101000 011",
"101001 101",
"101001 100",
"101011 110",
"111011 110",
"10 2",
"59 2",
"110010 2",
"100010 5",
"010010 4",
"001010 3",
"33 2",
"100010 7",
"011000 4",
"111000 3",
"001000 7",
"36 9",
"010000 3",
"011100 6",
"110010 8",
"010010 9",
"111000 6",
"101001 6",
"101010 13",
"010000 9",
"101110 12",
"001101 9",
"101000 9",
"111010 11",
"110010 5",
"100000 25",
"010000 48",
"100001 86",
"110101 74",
"110111 80",
"111111 100",
"010011 100"
],
"output": [
"3.14159265",
"2.93114293",
"1.08395920",
"1.12256994",
"3.1415926484\n",
"3.0774487433\n",
"3.1017425091\n",
"3.1415926422\n",
"1.6245984812\n",
"3.1414812017\n",
"3.1415926453\n",
"3.0651767230\n",
"3.1415926485\n",
"3.0523936924\n",
"3.1415419947\n",
"3.1414789615\n",
"3.1415926468\n",
"0.0000000000\n",
"3.1415926455\n",
"2.9341881325\n",
"3.1414814221\n",
"3.1414169392\n",
"2.3743407981\n",
"3.1415918284\n",
"3.1413899975\n",
"3.1415912015\n",
"3.1415926442\n",
"3.1413291780\n",
"3.1415908966\n",
"3.1415926424\n",
"3.1415926273\n",
"3.1415905865\n",
"3.1415926365\n",
"3.1413745197\n",
"3.1413705350\n",
"3.1415926314\n",
"3.1415926135\n",
"3.1415926263\n",
"3.1415926083\n",
"3.1415925904\n",
"3.1415925314\n",
"3.1415924341\n",
"3.1415924345\n",
"3.1415923987\n",
"3.1415624160\n",
"3.1415593799\n",
"3.1415587116\n",
"3.1415584018\n",
"3.1415614990\n",
"3.1415643426\n",
"3.1415643375\n",
"3.1415668976\n",
"3.1415642860\n",
"3.1415645425\n",
"3.1415901765\n",
"3.1415899202\n",
"3.1415923751\n",
"3.1415926267\n",
"3.1415924003\n",
"3.1415923776\n",
"3.1415650468\n",
"3.1415671072\n",
"3.1415617408\n",
"3.1415586368\n",
"3.1415924028\n",
"3.1415923982\n",
"3.1415923172\n",
"3.1415926212\n",
"3.1415923476\n",
"3.1415923507\n",
"3.1415923203\n",
"3.1415923777\n",
"2.6286555606\n",
"3.1267505318\n",
"3.1415926493\n",
"3.1415926391\n",
"3.1415915190\n",
"3.1415115988\n",
"3.0941731289\n",
"3.1415926329\n",
"3.1415917140\n",
"3.1415926469\n",
"3.1413859237\n",
"2.8962066388\n",
"3.1415918268\n",
"3.1415912276\n",
"3.1415926339\n",
"3.1415899717\n",
"3.1415926393\n",
"3.1415926364\n",
"3.1415926151\n",
"3.1415899664\n",
"3.1415926182\n",
"3.1413709383\n",
"3.1415926272\n",
"3.1415926268\n",
"3.1415926416\n",
"3.1415925771\n",
"3.1415778729\n",
"3.1415923880\n",
"3.1415924652\n",
"3.1415924499\n",
"3.1415924033\n",
"3.1415618087\n"
]
}
| 6AIZU
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Problem
Find the area of a regular N / K polygon inscribed in a circle with a radius of 1.
However, a regular N / K polygon is defined as "the outermost figure that takes N points on the circumference at equal intervals and connects each point every K-1".
For example, a 5/2 polygon can be drawn as follows. First, take five points at equal intervals on the circumference of radius 1.
Sample Input 2 diagram
Next, connect each point every other 2-1 = 1.
Sample Input 2 diagram
The outermost figure is a regular 5/2 square.
Sample Input 2 diagram
Constraints
The input satisfies the following constraints.
* 5 ≤ N ≤ 106
* 1 <K <N / 2
* N and K are integers that are relatively prime
Input
The input is given in the following format.
N K
Two integers N and K are given on one line.
Output
Output the area of a regular N / K polygon inscribed in a circle with a radius of 1 on one line. An error of 10-5 or less is acceptable.
Examples
Input
5 2
Output
1.12256994
Input
20 3
Output
2.93114293
Input
7 3
Output
1.08395920
Input
100000 3
Output
3.14159265
### Input:
100000 3
### Output:
3.14159265
### Input:
20 3
### Output:
2.93114293
### Code:
# AOJ 1593: Star
# Python3 2018.7.13 bal4u
import math
PI = 3.1415926535897932384626433832795
# area = n*r^2*sin(180/n)*cos(180k/n)*sec(180(k-1)/n), for n/k star
N, K = map(int, input().split())
print(N*math.sin(PI/N)*math.cos(K*PI/N)/math.cos((K-1)*PI/N))
|
p01830 Delete Files_10434
|
Example
Input
3
y 7
y 6
n 5
Output
1
|
import sys
readline = sys.stdin.readline
write = sys.stdout.write
def solve():
N = int(readline())
L = [0]*N; D = [0]*N
for i in range(N):
l, d = readline().split()
L[i] = +(l == 'y')
D[i] = int(d)
ans = 0
*I, = range(N)
I.sort(key = D.__getitem__)
U = [0]*N
for i in I:
if not L[i] or U[i]:
continue
d = D[i]
U[i] = 1
ans += 1
k = i-1
while k >= 0 and (L[k] or D[k] < d):
if L[k]:
U[k] = 1
k -= 1
k = i+1
while k < N and (L[k] or D[k] < d):
if L[k]:
U[k] = 1
k += 1
write("%d\n" % ans)
solve()
|
{
"input": [
"3\ny 7\ny 6\nn 5",
"3\ny 7\ny 2\nn 5",
"3\ny 7\ny 3\nn 5",
"3\ny 7\ny 3\nn 10",
"3\ny 2\ny 3\nn 10",
"3\ny 2\ny 6\nn 10",
"3\nx 2\ny 6\nn 10",
"3\ny 7\ny 11\nn 5",
"3\ny 8\ny 2\nn 5",
"3\ny 7\ny 6\nn 2",
"3\ny 0\ny 3\nn 10",
"3\ny 4\ny 3\nn 10",
"3\ny 2\ny 6\nn 14",
"3\ny 7\ny 11\nm 5",
"3\ny 7\nz 6\nn 2",
"3\ny 0\ny 5\nn 10",
"3\ny 4\ny 3\nn 12",
"3\nx 2\ny 9\nn 10",
"3\ny 7\ny 2\nn 1",
"3\ny 7\ny 3\nn 3",
"3\ny 11\ny 3\nn 10",
"3\ny 2\ny 3\nn 9",
"3\nx 2\ny 7\nn 10",
"3\ny 2\ny 2\nn 5",
"3\ny 2\ny 6\nn 2",
"3\ny 0\ny 1\nn 10",
"3\ny 6\ny 3\nn 12",
"3\ny 7\ny 2\no 1",
"3\ny 11\nx 3\nn 10",
"3\nx 2\ny 2\nn 5",
"3\ny 7\ny 2\np 1",
"3\ny 9\ny 2\np 1",
"3\ny 13\ny 6\nn 5",
"3\ny 7\ny 4\nn 5",
"3\ny 7\ny 3\nn 6",
"3\ny 3\ny 6\nn 10",
"3\nz 2\ny 6\nn 10",
"3\nx 2\ny 10\nn 10",
"3\ny 7\ny 11\nn 2",
"3\ny 7\ny 12\nm 5",
"3\ny 0\ny 6\nn 10",
"3\ny 4\ny 3\nn 6",
"3\ny 7\ny 2\nn 2",
"3\ny 7\ny 3\no 2",
"3\ny 11\ny 3\nn 1",
"3\ny 2\ny 0\nn 9",
"3\nx 0\ny 7\nn 10",
"3\ny 2\ny 2\nn 9",
"3\ny 2\ny 9\nn 2",
"3\ny 7\ny 3\nn 12",
"3\ny 11\nw 3\nn 10",
"3\ny 16\ny 2\np 1",
"3\ny 13\ny 6\nn 9",
"3\ny 7\ny 4\nn 0",
"3\nz 3\ny 6\nn 10",
"3\nz 2\ny 3\nn 10",
"3\nx 0\ny 10\nn 10",
"3\ny 7\ny 11\nn 0",
"3\ny 7\ny 12\nn 5",
"3\ny 0\ny 10\nn 10",
"3\ny 4\ny 3\nn 0",
"3\ny 7\ny 5\no 2",
"3\ny 11\ny 6\nn 1",
"3\ny 2\ny 0\nn 2",
"3\ny 0\ny 2\nn 9",
"3\ny 4\ny 9\nn 2",
"3\ny 11\nx 0\nn 10",
"3\ny 16\ny 2\np 0",
"3\ny 12\ny 4\nn 0",
"3\nz 2\ny 2\nn 10",
"3\nx 0\ny 10\nn 16",
"3\ny 3\ny 11\nn 0",
"3\ny 7\ny 24\nn 5",
"3\ny 0\ny 10\nn 19",
"3\ny 6\ny 3\nn 0",
"3\ny 7\ny 5\np 2",
"3\ny 2\ny 6\nn 1",
"3\ny 0\ny 3\nn 9",
"3\ny 4\ny 9\nm 2",
"3\ny 13\nx 0\nn 10",
"3\nz 2\ny 2\nn 7",
"3\ny 3\ny 13\nn 0",
"3\ny 6\ny 2\nn 0",
"3\ny 0\ny 6\nn 1",
"3\ny 0\ny 4\nn 9",
"3\ny 4\ny 4\nm 2",
"3\ny 13\nx 0\nn 17",
"3\ny 3\ny 13\nm 0",
"3\ny 6\nx 2\nn 0",
"3\nz 0\ny 6\nn 1",
"3\ny 0\ny 5\nn 9",
"3\ny 16\nx 0\nn 17",
"3\ny 3\ny 9\nm 0",
"3\ny 6\nx 4\nn 0",
"3\nz 1\ny 6\nn 1",
"3\ny 0\ny 5\nn 15",
"3\ny 16\nx 0\nn 5",
"3\ny 3\ny 10\nm 0",
"3\ny 6\nx 4\nn -1",
"3\nz 1\ny 6\nn 0",
"3\ny 0\ny 5\nn 19"
],
"output": [
"1",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n"
]
}
| 6AIZU
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Example
Input
3
y 7
y 6
n 5
Output
1
### Input:
3
y 7
y 6
n 5
### Output:
1
### Input:
3
y 7
y 2
n 5
### Output:
1
### Code:
import sys
readline = sys.stdin.readline
write = sys.stdout.write
def solve():
N = int(readline())
L = [0]*N; D = [0]*N
for i in range(N):
l, d = readline().split()
L[i] = +(l == 'y')
D[i] = int(d)
ans = 0
*I, = range(N)
I.sort(key = D.__getitem__)
U = [0]*N
for i in I:
if not L[i] or U[i]:
continue
d = D[i]
U[i] = 1
ans += 1
k = i-1
while k >= 0 and (L[k] or D[k] < d):
if L[k]:
U[k] = 1
k -= 1
k = i+1
while k < N and (L[k] or D[k] < d):
if L[k]:
U[k] = 1
k += 1
write("%d\n" % ans)
solve()
|
p02112 Hating Crowd_10437
|
Problem
Neat lives on the world line for a total of 360 days until the 30th of every month for 1 year and 12 months. In that world, N consecutive holidays with the same schedule were applied to people all over the world every year. Consecutive holidays i are consecutive Vi days starting from Mi month Di day.
NEET is NEET, so he is closed every day regardless of consecutive holidays. One day NEET decided to go out unusually, but I hate crowds, so I don't want to go out as much as possible on busy days due to the effects of consecutive holidays. Therefore, Neat is trying to find the day with the least congestion by calculating the congestion degree of each day by the following method.
* The number that represents the degree of influence of a date x by the holiday i is Si if the date x is included in the holiday i, otherwise max (0, Si − min (from x). The number of days until the first day of consecutive holidays i, the number of days from the last day of consecutive holidays i to x)))
* The degree of congestion on a certain date x is the degree of influence that is most affected by N consecutive holidays.
Please output the lowest degree of congestion in the year. However, consecutive holidays i may span years. In addition, the dates of consecutive holidays may overlap.
Constraints
The input satisfies the following conditions.
* 1 ≤ N ≤ 100
* 1 ≤ Mi ≤ 12
* 1 ≤ Di ≤ 30
* 1 ≤ Vi, Si ≤ 360
Input
The input is given in the following format.
N
M1 D1 V1 S1
M2 D2 V2 S2
...
MN DN VN SN
The integer N is given on the first line.
The integers Mi, Di, Vi, Si are given on the 2nd to N + 1th lines separated by blanks. (1 ≤ i ≤ N)
Output
Outputs the least congestion level on one line.
Examples
Input
1
1 1 359 1
Output
0
Input
2
2 4 25 306
1 9 7 321
Output
158
Input
8
2 9 297 297
8 6 359 211
8 16 28 288
7 9 113 143
3 18 315 190
10 18 277 300
9 5 276 88
3 5 322 40
Output
297
|
N = input()
N = int(N)+1
X = [0]
C = [0]*360
for i in range(1,N):
x = input()
X.append(x.split())
i_start = (int(X[i][0])-1)*30+int(X[i][1])-1
i_end = i_start+int(X[i][2])-1
for j in range(i_start,i_end+1):
C[j%360] = max(C[j%360],int(X[i][3]))
for k in range(1,int(X[i][3])+1):
C[(i_start-k+360)%360] = max(C[(i_start-k+360)%360],int(X[i][3])-k)
C[(i_end+k)%360] = max(C[(i_end+k)%360],int(X[i][3])-k)
print(min(C))
|
{
"input": [
"1\n1 1 359 1",
"2\n2 4 25 306\n1 9 7 321",
"8\n2 9 297 297\n8 6 359 211\n8 16 28 288\n7 9 113 143\n3 18 315 190\n10 18 277 300\n9 5 276 88\n3 5 322 40",
"1\n1 1 1 1",
"2\n2 4 25 104\n1 9 7 321",
"2\n2 4 25 28\n1 9 13 321",
"2\n2 4 4 51\n1 4 13 252",
"2\n3 4 4 51\n2 4 13 335",
"2\n3 4 4 51\n2 4 13 360",
"2\n2 4 24 306\n1 9 7 321",
"8\n2 9 297 297\n8 6 359 211\n8 16 28 233\n7 9 113 143\n3 18 315 190\n10 18 277 300\n9 5 276 88\n3 5 322 40",
"2\n2 4 25 28\n1 17 22 321",
"2\n2 4 25 86\n1 4 8 321",
"2\n2 4 4 51\n2 4 19 252",
"2\n2 5 25 28\n1 22 22 382",
"2\n4 4 15 28\n1 12 20 321",
"2\n3 4 4 51\n2 4 19 442",
"2\n3 4 4 4\n2 4 13 175",
"2\n4 4 27 86\n1 4 8 359",
"2\n4 3 25 123\n1 4 13 139",
"2\n3 4 4 51\n2 4 2 442",
"2\n3 4 4 4\n2 4 13 194",
"2\n2 4 25 58\n2 17 7 296",
"2\n4 7 4 51\n8 4 7 431",
"2\n4 4 27 86\n1 8 8 201",
"2\n3 4 5 4\n2 4 13 253",
"2\n2 4 35 58\n2 17 7 500",
"2\n6 4 13 141\n1 4 13 252",
"2\n9 4 13 141\n1 4 13 252",
"2\n9 6 13 141\n1 4 13 252",
"2\n3 4 5 7\n4 7 13 190",
"2\n3 5 5 7\n4 7 13 294",
"2\n4 0 6 48\n3 6 35 381",
"2\n4 0 6 48\n3 3 59 381",
"2\n2 11 10 8\n2 0 4 180",
"2\n4 3 5 0\n1 1 5 294",
"2\n4 3 5 0\n1 1 5 262",
"2\n2 11 10 8\n2 0 5 265",
"2\n2 21 10 13\n2 0 10 265",
"2\n2 4 25 28\n1 9 15 321",
"2\n2 4 25 48\n1 21 13 350",
"2\n2 4 4 51\n1 4 13 354",
"2\n3 4 4 51\n2 4 24 335",
"2\n2 4 14 306\n1 9 7 321",
"2\n3 4 4 51\n2 4 3 335",
"2\n2 4 25 58\n2 17 7 522",
"2\n2 5 1 28\n1 22 22 426",
"2\n3 4 4 51\n2 4 4 442",
"2\n4 4 27 86\n1 8 11 201",
"2\n5 4 13 93\n1 4 13 199",
"2\n3 4 5 4\n2 4 24 253",
"2\n2 4 35 58\n2 17 12 500",
"2\n9 6 13 141\n2 4 13 252",
"2\n4 0 6 48\n3 6 59 321",
"2\n4 0 6 48\n3 6 35 193",
"2\n4 5 5 0\n4 7 13 457",
"2\n4 3 5 0\n4 7 14 294",
"2\n4 0 1 46\n3 3 59 490",
"2\n2 21 10 13\n2 -1 10 430",
"2\n2 4 38 306\n1 10 7 321",
"2\n2 4 25 48\n1 21 13 242",
"2\n2 4 4 51\n1 5 3 252",
"2\n2 4 14 306\n1 9 7 212",
"2\n4 2 15 28\n1 12 20 277",
"2\n2 5 25 34\n1 21 13 382",
"2\n2 4 25 58\n2 17 3 522",
"2\n4 2 27 86\n1 4 1 359",
"2\n3 4 4 51\n2 4 4 314",
"2\n5 4 8 68\n2 4 8 252",
"2\n5 4 8 237\n1 4 13 252",
"2\n2 4 25 34\n1 3 13 186",
"2\n5 4 22 93\n1 4 13 199",
"2\n8 5 27 86\n1 8 8 201",
"2\n3 4 5 7\n2 2 5 253",
"2\n9 4 13 257\n1 4 16 252",
"2\n4 4 6 48\n3 6 25 271",
"2\n2 9 25 34\n1 1 19 188",
"2\n6 0 6 48\n3 10 39 381",
"2\n4 5 5 0\n4 7 1 457",
"2\n4 0 4 48\n3 8 9 381",
"2\n4 3 5 0\n1 2 1 294",
"2\n4 0 0 62\n3 3 18 381",
"2\n2 4 45 28\n1 22 18 321",
"2\n2 4 4 51\n1 7 13 362",
"2\n5 3 4 51\n1 4 6 268",
"2\n2 6 25 58\n4 9 7 196",
"2\n2 5 1 8\n1 22 22 455",
"2\n5 4 8 237\n1 4 13 488",
"2\n3 4 5 7\n2 2 5 423",
"2\n2 9 14 34\n2 3 13 177",
"2\n2 4 25 28\n1 9 7 321",
"2\n2 4 25 28\n1 17 13 321",
"2\n2 4 25 28\n1 21 13 321",
"2\n2 4 25 48\n1 21 13 321",
"2\n2 4 25 48\n1 4 13 321",
"2\n2 4 25 51\n1 4 13 321",
"2\n2 4 4 51\n1 4 13 321",
"2\n3 4 4 51\n1 4 13 252",
"2\n3 4 4 51\n2 4 13 252",
"2\n3 4 7 51\n2 4 13 360",
"1\n1 2 1 1",
"2\n2 4 25 52\n1 9 7 321",
"2\n2 4 25 1\n1 9 13 321"
],
"output": [
"0",
"158",
"297",
"0\n",
"144\n",
"147\n",
"78\n",
"161\n",
"186\n",
"158\n",
"297\n",
"152\n",
"145\n",
"81\n",
"213\n",
"151\n",
"271\n",
"1\n",
"183\n",
"8\n",
"263\n",
"20\n",
"119\n",
"254\n",
"25\n",
"79\n",
"323\n",
"98\n",
"83\n",
"82\n",
"16\n",
"120\n",
"218\n",
"230\n",
"2\n",
"116\n",
"84\n",
"87\n",
"90\n",
"148\n",
"176\n",
"180\n",
"167\n",
"153\n",
"156\n",
"345\n",
"257\n",
"264\n",
"26\n",
"32\n",
"85\n",
"326\n",
"97\n",
"170\n",
"30\n",
"283\n",
"121\n",
"339\n",
"255\n",
"164\n",
"68\n",
"73\n",
"133\n",
"107\n",
"208\n",
"343\n",
"179\n",
"136\n",
"76\n",
"128\n",
"12\n",
"37\n",
"44\n",
"75\n",
"142\n",
"103\n",
"17\n",
"220\n",
"277\n",
"205\n",
"114\n",
"210\n",
"150\n",
"188\n",
"91\n",
"19\n",
"286\n",
"314\n",
"245\n",
"3\n",
"144\n",
"147\n",
"147\n",
"147\n",
"147\n",
"147\n",
"147\n",
"78\n",
"78\n",
"186\n",
"0\n",
"144\n",
"147\n"
]
}
| 6AIZU
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Problem
Neat lives on the world line for a total of 360 days until the 30th of every month for 1 year and 12 months. In that world, N consecutive holidays with the same schedule were applied to people all over the world every year. Consecutive holidays i are consecutive Vi days starting from Mi month Di day.
NEET is NEET, so he is closed every day regardless of consecutive holidays. One day NEET decided to go out unusually, but I hate crowds, so I don't want to go out as much as possible on busy days due to the effects of consecutive holidays. Therefore, Neat is trying to find the day with the least congestion by calculating the congestion degree of each day by the following method.
* The number that represents the degree of influence of a date x by the holiday i is Si if the date x is included in the holiday i, otherwise max (0, Si − min (from x). The number of days until the first day of consecutive holidays i, the number of days from the last day of consecutive holidays i to x)))
* The degree of congestion on a certain date x is the degree of influence that is most affected by N consecutive holidays.
Please output the lowest degree of congestion in the year. However, consecutive holidays i may span years. In addition, the dates of consecutive holidays may overlap.
Constraints
The input satisfies the following conditions.
* 1 ≤ N ≤ 100
* 1 ≤ Mi ≤ 12
* 1 ≤ Di ≤ 30
* 1 ≤ Vi, Si ≤ 360
Input
The input is given in the following format.
N
M1 D1 V1 S1
M2 D2 V2 S2
...
MN DN VN SN
The integer N is given on the first line.
The integers Mi, Di, Vi, Si are given on the 2nd to N + 1th lines separated by blanks. (1 ≤ i ≤ N)
Output
Outputs the least congestion level on one line.
Examples
Input
1
1 1 359 1
Output
0
Input
2
2 4 25 306
1 9 7 321
Output
158
Input
8
2 9 297 297
8 6 359 211
8 16 28 288
7 9 113 143
3 18 315 190
10 18 277 300
9 5 276 88
3 5 322 40
Output
297
### Input:
1
1 1 359 1
### Output:
0
### Input:
2
2 4 25 306
1 9 7 321
### Output:
158
### Code:
N = input()
N = int(N)+1
X = [0]
C = [0]*360
for i in range(1,N):
x = input()
X.append(x.split())
i_start = (int(X[i][0])-1)*30+int(X[i][1])-1
i_end = i_start+int(X[i][2])-1
for j in range(i_start,i_end+1):
C[j%360] = max(C[j%360],int(X[i][3]))
for k in range(1,int(X[i][3])+1):
C[(i_start-k+360)%360] = max(C[(i_start-k+360)%360],int(X[i][3])-k)
C[(i_end+k)%360] = max(C[(i_end+k)%360],int(X[i][3])-k)
print(min(C))
|
p02252 Fractional Knapsack Problem_10440
|
You have $N$ items that you want to put them into a knapsack of capacity $W$. Item $i$ ($1 \le i \le N$) has weight $w_i$ and value $v_i$ for the weight.
When you put some items into the knapsack, the following conditions must be satisfied:
* The total value of the items is as large as possible.
* The total weight of the selected items is at most $W$.
* You can break some items if you want. If you put $w'$($0 \le w' \le w_i$) of item $i$, its value becomes $\displaystyle v_i \times \frac{w'}{w_i}.$
Find the maximum total value of items in the knapsack.
Constraints
* $1 \le N \le 10^5$
* $1 \le W \le 10^9$
* $1 \le v_i \le 10^9 (1 \le i \le N)$
* $1 \le w_i \le 10^9 (1 \le i \le N)$
Input
$N$ $W$
$v_1$ $w_1$
$v_2$ $w_2$
:
$v_N$ $w_N$
The first line consists of the integers $N$ and $W$. In the following $N$ lines, the value and weight of the $i$-th item are given.
Output
Print the maximum total value of the items in a line. The output must not contain an error greater than $10^{-6}$.
Examples
Input
3 50
60 10
100 20
120 30
Output
240
Input
3 50
60 13
100 23
120 33
Output
210.90909091
Input
1 100
100000 100000
Output
100
|
N, W = map(int, input().split())
W_calc = W
ans = 0
items = []
for _ in range(N):
v, w = map(int, input().split())
density = v / w
items.append([density, v, w])
items.sort(reverse=True)
for density, v, w in items:
if w < W_calc:
W_calc -= w
ans += v
else:
ans += W_calc * density
break
print(ans)
|
{
"input": [
"1 100\n100000 100000",
"3 50\n60 10\n100 20\n120 30",
"3 50\n60 13\n100 23\n120 33",
"3 50\n60 10\n110 20\n120 30",
"0 50\n60 10\n110 20\n120 30",
"3 14\n60 10\n100 20\n120 30",
"1 50\n60 13\n100 23\n120 33",
"3 50\n59 10\n110 20\n120 30",
"1 100\n100001 100000",
"3 8\n60 10\n100 20\n120 30",
"3 50\n59 10\n010 20\n120 30",
"1 38\n118 1\n010 20\n26 20",
"1 100\n100001 101000",
"3 50\n59 10\n010 20\n239 30",
"1 38\n62 1\n010 20\n26 20",
"1 63\n3 1\n000 20\n26 31",
"3 50\n59 10\n010 30\n239 30",
"1 22\n108 1\n000 20\n26 50",
"1 38\n73 1\n101 27\n26 30",
"1 63\n2 1\n000 20\n26 31",
"1 101\n100001 111000",
"3 50\n59 10\n010 30\n239 47",
"2 99\n60 25\n100 13\n120 33",
"3 50\n40 10\n010 30\n239 47",
"1 59\n26 1\n111 20\n26 34",
"2 38\n73 2\n101 27\n26 30",
"1 96\n113 10\n111 20\n120 31",
"1 001\n100001 111000",
"3 50\n38 10\n000 30\n239 47",
"1 38\n112 1\n110 20\n22 26",
"2 38\n118 1\n101 27\n26 30",
"1 77\n119 10\n111 20\n120 31",
"2 19\n118 1\n101 27\n26 30",
"1 77\n197 10\n111 20\n120 31",
"3 50\n38 18\n000 25\n239 47",
"3 50\n38 5\n000 25\n239 47",
"2 37\n118 1\n100 27\n50 30",
"1 2\n4 1\n000 39\n36 12",
"3 50\n38 5\n000 25\n104 47",
"3 50\n38 5\n000 25\n161 47",
"1 63\n122 3\n000 1\n16 0",
"1 45\n67 1\n110 20\n-1 30",
"3 50\n38 5\n100 9\n161 47",
"1 12\n6 2\n111 1\n50 1",
"3 50\n38 2\n100 9\n161 47",
"3 50\n38 1\n100 9\n161 47",
"3 50\n38 1\n100 9\n161 76",
"2 13\n26 4\n100 2\n8 1",
"3 50\n38 1\n110 9\n161 76",
"2 13\n26 4\n101 2\n8 1",
"3 50\n38 1\n110 9\n209 76",
"3 50\n62 1\n110 9\n209 76",
"3 50\n62 1\n110 9\n209 17",
"1 63\n140 5\n011 6\n51 0",
"1 60\n1 1\n010 1\n-1 6",
"1 3\n7 2\n001 19\n17 3",
"1 1\n14 1\n001 1\n17 0",
"3 18\n60 10\n100 20\n120 30",
"3 50\n60 13\n100 20\n120 33",
"3 14\n60 10\n100 27\n120 30",
"1 38\n75 5\n110 20\n26 30",
"1 63\n79 1\n111 20\n26 57",
"1 101\n100001 100000",
"3 50\n59 10\n010 20\n198 30",
"2 96\n60 10\n110 20\n120 30",
"1 38\n45 1\n010 20\n26 20",
"1 100\n100001 101001",
"1 101\n100011 111000",
"1 38\n23 1\n110 20\n26 31",
"3 50\n40 10\n010 30\n52 47",
"3 50\n40 14\n000 30\n239 47",
"2 38\n73 2\n101 45\n26 30",
"1 001\n100011 111000",
"3 50\n38 6\n000 30\n239 47",
"1 59\n30 1\n110 20\n36 34",
"3 50\n38 10\n100 30\n241 47",
"2 19\n228 1\n101 27\n26 30",
"3 50\n38 10\n000 25\n239 65",
"2 19\n24 1\n101 27\n50 30",
"1 59\n134 1\n111 13\n17 26",
"1 7\n25 2\n111 1\n97 1",
"3 50\n38 8\n000 25\n161 47",
"2 50\n38 5\n000 21\n161 47",
"3 59\n38 5\n000 5\n161 47",
"0 50\n60 10\n110 20\n65 30",
"0 50\n60 5\n110 20\n65 30",
"0 38\n60 5\n110 20\n65 30",
"0 38\n60 5\n110 20\n26 30",
"0 38\n118 5\n110 20\n26 30",
"0 38\n118 1\n110 20\n26 30",
"0 38\n118 1\n010 20\n26 30",
"0 38\n118 1\n000 20\n26 30",
"0 38\n118 1\n001 20\n26 30",
"0 38\n79 1\n001 20\n26 30",
"0 63\n79 1\n001 20\n26 30",
"0 63\n79 1\n011 20\n26 30",
"0 63\n79 1\n011 20\n26 57",
"0 63\n3 1\n011 20\n26 57",
"0 63\n3 1\n001 20\n26 57",
"0 63\n3 1\n001 20\n26 54",
"0 63\n3 1\n011 20\n26 54",
"0 63\n3 1\n010 20\n26 54",
"0 63\n3 1\n010 20\n26 7"
],
"output": [
"100",
"240",
"210.90909091",
"250.0000000000\n",
"0.0000000000\n",
"80.0000000000\n",
"60.0000000000\n",
"249.0000000000\n",
"100.0010000000\n",
"48.0000000000\n",
"184.0000000000\n",
"118.0000000000\n",
"99.0108910891\n",
"303.0000000000\n",
"62.0000000000\n",
"3.0000000000\n",
"301.3333333333\n",
"108.0000000000\n",
"73.0000000000\n",
"2.0000000000\n",
"90.9919009009\n",
"262.4042553191\n",
"160.0000000000\n",
"251.0000000000\n",
"26.0000000000\n",
"174.0000000000\n",
"113.0000000000\n",
"0.9009099099\n",
"250.4000000000\n",
"112.0000000000\n",
"219.0000000000\n",
"119.0000000000\n",
"185.3333333333\n",
"197.0000000000\n",
"245.3333333333\n",
"266.8297872340\n",
"218.0000000000\n",
"4.0000000000\n",
"137.5744680851\n",
"192.1489361702\n",
"122.0000000000\n",
"67.0000000000\n",
"261.3191489362\n",
"6.0000000000\n",
"271.5957446809\n",
"275.0212765957\n",
"222.7368421053\n",
"126.0000000000\n",
"232.7368421053\n",
"127.0000000000\n",
"258.0000000000\n",
"282.0000000000\n",
"381.0000000000\n",
"140.0000000000\n",
"1.0000000000\n",
"7.0000000000\n",
"14.0000000000\n",
"100.0000000000\n",
"221.8181818182\n",
"76.0000000000\n",
"75.0000000000\n",
"79.0000000000\n",
"101.0010100000\n",
"262.0000000000\n",
"170.0000000000\n",
"45.0000000000\n",
"99.0099107930\n",
"91.0010000000\n",
"23.0000000000\n",
"84.2553191489\n",
"247.5714285714\n",
"153.8000000000\n",
"0.9010000000\n",
"261.7446808511\n",
"30.0000000000\n",
"252.4000000000\n",
"295.3333333333\n",
"185.0769230769\n",
"91.3333333333\n",
"134.0000000000\n",
"25.0000000000\n",
"181.8723404255\n",
"38.0000000000\n",
"199.0000000000\n",
"0.0000000000\n",
"0.0000000000\n",
"0.0000000000\n",
"0.0000000000\n",
"0.0000000000\n",
"0.0000000000\n",
"0.0000000000\n",
"0.0000000000\n",
"0.0000000000\n",
"0.0000000000\n",
"0.0000000000\n",
"0.0000000000\n",
"0.0000000000\n",
"0.0000000000\n",
"0.0000000000\n",
"0.0000000000\n",
"0.0000000000\n",
"0.0000000000\n",
"0.0000000000\n"
]
}
| 6AIZU
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You have $N$ items that you want to put them into a knapsack of capacity $W$. Item $i$ ($1 \le i \le N$) has weight $w_i$ and value $v_i$ for the weight.
When you put some items into the knapsack, the following conditions must be satisfied:
* The total value of the items is as large as possible.
* The total weight of the selected items is at most $W$.
* You can break some items if you want. If you put $w'$($0 \le w' \le w_i$) of item $i$, its value becomes $\displaystyle v_i \times \frac{w'}{w_i}.$
Find the maximum total value of items in the knapsack.
Constraints
* $1 \le N \le 10^5$
* $1 \le W \le 10^9$
* $1 \le v_i \le 10^9 (1 \le i \le N)$
* $1 \le w_i \le 10^9 (1 \le i \le N)$
Input
$N$ $W$
$v_1$ $w_1$
$v_2$ $w_2$
:
$v_N$ $w_N$
The first line consists of the integers $N$ and $W$. In the following $N$ lines, the value and weight of the $i$-th item are given.
Output
Print the maximum total value of the items in a line. The output must not contain an error greater than $10^{-6}$.
Examples
Input
3 50
60 10
100 20
120 30
Output
240
Input
3 50
60 13
100 23
120 33
Output
210.90909091
Input
1 100
100000 100000
Output
100
### Input:
1 100
100000 100000
### Output:
100
### Input:
3 50
60 10
100 20
120 30
### Output:
240
### Code:
N, W = map(int, input().split())
W_calc = W
ans = 0
items = []
for _ in range(N):
v, w = map(int, input().split())
density = v / w
items.append([density, v, w])
items.sort(reverse=True)
for density, v, w in items:
if w < W_calc:
W_calc -= w
ans += v
else:
ans += W_calc * density
break
print(ans)
|
p02400 Circle_10444
|
Write a program which calculates the area and circumference of a circle for given radius r.
Constraints
* 0 < r < 10000
Input
A real number r is given.
Output
Print the area and circumference of the circle in a line. Put a single space between them. The output should not contain an absolute error greater than 10-5.
Examples
Input
2
Output
12.566371 12.566371
Input
3
Output
28.274334 18.849556
|
pi=3.141592653589
r=float(input())
print(f'{r*r*pi:7f} {2*r*pi}')
|
{
"input": [
"2",
"3",
"4",
"0",
"5",
"1",
"6",
"-1",
"10",
"-2",
"7",
"-4",
"11",
"-3",
"17",
"-5",
"13",
"-10",
"21",
"-13",
"34",
"-22",
"39",
"-8",
"74",
"8",
"76",
"-7",
"149",
"-6",
"12",
"-11",
"24",
"-14",
"46",
"-12",
"60",
"-17",
"14",
"-15",
"16",
"20",
"25",
"23",
"19",
"22",
"15",
"-9",
"9",
"-18",
"18",
"-34",
"-16",
"-54",
"-26",
"27",
"-48",
"30",
"-60",
"26",
"-68",
"44",
"-84",
"63",
"-113",
"85",
"-94",
"-19",
"-33",
"-27",
"-61",
"-51",
"-114",
"-28",
"-87",
"-23",
"-101",
"-29",
"-88",
"-36",
"-53",
"-66",
"-20",
"-40",
"-21",
"-67",
"49",
"-93",
"-32",
"-64",
"-38",
"-77",
"-65",
"36",
"-102",
"31",
"-124",
"53",
"-210",
"84",
"-215",
"71"
],
"output": [
"12.566371 12.566371",
"28.274334 18.849556",
"50.265482457 25.1327412287\n",
"0.000000000 0.0\n",
"78.539816340 31.4159265359\n",
"3.141592654 6.28318530718\n",
"113.097335529 37.6991118431\n",
"3.141592654 -6.28318530718\n",
"314.159265359 62.8318530718\n",
"12.566370614 -12.5663706144\n",
"153.938040026 43.9822971502\n",
"50.265482457 -25.1327412287\n",
"380.132711084 69.115038379\n",
"28.274333882 -18.8495559215\n",
"907.920276887 106.814150222\n",
"78.539816340 -31.4159265359\n",
"530.929158457 81.6814089933\n",
"314.159265359 -62.8318530718\n",
"1385.442360233 131.946891451\n",
"530.929158457 -81.6814089933\n",
"3631.681107549 213.628300444\n",
"1520.530844337 -138.230076758\n",
"4778.362426109 245.04422698\n",
"201.061929830 -50.2654824574\n",
"17203.361371053 464.955712731\n",
"201.061929830 50.2654824574\n",
"18145.839167130 477.522083346\n",
"153.938040026 -43.9822971502\n",
"69746.498502329 936.19461077\n",
"113.097335529 -37.6991118431\n",
"452.389342117 75.3982236861\n",
"380.132711084 -69.115038379\n",
"1809.557368467 150.796447372\n",
"615.752160103 -87.9645943005\n",
"6647.610054994 289.02652413\n",
"452.389342117 -75.3982236861\n",
"11309.733552920 376.991118431\n",
"907.920276887 -106.814150222\n",
"615.752160103 87.9645943005\n",
"706.858347058 -94.2477796077\n",
"804.247719319 100.530964915\n",
"1256.637061436 125.663706144\n",
"1963.495408493 157.079632679\n",
"1661.902513749 144.513262065\n",
"1134.114947946 119.380520836\n",
"1520.530844337 138.230076758\n",
"706.858347058 94.2477796077\n",
"254.469004941 -56.5486677646\n",
"254.469004941 56.5486677646\n",
"1017.876019763 -113.097335529\n",
"1017.876019763 113.097335529\n",
"3631.681107549 -213.628300444\n",
"804.247719319 -100.530964915\n",
"9160.884177866 -339.292006588\n",
"2123.716633826 -163.362817987\n",
"2290.221044466 169.646003294\n",
"7238.229473869 -301.592894745\n",
"2827.433388230 188.495559215\n",
"11309.733552920 -376.991118431\n",
"2123.716633826 163.362817987\n",
"14526.724430196 -427.256600888\n",
"6082.123377348 276.460153516\n",
"22167.077763724 -527.787565803\n",
"12468.981242095 395.840674352\n",
"40114.996593678 -709.999939711\n",
"22698.006922181 534.07075111\n",
"27759.112687112 -590.619418875\n",
"1134.114947946 -119.380520836\n",
"3421.194399758 -207.345115137\n",
"2290.221044466 -169.646003294\n",
"11689.866264005 -383.274303738\n",
"8171.282491985 -320.442450666\n",
"40828.138126043 -716.283125018\n",
"2463.008640414 -175.929188601\n",
"23778.714795015 -546.637121724\n",
"1661.902513749 -144.513262065\n",
"32047.386659261 -634.601716025\n",
"2642.079421668 -182.212373908\n",
"24328.493509393 -552.920307032\n",
"4071.504079051 -226.194671058\n",
"8824.733763932 -333.00882128\n",
"13684.777599034 -414.690230274\n",
"1256.637061436 -125.663706144\n",
"5026.548245742 -251.327412287\n",
"1385.442360233 -131.946891451\n",
"14102.609421961 -420.973415581\n",
"7542.963961267 307.876080052\n",
"27171.634860891 -584.336233568\n",
"3216.990877275 -201.06192983\n",
"12867.963509101 -402.123859659\n",
"4536.459791783 -238.761041673\n",
"18626.502843129 -483.805268653\n",
"13273.228961414 -408.407044967\n",
"4071.504079051 226.194671058\n",
"32685.129967940 -640.884901332\n",
"3019.070540099 194.778744523\n",
"48305.128641584 -779.11497809\n",
"8824.733763932 333.00882128\n",
"138544.236023275 -1319.46891451\n",
"22167.077763724 527.787565803\n",
"145220.120412152 -1350.88484104\n",
"15836.768566742 446.10615681\n"
]
}
| 6AIZU
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Write a program which calculates the area and circumference of a circle for given radius r.
Constraints
* 0 < r < 10000
Input
A real number r is given.
Output
Print the area and circumference of the circle in a line. Put a single space between them. The output should not contain an absolute error greater than 10-5.
Examples
Input
2
Output
12.566371 12.566371
Input
3
Output
28.274334 18.849556
### Input:
2
### Output:
12.566371 12.566371
### Input:
3
### Output:
28.274334 18.849556
### Code:
pi=3.141592653589
r=float(input())
print(f'{r*r*pi:7f} {2*r*pi}')
|
1003_B. Binary String Constructing_10454
|
You are given three integers a, b and x. Your task is to construct a binary string s of length n = a + b such that there are exactly a zeroes, exactly b ones and exactly x indices i (where 1 ≤ i < n) such that s_i ≠ s_{i + 1}. It is guaranteed that the answer always exists.
For example, for the string "01010" there are four indices i such that 1 ≤ i < n and s_i ≠ s_{i + 1} (i = 1, 2, 3, 4). For the string "111001" there are two such indices i (i = 3, 5).
Recall that binary string is a non-empty sequence of characters where each character is either 0 or 1.
Input
The first line of the input contains three integers a, b and x (1 ≤ a, b ≤ 100, 1 ≤ x < a + b).
Output
Print only one string s, where s is any binary string satisfying conditions described above. It is guaranteed that the answer always exists.
Examples
Input
2 2 1
Output
1100
Input
3 3 3
Output
101100
Input
5 3 6
Output
01010100
Note
All possible answers for the first example:
* 1100;
* 0011.
All possible answers for the second example:
* 110100;
* 101100;
* 110010;
* 100110;
* 011001;
* 001101;
* 010011;
* 001011.
|
a,b,x=map(int,input().split())
x+=1
y=x//2
c=0
if x%2:
if a>b:
a-=1;c=1
else:
b-=1;c=2
s=(a-y)*'0'+y*'01'+(b-y)*'1'
if c:s=s+'0'if c==1 else '1'+s
print(s)
|
{
"input": [
"5 3 6\n",
"2 2 1\n",
"3 3 3\n",
"3 2 1\n",
"2 1 2\n",
"2 3 3\n",
"10 40 1\n",
"91 87 11\n",
"7 99 14\n",
"67 81 40\n",
"30 34 44\n",
"7 8 7\n",
"55 56 110\n",
"83 83 83\n",
"100 1 2\n",
"6 84 12\n",
"50 47 18\n",
"15 26 24\n",
"100 100 100\n",
"1 1 1\n",
"99 41 17\n",
"1 100 1\n",
"73 61 122\n",
"2 2 2\n",
"3 4 6\n",
"5 4 2\n",
"2 15 4\n",
"3 2 4\n",
"66 11 22\n",
"2 3 4\n",
"3 5 6\n",
"9 89 18\n",
"100 100 199\n",
"5 6 2\n",
"1 100 2\n",
"4 9 6\n",
"10 6 10\n",
"3 3 2\n",
"78 67 117\n",
"100 99 100\n",
"100 1 1\n",
"12 74 22\n",
"52 12 17\n",
"0 2 1\n",
"3 2 2\n",
"2 3 1\n",
"10 29 1\n",
"91 87 15\n",
"67 131 40\n",
"7 8 9\n",
"83 137 83\n",
"7 84 12\n",
"67 47 18\n",
"100 100 110\n",
"81 41 17\n",
"0 100 1\n",
"2 4 2\n",
"6 4 6\n",
"5 4 1\n",
"2 15 2\n",
"3 2 5\n",
"66 11 5\n",
"1 110 2\n",
"10 9 10\n",
"1 3 2\n",
"78 94 117\n",
"100 150 100\n",
"100 2 1\n",
"52 16 17\n",
"3 1 3\n",
"1 2 1\n",
"3 5 2\n",
"2 3 2\n",
"10 29 2\n",
"129 87 15\n",
"44 131 40\n",
"7 8 12\n",
"83 137 11\n",
"7 146 12\n",
"67 80 18\n",
"110 100 110\n",
"81 41 29\n",
"4 4 2\n",
"5 0 1\n",
"2 15 1\n",
"66 11 9\n",
"1 2 2\n",
"100 3 1\n",
"56 16 17\n",
"2 1 3\n",
"10 55 2\n",
"129 87 9\n",
"80 131 40\n",
"7 9 12\n",
"83 137 18\n",
"7 280 12\n",
"67 113 18\n",
"110 100 100\n",
"81 44 29\n",
"5 1 1\n",
"3 15 1\n",
"66 11 2\n",
"100 4 1\n",
"15 16 17\n",
"4 1 3\n",
"10 55 1\n",
"228 87 9\n",
"80 242 40\n",
"11 9 12\n",
"83 137 35\n",
"67 152 18\n",
"110 110 100\n",
"81 48 29\n",
"9 1 1\n"
],
"output": [
"01010100\n",
"1100\n",
"101100\n",
"00011",
"010",
"10110\n",
"11111111111111111111111111111111111111110000000000",
"0101010101000000000000000000000000000000000000000000000000000000000000000000000000000000000000001111111111111111111111111111111111111111111111111111111111111111111111111111111111\n",
"1010101010101011111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111\n",
"1010101010101010101010101010101010101010000000000000000000000000000000000000000000000001111111111111111111111111111111111111111111111111111111111111\n",
"1010101010101010101010101010101010101010101000000000111111111111\n",
"101010111110000\n",
"101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101",
"1010101010101010101010101010101010101010101010101010101010101010101010101010101010111111111111111111111111111111111111111111000000000000000000000000000000000000000000\n",
"01000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\n",
"101010101010111111111111111111111111111111111111111111111111111111111111111111111111111111\n",
"0101010101010101011111111111111111111111111111111111111100000000000000000000000000000000000000000\n",
"10101010101010101010101000011111111111111\n",
"10101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010100000000000000000000000000000000000000000000000000011111111111111111111111111111111111111111111111111\n",
"10\n",
"01010101010101010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000111111111111111111111111111111111\n",
"11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111110",
"01010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101000000000000\n",
"1001\n",
"1010101",
"011110000\n",
"10101111111111111\n",
"01010",
"01010101010101010101010000000000000000000000000000000000000000000000000000000\n",
"10101",
"10101011\n",
"10101010101010101011111111111111111111111111111111111111111111111111111111111111111111111111111111\n",
"10101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010\n",
"10000011111\n",
"10111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111\n",
"1010100111111\n",
"0101010101100000\n",
"100011\n",
"0101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010100000000000000000000111111111\n",
"0101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101111111111111111111111111111111111111111111111111100000000000000000000000000000000000000000000000000\n",
"00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
"10101010101010101010100111111111111111111111111111111111111111111111111111111111111111\n",
"0101010101010101000000000000000000000000000000000000000000001111\n",
"11\n",
"01100\n",
"11100\n",
"111111111111111111111111111110000000000\n",
"0101010101010100000000000000000000000000000000000000000000000000000000000000000000000000000000000011111111111111111111111111111111111111111111111111111111111111111111111111111111\n",
"101010101010101010101010101010101010101000000000000000000000000000000000000000000000000111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111\n",
"101010101111000\n",
"1010101010101010101010101010101010101010101010101010101010101010101010101010101010111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111000000000000000000000000000000000000000000\n",
"1010101010100111111111111111111111111111111111111111111111111111111111111111111111111111111\n",
"010101010101010101111111111111111111111111111111111111110000000000000000000000000000000000000000000000000000000000\n",
"10101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010000000000000000000000000000000000000000000000111111111111111111111111111111111111111111111\n",
"01010101010101010000000000000000000000000000000000000000000000000000000000000000000000000111111111111111111111111111111111\n",
"1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111\n",
"100111\n",
"0101011000\n",
"000001111\n",
"10011111111111111\n",
"01010\n",
"01010000000000000000000000000000000000000000000000000000000000000000111111111\n",
"101111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111\n",
"0101010101111100000\n",
"1011\n",
"1010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101011111111111111111111111111111111111100000000000000000000\n",
"1010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010000000000000000000000000000000000000000000000000001111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111\n",
"000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011\n",
"01010101010101010000000000000000000000000000000000000000000011111111\n",
"0100\n",
"110\n",
"10001111\n",
"10011\n",
"100000000001111111111111111111111111111\n",
"010101010101010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011111111111111111111111111111111111111111111111111111111111111111111111111111111\n",
"1010101010101010101010101010101010101010000000000000000000000000111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111\n",
"101010101010011\n",
"1010101010111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111000000000000000000000000000000000000000000000000000000000000000000000000000000\n",
"101010101010011111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111\n",
"101010101010101010000000000000000000000000000000000000000000000000000000000011111111111111111111111111111111111111111111111111111111111111111111111\n",
"010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101011111111111111111111111111111111111111111111110000000000000000000000000000000000000000000000000000000\n",
"01010101010101010101010101010000000000000000000000000000000000000000000000000000000000000000000111111111111111111111111111\n",
"10000111\n",
"00000\n",
"11111111111111100\n",
"01010101000000000000000000000000000000000000000000000000000000000000001111111\n",
"101\n",
"0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000111\n",
"010101010101010100000000000000000000000000000000000000000000000011111111\n",
"010\n",
"10000000000111111111111111111111111111111111111111111111111111111\n",
"010101010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011111111111111111111111111111111111111111111111111111111111111111111111111111111111\n",
"1010101010101010101010101010101010101010000000000000000000000000000000000000000000000000000000000000111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111\n",
"1010101010100111\n",
"1010101010101010100000000000000000000000000000000000000000000000000000000000000000000000000011111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111\n",
"10101010101001111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111\n",
"101010101010101010000000000000000000000000000000000000000000000000000000000011111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111\n",
"010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010111111111111111111111111111111111111111111111111111000000000000000000000000000000000000000000000000000000000000\n",
"01010101010101010101010101010000000000000000000000000000000000000000000000000000000000000000000111111111111111111111111111111\n",
"000001\n",
"111111111111111000\n",
"01111111111100000000000000000000000000000000000000000000000000000000000000000\n",
"00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001111\n",
"1010101010101010111111110000000\n",
"01000\n",
"11111111111111111111111111111111111111111111111111111110000000000\n",
"010101010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011111111111111111111111111111111111111111111111111111111111111111111111111111111111\n",
"1010101010101010101010101010101010101010000000000000000000000000000000000000000000000000000000000000111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111\n",
"01010101010111100000\n",
"1010101010101010101010101010101010111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111000000000000000000000000000000000000000000000000000000000000000000\n",
"101010101010101010000000000000000000000000000000000000000000000000000000000011111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111\n",
"1010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010101010000000000000000000000000000000000000000000000000000000000000111111111111111111111111111111111111111111111111111111111111\n",
"010101010101010101010101010100000000000000000000000000000000000000000000000000000000000000000001111111111111111111111111111111111\n",
"0000000001\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You are given three integers a, b and x. Your task is to construct a binary string s of length n = a + b such that there are exactly a zeroes, exactly b ones and exactly x indices i (where 1 ≤ i < n) such that s_i ≠ s_{i + 1}. It is guaranteed that the answer always exists.
For example, for the string "01010" there are four indices i such that 1 ≤ i < n and s_i ≠ s_{i + 1} (i = 1, 2, 3, 4). For the string "111001" there are two such indices i (i = 3, 5).
Recall that binary string is a non-empty sequence of characters where each character is either 0 or 1.
Input
The first line of the input contains three integers a, b and x (1 ≤ a, b ≤ 100, 1 ≤ x < a + b).
Output
Print only one string s, where s is any binary string satisfying conditions described above. It is guaranteed that the answer always exists.
Examples
Input
2 2 1
Output
1100
Input
3 3 3
Output
101100
Input
5 3 6
Output
01010100
Note
All possible answers for the first example:
* 1100;
* 0011.
All possible answers for the second example:
* 110100;
* 101100;
* 110010;
* 100110;
* 011001;
* 001101;
* 010011;
* 001011.
### Input:
5 3 6
### Output:
01010100
### Input:
2 2 1
### Output:
1100
### Code:
a,b,x=map(int,input().split())
x+=1
y=x//2
c=0
if x%2:
if a>b:
a-=1;c=1
else:
b-=1;c=2
s=(a-y)*'0'+y*'01'+(b-y)*'1'
if c:s=s+'0'if c==1 else '1'+s
print(s)
|
1027_C. Minimum Value Rectangle_10458
|
You have n sticks of the given lengths.
Your task is to choose exactly four of them in such a way that they can form a rectangle. No sticks can be cut to pieces, each side of the rectangle must be formed by a single stick. No stick can be chosen multiple times. It is guaranteed that it is always possible to choose such sticks.
Let S be the area of the rectangle and P be the perimeter of the rectangle.
The chosen rectangle should have the value (P^2)/(S) minimal possible. The value is taken without any rounding.
If there are multiple answers, print any of them.
Each testcase contains several lists of sticks, for each of them you are required to solve the problem separately.
Input
The first line contains a single integer T (T ≥ 1) — the number of lists of sticks in the testcase.
Then 2T lines follow — lines (2i - 1) and 2i of them describe the i-th list. The first line of the pair contains a single integer n (4 ≤ n ≤ 10^6) — the number of sticks in the i-th list. The second line of the pair contains n integers a_1, a_2, ..., a_n (1 ≤ a_j ≤ 10^4) — lengths of the sticks in the i-th list.
It is guaranteed that for each list there exists a way to choose four sticks so that they form a rectangle.
The total number of sticks in all T lists doesn't exceed 10^6 in each testcase.
Output
Print T lines. The i-th line should contain the answer to the i-th list of the input. That is the lengths of the four sticks you choose from the i-th list, so that they form a rectangle and the value (P^2)/(S) of this rectangle is minimal possible. You can print these four lengths in arbitrary order.
If there are multiple answers, print any of them.
Example
Input
3
4
7 2 2 7
8
2 8 1 4 8 2 1 5
5
5 5 5 5 5
Output
2 7 7 2
2 2 1 1
5 5 5 5
Note
There is only one way to choose four sticks in the first list, they form a rectangle with sides 2 and 7, its area is 2 ⋅ 7 = 14, perimeter is 2(2 + 7) = 18. (18^2)/(14) ≈ 23.143.
The second list contains subsets of four sticks that can form rectangles with sides (1, 2), (2, 8) and (1, 8). Their values are (6^2)/(2) = 18, (20^2)/(16) = 25 and (18^2)/(8) = 40.5, respectively. The minimal one of them is the rectangle (1, 2).
You can choose any four of the 5 given sticks from the third list, they will form a square with side 5, which is still a rectangle with sides (5, 5).
|
super_ans = []
for i in range(int(input())):
n = input()
if n == '4':
super_ans.append(input())
continue
elif n == '5':
a = sorted(map(int, input().split()))
if a[0] == a[1] and a[2] == a[3]:
super_ans.append(' '.join([str(a[0]), str(a[0]), str(a[2]), str(a[2])]))
elif a[0] == a[1] and a[3] == a[4]:
super_ans.append(' '.join([str(a[0]), str(a[0]), str(a[3]), str(a[3])]))
else:
super_ans.append(' '.join([str(a[-1]), str(a[-1]), str(a[-3]), str(a[-3])]))
continue
d = 10 ** 9
t = tc = x = y = a1 = a2 = 0
for ai in sorted(map(int, input().split())):
if t == ai:
tc += 1
if tc == 2:
x = y
y = ai
if x and y / x < d:
d = y / x
a1, a2 = x, y
elif tc == 4:
a1 = a2 = t
break
else:
t = ai
tc = 1
super_ans.append(' '.join([str(a1), str(a1), str(a2), str(a2)]))
print('\n'.join(super_ans))
|
{
"input": [
"3\n4\n7 2 2 7\n8\n2 8 1 4 8 2 1 5\n5\n5 5 5 5 5\n",
"3\n4\n7 2 2 7\n8\n2 8 1 4 8 2 1 5\n5\n5 5 5 5 5\n",
"1\n4\n1 1 10000 10000\n",
"10\n9\n10 11 11 2 10 2 18 10 18\n6\n14 14 14 14 6 6\n11\n9 7 9 20 7 7 9 9 20 7 12\n7\n15 16 15 15 15 16 15\n17\n7 18 7 15 15 2 18 7 20 19 19 19 20 2 7 19 19\n5\n3 1 6 1 3\n8\n19 12 18 12 12 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n16 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n20\n10 14 10 14 10 7 10 10 14 10 7 9 10 8 14 10 10 8 14 9\n12\n7 2 2 2 2 16 16 7 18 17 17 18\n5\n7 13 17 13 7\n6\n10 10 9 9 10 10\n6\n17 19 17 19 14 14\n10\n10 13 5 18 13 13 13 10 18 5\n11\n3 4 16 4 4 3 4 13 4 16 13\n7\n17 19 1 17 17 1 19\n5\n17 17 19 17 19\n9\n13 15 13 18 13 18 13 15 13\n",
"1\n6\n9998 9998 9999 9999 10000 10000\n",
"10\n5\n10 4 10 4 4\n4\n7 14 14 7\n6\n13 3 13 3 5 5\n5\n8 6 8 17 6\n6\n6 13 6 6 6 13\n7\n12 11 5 5 11 12 12\n16\n5 12 2 5 2 5 8 5 8 2 2 8 12 5 2 8\n17\n3 9 9 1 1 1 1 15 15 1 1 1 1 1 1 3 1\n12\n9 10 13 11 13 14 13 13 11 10 14 9\n4\n15 17 17 15\n",
"3\n4\n7 2 2 7\n8\n2 8 1 4 8 1 1 5\n5\n5 5 5 5 5\n",
"10\n9\n10 11 11 2 10 2 18 10 18\n6\n14 14 14 14 6 6\n11\n9 7 9 20 7 7 9 9 20 7 12\n7\n15 16 15 15 15 16 15\n17\n7 18 7 15 15 2 18 7 20 19 19 19 20 2 7 19 19\n5\n3 1 6 1 3\n8\n13 12 18 12 12 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n16 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n20\n10 14 10 14 10 7 10 10 14 10 7 9 10 8 14 10 10 8 14 9\n12\n7 2 2 2 2 16 16 7 18 17 17 18\n5\n7 13 17 13 7\n6\n10 10 9 9 11 10\n6\n17 19 17 19 14 14\n10\n10 13 5 18 13 13 13 10 18 5\n11\n3 4 16 4 4 3 4 13 4 16 13\n7\n17 19 1 17 17 1 19\n5\n17 17 19 17 19\n9\n13 15 13 18 13 18 13 15 13\n",
"1\n6\n9998 9998 9999 9999 10100 10000\n",
"10\n5\n10 4 10 4 4\n4\n7 14 14 7\n6\n13 3 13 3 5 5\n5\n8 6 8 17 6\n6\n6 12 6 6 6 13\n7\n12 11 5 5 11 12 12\n16\n5 12 2 5 2 5 8 5 8 2 2 8 12 5 2 8\n17\n3 9 9 1 1 1 1 15 15 1 1 1 1 1 1 3 1\n12\n9 10 13 11 13 14 13 13 11 10 14 9\n4\n15 17 17 15\n",
"10\n9\n10 11 11 2 10 2 18 10 18\n6\n14 14 14 14 6 6\n11\n9 7 9 20 7 7 9 9 20 7 12\n7\n15 16 15 15 15 16 15\n17\n7 18 7 15 15 2 18 7 20 19 19 19 20 2 7 19 19\n5\n3 1 6 1 3\n8\n13 12 18 12 15 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n16 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n5\n10 4 10 4 4\n4\n7 14 14 7\n6\n13 3 13 3 5 5\n5\n8 6 8 17 6\n6\n6 12 6 6 6 13\n7\n12 11 5 5 11 12 12\n16\n5 12 2 5 2 5 8 5 8 2 2 8 12 5 2 8\n17\n3 9 9 1 1 1 1 15 15 1 1 1 1 1 1 3 1\n12\n9 10 13 11 13 14 16 13 11 10 14 9\n4\n15 17 17 15\n",
"10\n20\n10 14 10 14 10 7 10 10 14 10 7 9 10 8 14 10 10 8 14 15\n12\n7 2 2 2 2 16 16 7 18 17 17 18\n5\n7 13 17 13 7\n6\n10 10 9 9 10 10\n6\n17 19 17 19 14 14\n10\n10 13 5 18 13 13 13 10 18 5\n11\n3 4 16 4 4 3 4 13 4 16 13\n7\n17 19 1 17 17 1 19\n5\n17 17 19 17 19\n9\n13 15 13 18 13 18 13 15 13\n",
"3\n4\n7 2 2 7\n8\n2 8 1 2 8 1 1 5\n5\n5 5 6 5 5\n",
"10\n9\n10 11 11 2 10 2 18 10 18\n6\n14 14 14 14 6 6\n11\n5 7 9 20 7 7 9 9 20 9 12\n7\n15 16 15 15 15 16 15\n17\n7 18 7 15 15 2 18 7 20 19 32 19 20 2 7 19 19\n5\n3 1 6 1 3\n8\n13 12 18 12 15 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n16 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n9\n10 11 11 2 10 2 18 10 18\n6\n14 14 14 14 6 6\n11\n5 7 9 20 7 7 9 9 20 7 12\n7\n15 16 15 15 28 16 15\n17\n7 18 7 15 15 2 18 7 20 19 32 19 20 2 11 19 19\n5\n3 1 6 1 3\n8\n13 12 18 12 15 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n32 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n9\n10 11 11 3 10 2 18 10 18\n6\n14 14 14 14 6 6\n11\n12 7 9 20 7 7 9 9 20 7 12\n7\n15 16 15 15 15 16 15\n17\n7 18 7 15 15 2 18 7 20 19 19 19 20 2 7 19 19\n5\n3 1 6 1 3\n8\n19 12 18 12 16 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n16 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n9\n10 11 11 3 10 2 18 10 18\n6\n14 24 14 14 6 6\n11\n12 7 9 20 7 7 9 9 20 7 12\n7\n15 16 15 15 15 14 15\n17\n7 18 7 15 15 2 18 7 20 19 19 19 20 2 7 19 19\n5\n3 1 2 1 3\n8\n19 12 18 12 16 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n16 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n9\n10 11 11 2 10 2 18 10 18\n6\n14 14 14 14 6 6\n11\n9 7 9 20 7 7 9 9 22 7 12\n7\n15 16 15 15 9 16 15\n17\n7 18 13 9 15 2 18 7 20 19 19 19 20 2 7 19 19\n5\n3 1 6 1 3\n8\n13 12 18 8 15 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 22 11\n5\n16 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n9\n10 11 11 3 10 2 18 10 18\n6\n14 24 14 14 6 6\n11\n12 7 9 20 7 7 9 9 20 2 12\n7\n15 16 15 15 15 14 15\n17\n7 18 7 15 15 2 18 7 20 19 19 19 20 2 7 19 19\n5\n3 1 2 1 3\n8\n19 12 18 12 16 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n16 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"1\n6\n9998 9998 9999 6517 10000 10000\n",
"10\n9\n10 11 11 2 10 2 18 10 18\n6\n14 14 14 14 6 6\n11\n9 7 9 20 7 11 9 9 20 7 12\n7\n15 16 15 15 15 16 15\n17\n7 18 7 15 15 2 18 7 20 19 19 19 20 2 7 19 19\n5\n3 1 6 1 3\n8\n13 12 18 12 12 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n16 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n9\n10 11 11 2 10 2 18 10 18\n6\n14 14 14 11 6 6\n11\n9 7 9 20 7 7 9 9 20 7 12\n7\n15 16 15 15 15 16 15\n17\n7 18 7 15 15 2 18 7 20 19 19 19 20 2 7 19 19\n5\n3 1 6 1 3\n8\n13 12 18 12 15 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n16 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n5\n10 4 10 4 4\n4\n7 14 14 7\n6\n13 3 13 3 5 5\n5\n8 6 8 17 6\n6\n6 13 6 2 6 13\n7\n12 11 5 5 11 12 12\n16\n5 12 2 5 2 5 8 5 8 2 2 8 12 5 2 8\n17\n3 9 9 1 1 1 1 15 15 1 1 1 1 1 1 3 1\n12\n9 10 13 11 13 14 6 13 11 10 14 9\n4\n15 17 17 15\n",
"10\n9\n10 11 11 2 10 2 18 10 18\n6\n1 14 14 14 6 6\n11\n5 7 9 20 7 7 9 9 20 9 12\n7\n15 16 15 15 15 16 15\n17\n7 18 7 15 15 2 18 7 20 19 32 19 20 2 7 19 19\n5\n3 1 6 1 3\n8\n13 12 18 12 15 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n16 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n9\n10 11 11 2 10 2 18 10 18\n6\n14 14 14 14 6 6\n11\n5 7 9 20 7 7 9 9 20 7 12\n7\n15 16 15 15 28 16 15\n17\n7 18 7 15 15 2 18 7 20 19 32 19 20 2 11 19 19\n5\n3 1 6 1 3\n8\n13 13 18 12 15 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n32 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n9\n10 11 11 3 10 2 18 10 18\n6\n14 14 14 14 6 6\n11\n12 7 9 20 7 7 9 9 20 7 12\n7\n15 16 15 15 15 16 15\n17\n7 18 7 15 15 2 18 7 20 19 19 19 20 2 7 19 19\n5\n3 1 6 1 3\n8\n19 12 18 12 12 18 19 12\n13\n11 19 15 7 20 6 7 20 19 7 15 11 11\n5\n16 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n9\n10 11 11 2 10 2 18 10 18\n6\n14 14 14 14 6 6\n11\n9 7 9 20 7 7 9 9 22 7 12\n7\n15 16 15 15 15 16 15\n17\n7 18 7 9 15 2 18 7 20 19 19 19 20 2 7 19 19\n5\n3 1 6 1 3\n8\n13 12 18 8 15 18 19 12\n13\n19 19 15 7 20 11 7 20 19 7 15 11 11\n5\n16 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n9\n10 11 11 2 10 2 18 10 18\n6\n14 14 14 14 6 6\n11\n9 7 11 20 7 11 9 9 20 7 12\n7\n15 16 15 15 15 16 15\n17\n7 18 7 15 15 2 18 7 20 19 19 19 20 2 7 19 19\n5\n3 1 6 1 3\n8\n13 12 18 12 12 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n16 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n9\n10 11 11 2 10 2 18 10 18\n6\n14 14 14 11 6 6\n11\n9 7 9 20 7 7 9 9 20 7 12\n7\n15 16 15 15 15 16 15\n17\n7 18 7 15 15 2 18 7 20 19 19 19 20 2 7 19 19\n5\n3 1 6 1 3\n8\n13 12 18 12 15 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n16 3 3 14 14\n7\n4 8 8 1 1 13 2\n",
"10\n9\n10 11 11 3 10 2 18 10 18\n6\n9 14 14 14 6 6\n11\n9 7 9 20 7 7 9 9 20 7 12\n7\n15 16 15 15 10 16 15\n17\n7 18 7 15 15 2 18 7 20 19 19 19 20 2 7 19 19\n5\n3 1 6 1 3\n8\n19 12 18 12 12 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n16 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n9\n10 11 11 2 10 2 18 10 18\n6\n1 14 14 14 6 6\n11\n5 7 9 20 7 7 9 9 20 9 12\n7\n15 16 15 15 15 16 15\n17\n7 18 7 15 15 2 18 7 20 19 32 19 20 2 7 19 19\n5\n3 1 6 1 3\n8\n13 12 18 12 15 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n16 3 3 14 14\n7\n2 8 8 1 1 13 4\n",
"3\n4\n7 2 2 7\n8\n3 8 1 4 8 2 1 5\n5\n5 5 5 5 5\n",
"3\n4\n7 2 2 7\n8\n2 8 1 4 8 1 1 5\n5\n5 5 6 5 5\n",
"3\n4\n7 2 2 7\n8\n2 8 1 8 8 1 1 5\n5\n5 5 6 5 5\n",
"10\n9\n10 11 11 2 10 2 18 10 18\n6\n14 14 14 14 6 6\n11\n5 7 9 20 7 7 9 9 20 7 12\n7\n15 16 15 15 15 16 15\n17\n7 18 7 15 15 2 18 7 20 19 19 19 20 2 7 19 19\n5\n3 1 6 1 3\n8\n13 12 18 12 15 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n16 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n5\n10 4 10 4 4\n4\n7 14 14 7\n6\n13 3 13 3 5 5\n5\n8 6 8 17 6\n6\n6 12 6 6 6 13\n7\n12 11 5 5 11 12 12\n16\n5 12 2 5 2 5 8 5 8 2 2 8 12 5 2 8\n17\n3 9 9 1 1 1 1 15 15 1 1 1 1 1 1 3 1\n12\n9 10 13 11 13 14 16 16 11 10 14 9\n4\n15 17 17 15\n",
"10\n9\n10 11 11 2 10 2 18 10 18\n6\n14 14 14 14 6 6\n11\n5 7 9 20 7 7 9 9 20 7 12\n7\n15 16 15 15 15 16 15\n17\n7 18 7 15 15 2 18 7 20 19 32 19 20 2 7 19 19\n5\n3 1 6 1 3\n8\n13 12 18 12 15 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n16 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n9\n10 11 11 2 10 2 18 10 18\n6\n14 14 14 14 6 6\n11\n5 7 9 20 7 7 9 9 20 7 12\n7\n15 16 15 15 15 16 15\n17\n7 18 7 15 15 2 18 7 20 19 32 19 20 2 7 19 19\n5\n3 1 6 1 3\n8\n13 12 18 12 15 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n32 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n9\n10 11 11 2 10 2 18 10 18\n6\n14 14 14 14 6 6\n11\n5 7 9 20 7 7 9 9 20 7 12\n7\n15 16 15 15 28 16 15\n17\n7 18 7 15 15 2 18 7 20 19 32 19 20 2 7 19 19\n5\n3 1 6 1 3\n8\n13 12 18 12 15 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n32 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n9\n10 11 11 3 10 2 18 10 18\n6\n14 14 14 14 6 6\n11\n9 7 9 20 7 7 9 9 20 7 12\n7\n15 16 15 15 15 16 15\n17\n7 18 7 15 15 2 18 7 20 19 19 19 20 2 7 19 19\n5\n3 1 6 1 3\n8\n19 12 18 12 12 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n16 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n5\n10 4 10 4 4\n4\n7 14 14 7\n6\n13 3 13 3 5 5\n5\n8 6 8 17 6\n6\n6 13 6 6 6 13\n7\n12 11 5 5 11 12 12\n16\n5 12 2 5 2 5 8 5 8 2 2 8 12 5 2 8\n17\n3 9 9 1 1 1 1 15 15 1 1 1 1 1 1 3 1\n12\n9 10 13 11 13 14 6 13 11 10 14 9\n4\n15 17 17 15\n",
"10\n9\n10 11 11 2 10 2 18 10 18\n6\n14 14 14 14 11 6\n11\n9 7 9 20 7 7 9 9 20 7 12\n7\n15 16 15 15 15 16 15\n17\n7 18 7 15 15 2 18 7 20 19 19 19 20 2 7 19 19\n5\n3 1 6 1 3\n8\n13 12 18 12 12 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n16 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n20\n10 14 10 14 10 7 10 10 14 10 7 9 10 8 14 10 10 8 14 9\n12\n7 2 2 2 2 16 16 7 18 17 17 18\n5\n7 13 17 13 7\n6\n10 10 9 9 11 10\n6\n17 19 17 19 14 14\n10\n10 13 5 18 13 13 13 10 18 5\n11\n3 4 16 4 4 3 4 13 4 12 13\n7\n17 19 1 17 17 1 19\n5\n17 17 19 17 19\n9\n13 15 13 18 13 18 13 15 13\n",
"10\n9\n10 11 11 2 10 2 18 10 18\n6\n14 14 14 14 6 6\n11\n9 7 9 20 7 7 9 9 22 7 12\n7\n15 16 15 15 15 16 15\n17\n7 18 7 15 15 2 18 7 20 19 19 19 20 2 7 19 19\n5\n3 1 6 1 3\n8\n13 12 18 12 15 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n16 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n9\n10 11 11 2 10 2 18 10 18\n6\n14 14 14 14 6 6\n11\n5 7 9 20 7 7 9 9 20 7 12\n7\n16 16 15 15 15 16 15\n17\n7 18 7 15 15 2 18 7 20 19 19 19 20 2 7 19 19\n5\n3 1 6 1 3\n8\n13 12 18 12 15 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n16 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n9\n10 11 11 2 10 2 18 10 18\n6\n14 14 14 14 6 6\n11\n5 7 9 20 7 7 9 9 20 7 12\n7\n15 16 15 4 15 16 15\n17\n7 18 7 15 15 2 18 7 20 19 32 19 20 2 7 19 19\n5\n3 1 6 1 3\n8\n13 12 18 12 15 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n32 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n9\n10 11 11 3 10 2 18 10 18\n6\n14 14 14 14 6 6\n11\n12 7 9 20 7 7 9 9 20 7 12\n7\n15 16 15 15 15 16 15\n17\n7 18 7 15 15 2 18 7 20 19 19 19 20 2 7 19 19\n5\n3 1 6 1 3\n8\n19 12 18 12 12 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n16 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n9\n10 11 11 2 10 2 18 10 18\n6\n14 14 14 14 11 6\n11\n9 7 9 20 7 7 9 9 20 7 12\n7\n23 16 15 15 15 16 15\n17\n7 18 7 15 15 2 18 7 20 19 19 19 20 2 7 19 19\n5\n3 1 6 1 3\n8\n13 12 18 12 12 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n16 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n9\n10 11 11 2 10 2 18 10 18\n6\n14 14 14 14 6 6\n11\n9 7 9 20 7 7 9 9 22 7 12\n7\n15 16 15 15 15 16 15\n17\n7 18 7 9 15 2 18 7 20 19 19 19 20 2 7 19 19\n5\n3 1 6 1 3\n8\n13 12 18 12 15 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n16 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n9\n10 11 11 2 10 2 18 10 18\n6\n14 14 14 14 6 6\n11\n5 7 9 20 7 7 9 9 20 9 12\n7\n15 16 15 15 15 16 15\n17\n7 18 7 15 2 2 18 7 20 19 32 19 20 2 7 19 19\n5\n3 1 6 1 3\n8\n13 12 18 12 15 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n16 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n9\n10 11 11 2 10 2 18 10 18\n6\n14 14 14 14 6 6\n11\n5 7 9 20 7 7 9 9 20 7 12\n7\n15 16 15 15 17 16 15\n17\n7 18 7 15 15 2 18 7 20 19 32 19 20 2 11 19 19\n5\n3 1 6 1 3\n8\n13 12 18 12 15 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n32 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n9\n10 11 11 2 10 2 18 10 18\n6\n14 14 14 14 6 6\n11\n9 7 9 20 7 7 9 9 22 7 12\n7\n15 16 15 15 15 16 15\n17\n7 18 7 9 15 2 18 7 20 19 19 19 20 2 7 19 19\n5\n3 1 6 1 3\n8\n13 12 18 8 15 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n16 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n9\n10 11 11 2 10 2 18 10 18\n6\n14 14 14 14 6 6\n11\n5 7 9 20 7 7 9 9 20 7 12\n7\n15 21 15 15 17 16 15\n17\n7 18 7 15 15 2 18 7 20 19 32 19 20 2 11 19 19\n5\n3 1 6 1 3\n8\n13 12 18 12 15 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n32 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n9\n10 11 11 3 10 2 18 10 18\n6\n14 14 14 14 6 6\n11\n12 7 9 20 7 7 9 9 20 7 12\n7\n15 16 15 15 15 14 15\n17\n7 18 7 15 15 2 18 7 20 19 19 19 20 2 7 19 19\n5\n3 1 6 1 3\n8\n19 12 18 12 16 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n16 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n9\n10 11 11 2 10 2 18 10 18\n6\n14 14 14 14 6 6\n11\n9 7 9 20 7 7 9 9 22 7 12\n7\n15 16 15 15 9 16 15\n17\n7 18 7 9 15 2 18 7 20 19 19 19 20 2 7 19 19\n5\n3 1 6 1 3\n8\n13 12 18 8 15 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n16 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n9\n10 11 11 2 10 2 18 10 18\n6\n14 14 14 14 6 6\n11\n5 7 9 20 7 7 9 9 20 7 12\n7\n15 21 15 15 17 16 15\n17\n7 18 7 1 15 2 18 7 20 19 32 19 20 2 11 19 19\n5\n3 1 6 1 3\n8\n13 12 18 12 15 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n32 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n9\n10 11 11 3 10 2 18 10 18\n6\n14 14 14 14 6 6\n11\n12 7 9 20 7 7 9 9 20 7 12\n7\n15 16 15 15 15 14 15\n17\n7 18 7 15 15 2 18 7 20 19 19 19 20 2 7 19 19\n5\n3 1 2 1 3\n8\n19 12 18 12 16 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n16 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n9\n10 11 11 2 10 2 18 10 18\n6\n14 14 14 14 6 6\n11\n9 7 9 20 7 7 9 9 22 7 12\n7\n15 16 15 15 9 16 15\n17\n7 18 13 9 15 2 18 7 20 19 19 19 20 2 7 19 19\n5\n3 1 6 1 3\n8\n13 12 18 8 15 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n16 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n9\n10 11 11 3 10 2 18 10 18\n6\n14 24 14 14 6 6\n11\n12 7 9 20 7 7 9 9 20 2 12\n7\n15 16 15 15 15 14 15\n17\n7 18 7 15 15 2 18 7 20 19 19 19 20 2 7 1 19\n5\n3 1 2 1 3\n8\n19 12 18 12 16 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n16 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n20\n10 14 10 14 10 7 10 10 14 10 7 9 10 8 14 10 10 8 14 6\n12\n7 2 2 2 2 16 16 7 18 17 17 18\n5\n7 13 17 13 7\n6\n10 10 9 9 10 10\n6\n17 19 17 19 14 14\n10\n10 13 5 18 13 13 13 10 18 5\n11\n3 4 16 4 4 3 4 13 4 16 13\n7\n17 19 1 17 17 1 19\n5\n17 17 19 17 19\n9\n13 15 13 18 13 18 13 15 13\n",
"10\n5\n10 4 10 4 4\n4\n7 14 14 7\n6\n13 3 13 3 5 5\n5\n8 6 8 17 6\n6\n6 13 6 6 6 13\n7\n12 11 5 5 11 12 12\n16\n5 12 2 5 2 5 8 5 8 2 2 8 12 5 2 8\n17\n3 9 9 1 1 1 1 15 15 1 1 1 1 1 1 3 1\n12\n9 10 13 17 13 14 13 13 11 10 14 9\n4\n15 17 17 15\n",
"3\n4\n7 2 2 7\n8\n2 8 1 4 8 2 1 5\n5\n4 5 5 5 5\n",
"3\n4\n7 2 2 7\n8\n2 8 1 4 8 1 1 5\n5\n5 5 5 8 5\n",
"10\n20\n10 14 10 14 10 7 10 10 14 10 7 9 10 8 14 10 10 8 14 9\n12\n7 2 2 2 2 16 16 7 18 17 17 18\n5\n7 13 17 13 7\n6\n10 10 9 9 11 10\n6\n17 19 17 19 14 14\n10\n10 13 5 18 13 13 13 10 18 5\n11\n3 4 16 4 4 3 4 13 4 16 13\n7\n17 19 1 17 17 1 19\n5\n17 17 19 8 19\n9\n13 15 13 18 13 18 13 15 13\n",
"3\n4\n7 2 2 7\n8\n3 8 1 4 8 2 1 5\n5\n5 1 5 5 5\n",
"10\n5\n10 4 10 4 4\n4\n7 14 14 7\n6\n13 3 13 3 5 5\n5\n8 6 8 17 6\n6\n6 12 6 6 6 13\n7\n12 11 5 5 11 12 12\n16\n5 12 1 5 2 5 8 5 8 2 2 8 12 5 2 8\n17\n3 9 9 1 1 1 1 15 15 1 1 1 1 1 1 3 1\n12\n9 10 13 11 13 14 16 13 11 10 14 9\n4\n15 17 17 15\n",
"10\n9\n10 11 11 2 10 2 18 10 18\n6\n14 14 14 14 6 6\n11\n5 7 9 20 7 7 9 9 20 7 12\n7\n15 16 15 15 15 16 15\n17\n7 18 7 15 15 2 18 7 20 19 32 19 20 2 7 14 19\n5\n3 1 6 1 3\n8\n13 12 18 12 15 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n16 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n9\n10 11 11 2 10 2 18 10 18\n6\n14 14 14 14 6 6\n11\n5 7 9 20 7 7 9 9 20 7 12\n7\n15 16 15 15 15 16 15\n17\n7 18 7 15 15 2 18 7 20 19 32 19 20 2 7 19 19\n5\n3 1 6 1 3\n8\n13 12 18 12 15 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n17 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n9\n10 11 11 2 10 2 18 10 29\n6\n14 14 14 14 6 6\n11\n5 7 9 20 7 7 9 9 20 7 12\n7\n15 16 15 15 28 16 15\n17\n7 18 7 15 15 2 18 7 20 19 32 19 20 2 7 19 19\n5\n3 1 6 1 3\n8\n13 12 18 12 15 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n32 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n9\n10 11 11 3 10 2 18 10 18\n6\n14 14 14 14 6 6\n11\n9 7 9 20 7 7 9 9 20 7 12\n7\n15 16 15 15 10 16 15\n17\n7 18 7 15 15 2 18 7 20 19 19 19 20 2 7 19 19\n5\n3 1 6 1 3\n8\n19 12 18 12 12 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n16 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n20\n10 14 10 14 10 7 10 10 14 10 7 9 10 8 14 10 10 8 14 27\n12\n7 2 2 2 2 16 16 7 18 17 17 18\n5\n7 13 17 13 7\n6\n10 10 9 9 10 10\n6\n17 19 17 19 14 14\n10\n10 13 5 18 13 13 13 10 18 5\n11\n3 4 16 4 4 3 4 13 4 16 13\n7\n17 19 1 17 17 1 19\n5\n17 17 19 17 19\n9\n13 15 13 18 13 18 13 15 13\n",
"10\n9\n10 11 11 2 10 2 18 10 18\n6\n14 14 14 14 11 6\n11\n9 7 9 20 7 7 9 9 20 7 12\n7\n15 16 15 15 15 16 15\n17\n7 5 7 15 15 2 18 7 20 19 19 19 20 2 7 19 19\n5\n3 1 6 1 3\n8\n13 12 18 12 12 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n16 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n9\n10 11 11 2 10 2 18 10 18\n6\n14 14 14 14 6 6\n11\n5 7 9 20 7 7 9 9 20 7 12\n7\n15 16 15 4 15 16 15\n17\n7 18 7 15 15 2 18 7 20 19 32 19 20 2 7 19 19\n5\n3 1 6 1 3\n8\n13 12 18 12 15 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n32 3 3 14 14\n7\n2 8 8 1 1 2 2\n",
"10\n9\n10 11 11 2 10 3 18 10 18\n6\n14 14 14 14 11 6\n11\n9 7 9 20 7 7 9 9 20 7 12\n7\n23 16 15 15 15 16 15\n17\n7 18 7 15 15 2 18 7 20 19 19 19 20 2 7 19 19\n5\n3 1 6 1 3\n8\n13 12 18 12 12 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n16 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n9\n10 11 11 2 10 2 18 10 18\n6\n14 14 14 14 6 6\n11\n9 7 9 20 7 7 9 9 22 7 12\n7\n15 16 15 15 15 16 15\n17\n7 18 5 9 15 2 18 7 20 19 19 19 20 2 7 19 19\n5\n3 1 6 1 3\n8\n13 12 18 12 15 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n16 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n9\n10 11 11 2 10 2 18 10 18\n6\n14 14 14 14 6 6\n11\n5 7 9 20 7 7 9 9 20 9 12\n7\n15 16 15 15 15 16 29\n17\n7 18 7 15 2 2 18 7 20 19 32 19 20 2 7 19 19\n5\n3 1 6 1 3\n8\n13 12 18 12 15 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n16 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n9\n10 11 11 2 10 2 18 10 18\n6\n14 14 14 14 6 6\n11\n3 7 9 20 7 7 9 9 20 7 12\n7\n15 21 15 15 17 16 15\n17\n7 18 7 15 15 2 18 7 20 19 32 19 20 2 11 19 19\n5\n3 1 6 1 3\n8\n13 12 18 12 15 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n32 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n9\n10 11 11 3 10 2 18 10 18\n6\n14 14 14 14 6 6\n11\n12 7 9 20 7 7 14 9 20 7 12\n7\n15 16 15 15 15 14 15\n17\n7 18 7 15 15 2 18 7 20 19 19 19 20 2 7 19 19\n5\n3 1 6 1 3\n8\n19 12 18 12 16 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n16 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n9\n10 11 11 2 10 2 18 10 18\n6\n14 14 14 14 6 6\n11\n9 7 9 20 7 7 9 9 22 7 12\n7\n15 16 15 15 9 16 15\n17\n7 18 7 9 15 2 18 7 20 19 19 19 20 2 7 6 19\n5\n3 1 6 1 3\n8\n13 12 18 8 15 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n16 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n9\n10 11 11 2 10 2 18 10 18\n6\n14 14 14 14 6 6\n11\n5 7 9 20 7 7 9 9 20 7 12\n7\n15 21 15 15 17 16 15\n17\n7 18 7 1 15 2 18 7 20 19 32 19 20 1 11 19 19\n5\n3 1 6 1 3\n8\n13 12 18 12 15 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n32 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n9\n10 11 11 3 10 2 18 10 18\n6\n14 14 14 14 6 6\n11\n12 7 9 20 7 7 9 9 20 7 12\n7\n15 16 15 15 15 14 15\n17\n7 18 7 15 15 2 18 7 20 19 19 19 20 2 7 19 19\n5\n3 1 2 1 3\n8\n19 12 18 12 16 18 19 12\n13\n11 28 15 7 20 11 7 20 19 7 15 11 11\n5\n16 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n9\n10 11 11 2 10 2 18 10 18\n6\n14 14 14 14 6 6\n11\n9 7 9 20 7 7 9 9 22 7 12\n7\n15 15 15 15 9 16 15\n17\n7 18 13 9 15 2 18 7 20 19 19 19 20 2 7 19 19\n5\n3 1 6 1 3\n8\n13 12 18 8 15 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n16 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n9\n10 11 11 3 10 2 18 10 18\n6\n14 24 14 16 6 6\n11\n12 7 9 20 7 7 9 9 20 2 12\n7\n15 16 15 15 15 14 15\n17\n7 18 7 15 15 2 18 7 20 19 19 19 20 2 7 19 19\n5\n3 1 2 1 3\n8\n19 12 18 12 16 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n16 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n9\n10 11 11 3 10 2 21 10 18\n6\n14 24 14 14 6 6\n11\n12 7 9 20 7 7 9 9 20 2 12\n7\n15 16 15 15 15 14 15\n17\n7 18 7 15 15 2 18 7 20 19 19 19 20 2 7 1 19\n5\n3 1 2 1 3\n8\n19 12 18 12 16 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n16 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n20\n10 14 10 14 10 7 10 10 14 10 7 9 10 8 14 10 10 8 14 6\n12\n7 2 2 2 2 16 16 7 18 17 17 18\n5\n7 13 17 13 7\n6\n10 10 9 9 10 10\n6\n17 19 17 19 14 14\n10\n10 13 5 18 13 13 13 10 15 5\n11\n3 4 16 4 4 3 4 13 4 16 13\n7\n17 19 1 17 17 1 19\n5\n17 17 19 17 19\n9\n13 15 13 18 13 18 13 15 13\n",
"10\n5\n10 4 10 4 4\n4\n7 14 14 7\n6\n13 3 13 3 5 5\n5\n8 6 8 17 6\n6\n6 13 6 6 6 9\n7\n12 11 5 5 11 12 12\n16\n5 12 2 5 2 5 8 5 8 2 2 8 12 5 2 8\n17\n3 9 9 1 1 1 1 15 15 1 1 1 1 1 1 3 1\n12\n9 10 13 17 13 14 13 13 11 10 14 9\n4\n15 17 17 15\n",
"3\n4\n7 2 2 7\n8\n2 8 1 4 8 1 1 2\n5\n5 5 5 8 5\n",
"10\n5\n10 4 10 4 4\n4\n7 14 14 7\n6\n13 3 13 3 5 5\n5\n8 6 8 17 6\n6\n6 12 6 6 6 13\n7\n12 11 5 5 11 12 12\n16\n5 12 1 5 2 5 8 5 8 2 2 8 12 5 2 8\n17\n3 9 9 1 1 1 1 15 15 1 1 1 1 1 1 1 1\n12\n9 10 13 11 13 14 16 13 11 10 14 9\n4\n15 17 17 15\n",
"10\n9\n10 11 11 2 10 2 18 10 3\n6\n14 14 14 14 6 6\n11\n5 7 9 20 7 7 9 9 20 7 12\n7\n15 16 15 15 15 16 15\n17\n7 18 7 15 15 2 18 7 20 19 32 19 20 2 7 14 19\n5\n3 1 6 1 3\n8\n13 12 18 12 15 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n16 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n9\n10 11 11 2 10 2 18 10 18\n6\n14 14 14 14 6 6\n11\n5 7 9 20 7 7 9 9 20 7 12\n7\n15 16 15 15 15 16 15\n17\n7 18 9 15 15 2 18 7 20 19 32 19 20 2 7 19 19\n5\n3 1 6 1 3\n8\n13 12 18 12 15 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n17 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n9\n10 11 11 2 10 2 18 10 29\n6\n14 14 14 14 6 6\n11\n5 7 9 20 7 7 9 9 20 7 12\n7\n15 16 15 15 28 16 15\n17\n7 18 7 15 15 2 18 7 20 19 32 19 20 2 7 19 19\n5\n3 1 6 1 3\n8\n13 12 18 12 15 18 19 12\n13\n11 19 15 11 20 11 7 20 19 7 15 11 11\n5\n32 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n20\n10 14 10 14 10 7 10 10 14 10 7 9 10 8 14 10 10 8 14 27\n12\n7 2 2 2 2 16 16 7 18 17 17 18\n5\n7 13 17 13 7\n6\n10 10 9 9 10 10\n6\n17 19 17 19 14 14\n10\n10 13 5 18 13 13 13 10 18 5\n11\n3 4 16 4 4 3 4 13 4 16 13\n7\n17 19 1 17 17 1 19\n5\n17 17 19 17 19\n9\n13 15 13 18 13 18 13 2 13\n",
"10\n9\n10 11 11 2 10 2 18 10 18\n6\n14 14 14 14 11 6\n11\n9 7 9 20 7 7 9 9 20 7 12\n7\n15 16 15 15 15 16 15\n17\n7 5 7 15 15 2 18 7 20 19 19 19 20 2 7 19 19\n5\n3 1 6 1 3\n8\n13 12 18 12 15 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n16 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n9\n10 11 11 2 10 2 18 10 18\n6\n14 14 14 14 6 6\n11\n5 7 9 20 7 7 9 9 20 7 12\n7\n15 16 15 4 15 16 15\n17\n7 18 7 15 15 2 18 7 20 19 32 19 20 2 7 19 19\n5\n3 1 11 1 3\n8\n13 12 18 12 15 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n32 3 3 14 14\n7\n2 8 8 1 1 2 2\n",
"10\n9\n10 11 11 2 10 2 23 10 18\n6\n14 14 14 14 6 6\n11\n5 7 9 20 7 7 9 9 20 7 12\n7\n15 16 15 15 28 16 15\n17\n7 18 7 15 15 2 18 7 20 19 32 19 20 2 11 19 19\n5\n3 1 6 1 3\n8\n13 13 18 12 15 18 19 12\n13\n11 19 15 7 20 11 7 20 19 7 15 11 11\n5\n32 3 3 14 14\n7\n2 8 8 1 1 13 2\n",
"10\n9\n10 11 11 3 10 2 18 10 18\n6\n14 14 14 14 6 6\n11\n12 7 9 20 7 7 9 9 18 7 12\n7\n15 16 15 15 15 16 15\n17\n7 18 7 15 15 2 18 7 20 19 19 19 20 2 7 19 19\n5\n3 1 6 1 3\n8\n19 12 18 12 12 18 19 12\n13\n11 19 15 7 20 6 7 20 19 7 15 11 11\n5\n16 3 3 14 14\n7\n2 8 8 1 1 13 2\n"
],
"output": [
"2 2 7 7\n1 1 2 2\n5 5 5 5\n",
"2 2 7 7\n1 1 2 2\n5 5 5 5\n",
"1 1 10000 10000\n",
"10 10 11 11\n14 14 14 14\n7 7 7 7\n15 15 15 15\n7 7 7 7\n1 1 3 3\n12 12 12 12\n11 11 11 11\n3 3 14 14\n1 1 2 2\n",
"10 10 10 10\n2 2 2 2\n7 7 13 13\n10 10 10 10\n17 17 19 19\n13 13 13 13\n4 4 4 4\n17 17 19 19\n17 17 19 19\n13 13 13 13\n",
"9999 9999 10000 10000\n",
"4 4 10 10\n7 7 14 14\n3 3 5 5\n6 6 8 8\n6 6 6 6\n11 11 12 12\n2 2 2 2\n1 1 1 1\n13 13 13 13\n15 15 17 17\n",
"2 2 7 7 \n1 1 8 8 \n5 5 5 5 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n12 12 12 12 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 10 10 \n2 2 2 2 \n7 7 13 13 \n9 9 10 10 \n17 17 19 19 \n13 13 13 13 \n4 4 4 4 \n17 17 19 19 \n17 17 19 19 \n13 13 13 13 \n",
"9998 9998 9999 9999 \n",
"4 4 10 10 \n7 7 14 14 \n3 3 5 5 \n6 6 8 8 \n6 6 6 6 \n11 11 12 12 \n2 2 2 2 \n1 1 1 1 \n13 13 13 13 \n15 15 17 17 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n12 12 18 18 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"4 4 10 10 \n7 7 14 14 \n3 3 5 5 \n6 6 8 8 \n6 6 6 6 \n11 11 12 12 \n2 2 2 2 \n1 1 1 1 \n13 13 14 14 \n15 15 17 17 \n",
"10 10 10 10 \n2 2 2 2 \n7 7 13 13 \n10 10 10 10 \n17 17 19 19 \n13 13 13 13 \n4 4 4 4 \n17 17 19 19 \n17 17 19 19 \n13 13 13 13 \n",
"2 2 7 7 \n1 1 2 2 \n5 5 5 5 \n",
"10 10 11 11 \n14 14 14 14 \n9 9 9 9 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n12 12 18 18 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n19 19 19 19 \n1 1 3 3 \n12 12 18 18 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n18 18 19 19 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n6 6 14 14 \n7 7 7 7 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n18 18 19 19 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n19 19 19 19 \n1 1 3 3 \n12 12 18 18 \n19 19 20 20 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n6 6 14 14 \n7 7 9 9 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n18 18 19 19 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"9998 9998 10000 10000 \n",
"10 10 11 11 \n14 14 14 14 \n9 9 9 9 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n12 12 12 12 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n6 6 14 14 \n7 7 7 7 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n12 12 18 18 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"4 4 10 10 \n7 7 14 14 \n3 3 5 5 \n6 6 8 8 \n6 6 13 13 \n11 11 12 12 \n2 2 2 2 \n1 1 1 1 \n13 13 14 14 \n15 15 17 17 \n",
"10 10 11 11 \n6 6 14 14 \n9 9 9 9 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n12 12 18 18 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n19 19 19 19 \n1 1 3 3 \n12 12 13 13 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n12 12 12 12 \n19 19 20 20 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n12 12 18 18 \n19 19 20 20 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n14 14 14 14 \n9 9 11 11 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n12 12 12 12 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n6 6 14 14 \n7 7 7 7 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n12 12 18 18 \n11 11 11 11 \n3 3 14 14 \n1 1 8 8 \n",
"10 10 11 11 \n6 6 14 14 \n7 7 7 7 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n12 12 12 12 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n6 6 14 14 \n9 9 9 9 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n12 12 18 18 \n11 11 11 11 \n3 3 14 14 \n1 1 8 8 \n",
"2 2 7 7 \n1 1 8 8 \n5 5 5 5 \n",
"2 2 7 7 \n1 1 8 8 \n5 5 5 5 \n",
"2 2 7 7 \n1 1 8 8 \n5 5 5 5 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n12 12 18 18 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"4 4 10 10 \n7 7 14 14 \n3 3 5 5 \n6 6 8 8 \n6 6 6 6 \n11 11 12 12 \n2 2 2 2 \n1 1 1 1 \n13 13 14 14 \n15 15 17 17 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n12 12 18 18 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n12 12 18 18 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n12 12 18 18 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n12 12 12 12 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"4 4 10 10 \n7 7 14 14 \n3 3 5 5 \n6 6 8 8 \n6 6 6 6 \n11 11 12 12 \n2 2 2 2 \n1 1 1 1 \n13 13 14 14 \n15 15 17 17 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n12 12 12 12 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 10 10 \n2 2 2 2 \n7 7 13 13 \n9 9 10 10 \n17 17 19 19 \n13 13 13 13 \n4 4 4 4 \n17 17 19 19 \n17 17 19 19 \n13 13 13 13 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n12 12 18 18 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n12 12 18 18 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n12 12 18 18 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n12 12 12 12 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n12 12 12 12 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n12 12 18 18 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n14 14 14 14 \n9 9 9 9 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n12 12 18 18 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n19 19 19 19 \n1 1 3 3 \n12 12 18 18 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n12 12 18 18 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n19 19 19 19 \n1 1 3 3 \n12 12 18 18 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n18 18 19 19 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n12 12 18 18 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n19 19 19 19 \n1 1 3 3 \n12 12 18 18 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n18 18 19 19 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n19 19 19 19 \n1 1 3 3 \n12 12 18 18 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n6 6 14 14 \n7 7 9 9 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n18 18 19 19 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 10 10 \n2 2 2 2 \n7 7 13 13 \n10 10 10 10 \n17 17 19 19 \n13 13 13 13 \n4 4 4 4 \n17 17 19 19 \n17 17 19 19 \n13 13 13 13 \n",
"4 4 10 10 \n7 7 14 14 \n3 3 5 5 \n6 6 8 8 \n6 6 6 6 \n11 11 12 12 \n2 2 2 2 \n1 1 1 1 \n13 13 13 13 \n15 15 17 17 \n",
"2 2 7 7 \n1 1 2 2 \n5 5 5 5 \n",
"2 2 7 7 \n1 1 8 8 \n5 5 5 5 \n",
"10 10 10 10 \n2 2 2 2 \n7 7 13 13 \n9 9 10 10 \n17 17 19 19 \n13 13 13 13 \n4 4 4 4 \n17 17 19 19 \n17 17 19 19 \n13 13 13 13 \n",
"2 2 7 7 \n1 1 8 8 \n5 5 5 5 \n",
"4 4 10 10 \n7 7 14 14 \n3 3 5 5 \n6 6 8 8 \n6 6 6 6 \n11 11 12 12 \n2 2 2 2 \n1 1 1 1 \n13 13 14 14 \n15 15 17 17 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n12 12 18 18 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n12 12 18 18 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n12 12 18 18 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n12 12 12 12 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 10 10 \n2 2 2 2 \n7 7 13 13 \n10 10 10 10 \n17 17 19 19 \n13 13 13 13 \n4 4 4 4 \n17 17 19 19 \n17 17 19 19 \n13 13 13 13 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n12 12 12 12 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n12 12 18 18 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n12 12 12 12 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n19 19 19 19 \n1 1 3 3 \n12 12 18 18 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n14 14 14 14 \n9 9 9 9 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n12 12 18 18 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n19 19 19 19 \n1 1 3 3 \n12 12 18 18 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n18 18 19 19 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n12 12 18 18 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n19 19 19 19 \n1 1 3 3 \n12 12 18 18 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n18 18 19 19 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n19 19 19 19 \n1 1 3 3 \n12 12 18 18 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n6 6 14 14 \n7 7 9 9 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n18 18 19 19 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n6 6 14 14 \n7 7 9 9 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n18 18 19 19 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 10 10 \n2 2 2 2 \n7 7 13 13 \n10 10 10 10 \n17 17 19 19 \n13 13 13 13 \n4 4 4 4 \n17 17 19 19 \n17 17 19 19 \n13 13 13 13 \n",
"4 4 10 10 \n7 7 14 14 \n3 3 5 5 \n6 6 8 8 \n6 6 6 6 \n11 11 12 12 \n2 2 2 2 \n1 1 1 1 \n13 13 13 13 \n15 15 17 17 \n",
"2 2 7 7 \n1 1 2 2 \n5 5 5 5 \n",
"4 4 10 10 \n7 7 14 14 \n3 3 5 5 \n6 6 8 8 \n6 6 6 6 \n11 11 12 12 \n2 2 2 2 \n1 1 1 1 \n13 13 14 14 \n15 15 17 17 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n12 12 18 18 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n19 19 19 19 \n1 1 3 3 \n12 12 18 18 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n12 12 18 18 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 10 10 \n2 2 2 2 \n7 7 13 13 \n10 10 10 10 \n17 17 19 19 \n13 13 13 13 \n4 4 4 4 \n17 17 19 19 \n17 17 19 19 \n13 13 13 13 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n12 12 18 18 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n12 12 18 18 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n19 19 19 19 \n1 1 3 3 \n12 12 13 13 \n11 11 11 11 \n3 3 14 14 \n1 1 2 2 \n",
"10 10 11 11 \n14 14 14 14 \n7 7 7 7 \n15 15 15 15 \n7 7 7 7 \n1 1 3 3 \n12 12 12 12 \n19 19 20 20 \n3 3 14 14 \n1 1 2 2 \n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You have n sticks of the given lengths.
Your task is to choose exactly four of them in such a way that they can form a rectangle. No sticks can be cut to pieces, each side of the rectangle must be formed by a single stick. No stick can be chosen multiple times. It is guaranteed that it is always possible to choose such sticks.
Let S be the area of the rectangle and P be the perimeter of the rectangle.
The chosen rectangle should have the value (P^2)/(S) minimal possible. The value is taken without any rounding.
If there are multiple answers, print any of them.
Each testcase contains several lists of sticks, for each of them you are required to solve the problem separately.
Input
The first line contains a single integer T (T ≥ 1) — the number of lists of sticks in the testcase.
Then 2T lines follow — lines (2i - 1) and 2i of them describe the i-th list. The first line of the pair contains a single integer n (4 ≤ n ≤ 10^6) — the number of sticks in the i-th list. The second line of the pair contains n integers a_1, a_2, ..., a_n (1 ≤ a_j ≤ 10^4) — lengths of the sticks in the i-th list.
It is guaranteed that for each list there exists a way to choose four sticks so that they form a rectangle.
The total number of sticks in all T lists doesn't exceed 10^6 in each testcase.
Output
Print T lines. The i-th line should contain the answer to the i-th list of the input. That is the lengths of the four sticks you choose from the i-th list, so that they form a rectangle and the value (P^2)/(S) of this rectangle is minimal possible. You can print these four lengths in arbitrary order.
If there are multiple answers, print any of them.
Example
Input
3
4
7 2 2 7
8
2 8 1 4 8 2 1 5
5
5 5 5 5 5
Output
2 7 7 2
2 2 1 1
5 5 5 5
Note
There is only one way to choose four sticks in the first list, they form a rectangle with sides 2 and 7, its area is 2 ⋅ 7 = 14, perimeter is 2(2 + 7) = 18. (18^2)/(14) ≈ 23.143.
The second list contains subsets of four sticks that can form rectangles with sides (1, 2), (2, 8) and (1, 8). Their values are (6^2)/(2) = 18, (20^2)/(16) = 25 and (18^2)/(8) = 40.5, respectively. The minimal one of them is the rectangle (1, 2).
You can choose any four of the 5 given sticks from the third list, they will form a square with side 5, which is still a rectangle with sides (5, 5).
### Input:
3
4
7 2 2 7
8
2 8 1 4 8 2 1 5
5
5 5 5 5 5
### Output:
2 2 7 7
1 1 2 2
5 5 5 5
### Input:
3
4
7 2 2 7
8
2 8 1 4 8 2 1 5
5
5 5 5 5 5
### Output:
2 2 7 7
1 1 2 2
5 5 5 5
### Code:
super_ans = []
for i in range(int(input())):
n = input()
if n == '4':
super_ans.append(input())
continue
elif n == '5':
a = sorted(map(int, input().split()))
if a[0] == a[1] and a[2] == a[3]:
super_ans.append(' '.join([str(a[0]), str(a[0]), str(a[2]), str(a[2])]))
elif a[0] == a[1] and a[3] == a[4]:
super_ans.append(' '.join([str(a[0]), str(a[0]), str(a[3]), str(a[3])]))
else:
super_ans.append(' '.join([str(a[-1]), str(a[-1]), str(a[-3]), str(a[-3])]))
continue
d = 10 ** 9
t = tc = x = y = a1 = a2 = 0
for ai in sorted(map(int, input().split())):
if t == ai:
tc += 1
if tc == 2:
x = y
y = ai
if x and y / x < d:
d = y / x
a1, a2 = x, y
elif tc == 4:
a1 = a2 = t
break
else:
t = ai
tc = 1
super_ans.append(' '.join([str(a1), str(a1), str(a2), str(a2)]))
print('\n'.join(super_ans))
|
1070_A. Find a Number_10463
|
You are given two positive integers d and s. Find minimal positive integer n which is divisible by d and has sum of digits equal to s.
Input
The first line contains two positive integers d and s (1 ≤ d ≤ 500, 1 ≤ s ≤ 5000) separated by space.
Output
Print the required number or -1 if it doesn't exist.
Examples
Input
13 50
Output
699998
Input
61 2
Output
1000000000000000000000000000001
Input
15 50
Output
-1
|
import os
import sys
from io import BytesIO, IOBase
_print = print
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = 'x' in file.mode or 'r' not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b'\n') + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode('ascii'))
self.read = lambda: self.buffer.read().decode('ascii')
self.readline = lambda: self.buffer.readline().decode('ascii')
def inp():
return sys.stdin.readline().rstrip()
def mpint():
return map(int, inp().split(' '))
def itg():
return int(inp())
# ############################## import
# ############################## main
from collections import deque
def solve():
d, s = mpint()
dp = [[(-1, -1)] * (d + 1) for _ in range(s + 1)]
# last_digit, prev_mod
dq = deque([(0, 0)]) # (digit_sum, mod)
# bfs
while dq:
digit_sum, mod = dq.popleft()
for dg in range(10):
dg_sum = digit_sum + dg
m = (mod * 10 + dg) % d
if dg_sum <= s and dp[dg_sum][m][0] == -1:
dp[dg_sum][m] = dg, mod
dq.append((dg_sum, m))
# Found the answer
# Early termination to speed up
if dp[s][0][0] != -1:
break
# No such answer
if dp[s][0][0] == -1:
return -1
# backtrace to get answer
ans = [] # char list, reverse at the end
d = 0
while s:
dg, d = dp[s][d]
s -= dg
ans.append(chr(dg + 48))
return ''.join(reversed(ans))
def main():
print(solve())
DEBUG = 0
URL = 'https://codeforces.com/contest/1070/problem/A'
if __name__ == '__main__':
# 0: normal, 1: runner, 2: debug, 3: interactive
if DEBUG == 1:
import requests
from ACgenerator.Y_Test_Case_Runner import TestCaseRunner
runner = TestCaseRunner(main, URL)
inp = runner.input_stream
print = runner.output_stream
runner.checking()
else:
if DEBUG != 2:
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
if DEBUG:
def print(*args, **kwargs):
_print(*args, **kwargs)
sys.stdout.flush()
main()
# Please check!
|
{
"input": [
"15 50\n",
"61 2\n",
"13 50\n",
"2 5000\n",
"3 5000\n",
"182 6\n",
"364 4\n",
"1 5000\n",
"72 72\n",
"5 1\n",
"500 5000\n",
"75 16\n",
"212 14\n",
"277 5\n",
"4 5\n",
"321 24\n",
"4 3\n",
"500 1\n",
"481 11\n",
"76 2\n",
"496 4\n",
"74 9\n",
"100 5000\n",
"166 5\n",
"242 6\n",
"73 1\n",
"495 3\n",
"154 4\n",
"71 80\n",
"6 1\n",
"161 3\n",
"4 4999\n",
"251 17\n",
"6 2\n",
"76 9\n",
"5 3\n",
"496 2\n",
"498 5000\n",
"499 3\n",
"496 1\n",
"495 4\n",
"86 5\n",
"407 21\n",
"286 6\n",
"73 80\n",
"47 2\n",
"1 1\n",
"73 4\n",
"4 4997\n",
"400 5000\n",
"79 5\n",
"434 9\n",
"163 4\n",
"73 9\n",
"500 4992\n",
"286 25\n",
"242 1503\n",
"5 2\n",
"1 2\n",
"5 4\n",
"78 72\n",
"2 1\n",
"74 1\n",
"4 1\n",
"418 11\n",
"500 2\n",
"80 80\n",
"495 2295\n",
"80 79\n",
"182 4\n",
"303 18\n",
"242 29\n",
"3 75\n",
"1 4997\n",
"499 2719\n",
"499 4\n",
"79 80\n",
"4 4998\n",
"217 7\n",
"498 4995\n",
"500 3\n",
"498 3\n",
"49 2\n",
"1 4998\n",
"3 6\n",
"202 8\n",
"360 4995\n",
"74 16\n",
"286 11\n",
"374 11\n",
"200 5000\n",
"3 4999\n",
"316 4\n",
"3 4998\n",
"206 8\n",
"69 72\n",
"76 4\n",
"462 3771\n",
"454 9\n",
"495 4257\n",
"6 4\n",
"182 8\n",
"345 4992\n",
"498 4\n",
"77 74\n",
"314 6\n",
"500 4\n",
"4 2\n",
"3 4\n",
"482 5\n",
"6 5\n",
"73 16\n",
"4 4\n",
"346 15\n",
"2 2\n",
"202 4\n",
"497 3\n",
"242 13\n",
"360 5000\n",
"67 4\n",
"70 72\n",
"197 4\n",
"2 72\n",
"75 4\n",
"75 78\n",
"2 4999\n",
"491 2\n",
"146 4\n",
"314 4\n",
"75 1\n",
"3 2\n",
"2 4997\n",
"286 29\n",
"74 4\n",
"346 4\n",
"499 2\n",
"364 8\n",
"3 5\n",
"2 4998\n",
"3 1\n",
"5 5\n",
"68 2\n",
"494 8\n",
"6 6\n",
"495 2\n",
"1 4999\n",
"303 27\n",
"495 1\n",
"217 6\n",
"286 4\n",
"76 16\n",
"499 4995\n",
"497 2\n",
"497 4\n",
"59 2\n",
"4 6\n",
"6 3\n",
"3 3\n",
"3 4997\n",
"76 1\n",
"483 901\n",
"4 5000\n",
"496 3\n",
"498 1\n",
"224 6\n",
"221 8\n",
"74 73\n",
"112 7\n",
"308 4\n",
"374 4923\n",
"75 53\n",
"497 1\n",
"498 2\n",
"75 9\n",
"314 7\n",
"224 10\n",
"5 6\n",
"292 4\n",
"499 1\n",
"274 4\n",
"256 5000\n",
"158 4\n",
"2 4555\n",
"192 6\n",
"72 12\n",
"8 1\n",
"97 16\n",
"212 7\n",
"4 8\n",
"8 2\n",
"481 18\n",
"416 2\n",
"100 20\n",
"166 9\n",
"242 8\n",
"206 4\n",
"251 22\n",
"76 5\n",
"119 3\n",
"86 3\n",
"374 5\n",
"321 28\n",
"57 2\n",
"74 7\n",
"81 1\n",
"495 6\n",
"72 80\n",
"467 1\n",
"45 4\n"
],
"output": [
"-1",
"1000000000000000000000000000001",
"699998",
"6999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999998",
"-1",
"12012",
"20020",
"5999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999",
"399999888",
"10",
"999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999500",
"-1",
"4028",
"11200000001",
"32",
"6099",
"12",
"1000",
"2405",
"100000000100",
"310000",
"1332",
"599999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999900",
"200030",
"201102",
"-1",
"-1",
"2002",
"2699999999",
"-1",
"20000000000000000000000001",
"6999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999988",
"7028",
"-1",
"2052",
"30",
"-1",
"-1",
"10000000000000000000000000100000000000000000000001",
"-1",
"-1",
"20210",
"17094",
"12012",
"1997999999",
"100000000000000000000001",
"1",
"20002",
"4999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999988",
"799999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999998800",
"3002",
"203112",
"1101000000001",
"1314",
"199999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999500",
"20878",
"2099999899999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999998",
"20",
"2",
"40",
"299998998",
"10",
"-1",
"100",
"2090",
"2000",
"29999998880",
"50989999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999995",
"19999998880",
"2002",
"909",
"40898",
"399999999",
"2999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999",
"299999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999899999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999",
"10000000001000000100001",
"2989999979",
"5999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999988",
"23002",
"2999999999999999999999999999999999999989999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999998",
"3000",
"101000000010",
"1000000000000000000001",
"3999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999",
"6",
"404",
"29999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999880",
"592",
"20306",
"200090",
"699999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999800",
"-1",
"12000100",
"3999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999",
"206",
"279999999",
"11020",
"2099999899999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999998",
"20430",
"5098999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999995",
"-1",
"4004",
"2999999999999999999998999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999995",
"-1",
"1299989999",
"2030010",
"4000",
"20",
"-1",
"200030",
"-1",
"1168",
"4",
"2076",
"2",
"202",
"100010000000000000000000000000000000001",
"20812",
"-1",
"1000002001",
"1899999990",
"1000000000201",
"199999998",
"-1",
"3999999975",
"5999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999998",
"100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
"20002",
"2001000000010",
"-1",
"-1",
"3999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999998",
"40898",
"-1",
"200000110",
"1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001",
"4004",
"-1",
"4999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999998",
"-1",
"5",
"10000000100",
"205010",
"6",
"-1",
"4999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999",
"19089",
"-1",
"1302",
"2002",
"1672",
"1999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999899999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999",
"-1",
"11000101",
"100000000000000000000000000001",
"24",
"12",
"3",
"-1",
"-1",
"-1",
"7999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999988",
"100000110000",
"-1",
"420000",
"1000025",
"2369999998",
"70000",
"20020",
"209999999899999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999998",
"-1",
"-1",
"-1",
"225",
"20410",
"28000",
"15",
"200020",
"-1",
"20002",
"19999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999989989888",
"1200010",
"299999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999998\n",
"2112\n",
"-1\n",
"1000\n",
"97\n",
"1060\n",
"8\n",
"200\n",
"4329\n",
"100100000\n",
"29900\n",
"22410\n",
"242\n",
"1030\n",
"5773\n",
"30020\n",
"1100000000001\n",
"1000000002\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You are given two positive integers d and s. Find minimal positive integer n which is divisible by d and has sum of digits equal to s.
Input
The first line contains two positive integers d and s (1 ≤ d ≤ 500, 1 ≤ s ≤ 5000) separated by space.
Output
Print the required number or -1 if it doesn't exist.
Examples
Input
13 50
Output
699998
Input
61 2
Output
1000000000000000000000000000001
Input
15 50
Output
-1
### Input:
15 50
### Output:
-1
### Input:
61 2
### Output:
1000000000000000000000000000001
### Code:
import os
import sys
from io import BytesIO, IOBase
_print = print
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = 'x' in file.mode or 'r' not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b'\n') + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode('ascii'))
self.read = lambda: self.buffer.read().decode('ascii')
self.readline = lambda: self.buffer.readline().decode('ascii')
def inp():
return sys.stdin.readline().rstrip()
def mpint():
return map(int, inp().split(' '))
def itg():
return int(inp())
# ############################## import
# ############################## main
from collections import deque
def solve():
d, s = mpint()
dp = [[(-1, -1)] * (d + 1) for _ in range(s + 1)]
# last_digit, prev_mod
dq = deque([(0, 0)]) # (digit_sum, mod)
# bfs
while dq:
digit_sum, mod = dq.popleft()
for dg in range(10):
dg_sum = digit_sum + dg
m = (mod * 10 + dg) % d
if dg_sum <= s and dp[dg_sum][m][0] == -1:
dp[dg_sum][m] = dg, mod
dq.append((dg_sum, m))
# Found the answer
# Early termination to speed up
if dp[s][0][0] != -1:
break
# No such answer
if dp[s][0][0] == -1:
return -1
# backtrace to get answer
ans = [] # char list, reverse at the end
d = 0
while s:
dg, d = dp[s][d]
s -= dg
ans.append(chr(dg + 48))
return ''.join(reversed(ans))
def main():
print(solve())
DEBUG = 0
URL = 'https://codeforces.com/contest/1070/problem/A'
if __name__ == '__main__':
# 0: normal, 1: runner, 2: debug, 3: interactive
if DEBUG == 1:
import requests
from ACgenerator.Y_Test_Case_Runner import TestCaseRunner
runner = TestCaseRunner(main, URL)
inp = runner.input_stream
print = runner.output_stream
runner.checking()
else:
if DEBUG != 2:
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
if DEBUG:
def print(*args, **kwargs):
_print(*args, **kwargs)
sys.stdout.flush()
main()
# Please check!
|
1091_E. New Year and the Acquaintance Estimation_10467
|
Bob is an active user of the social network Faithbug. On this network, people are able to engage in a mutual friendship. That is, if a is a friend of b, then b is also a friend of a. Each user thus has a non-negative amount of friends.
This morning, somebody anonymously sent Bob the following link: [graph realization problem](https://en.wikipedia.org/wiki/Graph_realization_problem) and Bob wants to know who that was. In order to do that, he first needs to know how the social network looks like. He investigated the profile of every other person on the network and noted down the number of his friends. However, he neglected to note down the number of his friends. Help him find out how many friends he has. Since there may be many possible answers, print all of them.
Input
The first line contains one integer n (1 ≤ n ≤ 5 ⋅ 10^5), the number of people on the network excluding Bob.
The second line contains n numbers a_1,a_2, ..., a_n (0 ≤ a_i ≤ n), with a_i being the number of people that person i is a friend of.
Output
Print all possible values of a_{n+1} — the amount of people that Bob can be friend of, in increasing order.
If no solution exists, output -1.
Examples
Input
3
3 3 3
Output
3
Input
4
1 1 1 1
Output
0 2 4
Input
2
0 2
Output
-1
Input
35
21 26 18 4 28 2 15 13 16 25 6 32 11 5 31 17 9 3 24 33 14 27 29 1 20 4 12 7 10 30 34 8 19 23 22
Output
13 15 17 19 21
Note
In the first test case, the only solution is that everyone is friends with everyone. That is why Bob should have 3 friends.
In the second test case, there are three possible solutions (apart from symmetries):
* a is friend of b, c is friend of d, and Bob has no friends, or
* a is a friend of b and both c and d are friends with Bob, or
* Bob is friends of everyone.
The third case is impossible to solve, as the second person needs to be a friend with everybody, but the first one is a complete stranger.
|
def main():
n=int(input())
a=list(map(int,input().split()))
a.sort(reverse=True)
mod=sum(a)%2
counts=[0]*(n+1)
for guy in a:
counts[guy]+=1
cumcounts=[counts[0]]
for i in range(n):
cumcounts.append(cumcounts[-1]+counts[i+1])
partialsums=[0]
curr=0
for i in range(n):
curr+=(i+1)*counts[i+1]
partialsums.append(curr)
partialsums.append(0)
cumcounts.append(0)
sumi=0
diffs=[]
altdiffs=[]
for i in range(n):
sumi+=a[i]
rhs=i*(i+1)
if a[i]>i:
rhs+=partialsums[i]+(i+1)*(n-i-1-cumcounts[i])
else:
rhs+=partialsums[a[i]-1]+a[i]*(n-i-1-cumcounts[a[i]-1])
diffs.append(sumi-rhs)
rhs2=(i+1)*(i+2)
if a[i]>i+1:
rhs2+=partialsums[i+1]+(i+2)*(n-i-1-cumcounts[i+1])
else:
rhs2+=partialsums[a[i]-1]+a[i]*(n-i-1-cumcounts[a[i]-1])
altdiffs.append(sumi-rhs2)
mini=max(diffs)
maxi=-max(altdiffs)
mini=max(mini,0)
maxi=min(maxi,n)
out=""
if mini%2!=mod:
mini+=1
if maxi%2==mod:
maxi+=1
for guy in range(mini,maxi,2):
out+=str(guy)+" "
if mini>maxi:
print(-1)
else:
print(out)
main()
|
{
"input": [
"2\n0 2\n",
"4\n1 1 1 1\n",
"35\n21 26 18 4 28 2 15 13 16 25 6 32 11 5 31 17 9 3 24 33 14 27 29 1 20 4 12 7 10 30 34 8 19 23 22\n",
"3\n3 3 3\n",
"8\n3 8 8 4 8 3 4 3\n",
"4\n2 2 3 4\n",
"4\n1 2 4 3\n",
"5\n5 4 3 2 1\n",
"1\n0\n",
"3\n3 2 1\n",
"4\n4 4 3 3\n",
"10\n3 7 1 2 6 5 4 10 9 8\n",
"1\n1\n",
"19\n2 3 2 2 2 2 2 2 2 2 19 3 2 2 2 2 2 2 19\n",
"19\n2 2 2 2 2 2 2 2 19 19 2 2 2 2 2 2 2 2 2\n",
"10\n3 10 3 3 3 10 10 3 3 3\n",
"2\n2 2\n",
"5\n4 3 2 1 5\n",
"9\n4 7 8 4 1 9 5 6 2\n",
"10\n4 2 3 6 8 9 5 2 7 1\n",
"19\n2 19 2 2 2 2 19 2 2 3 2 2 2 2 2 2 2 2 2\n",
"4\n4 2 3 4\n",
"4\n2 2 4 3\n",
"5\n5 4 5 2 1\n",
"10\n3 7 1 2 6 6 4 10 9 8\n",
"2\n1 2\n",
"9\n4 7 8 6 1 9 5 6 2\n",
"35\n21 26 18 7 28 2 15 13 16 25 6 32 11 5 31 17 9 3 24 33 14 27 29 1 20 4 12 7 10 30 34 8 19 23 22\n",
"9\n4 7 8 6 1 9 5 7 2\n",
"35\n21 26 18 7 28 2 16 13 16 25 6 32 11 5 31 17 9 3 24 33 14 27 29 1 20 4 12 7 10 30 34 8 19 23 22\n",
"35\n21 26 18 7 28 2 16 13 16 25 6 32 11 5 31 17 9 3 24 33 14 27 29 1 20 4 15 7 10 30 34 8 19 23 22\n",
"4\n3 2 4 3\n",
"10\n3 7 1 2 6 6 4 10 9 5\n",
"9\n4 7 8 6 1 9 5 6 4\n",
"35\n21 26 18 7 28 2 15 13 16 25 6 32 11 5 31 17 9 3 24 33 14 27 29 1 20 4 12 7 10 30 34 8 9 23 22\n",
"4\n4 1 3 2\n",
"2\n1 1\n",
"35\n21 26 18 7 28 2 16 13 16 25 6 32 11 5 31 17 9 3 24 33 14 27 29 1 20 4 12 9 10 30 34 8 19 23 22\n",
"35\n21 26 18 7 28 2 16 13 16 25 6 32 11 5 31 17 9 3 24 33 14 27 29 1 20 4 15 0 10 30 34 8 19 23 22\n",
"8\n4 8 8 6 8 3 4 3\n",
"10\n3 7 3 3 3 10 10 3 2 3\n",
"35\n21 26 18 4 28 3 15 13 16 25 6 25 11 5 31 17 9 3 24 33 14 27 29 1 20 4 12 7 10 30 34 8 19 23 22\n",
"9\n4 7 8 6 1 9 7 6 4\n",
"35\n21 26 18 7 28 2 15 13 16 25 6 32 11 5 31 17 9 3 24 33 14 27 29 1 20 4 12 7 10 30 34 8 9 10 22\n",
"35\n21 26 18 7 28 2 16 13 16 25 6 32 11 5 31 17 18 3 24 33 14 27 29 1 20 4 12 9 10 30 34 8 19 23 22\n",
"5\n0 3 2 1 5\n",
"4\n4 1 3 4\n",
"2\n0 1\n",
"9\n4 7 8 6 1 9 4 7 2\n",
"8\n4 8 8 4 8 3 4 3\n",
"5\n5 4 1 2 1\n",
"3\n2 2 1\n",
"4\n4 0 3 3\n",
"10\n3 7 1 2 6 5 4 10 9 1\n",
"19\n2 2 2 2 2 2 2 2 19 19 2 2 2 2 2 2 3 2 2\n",
"10\n3 10 3 3 3 10 10 3 2 3\n",
"2\n2 1\n",
"5\n4 4 2 1 5\n",
"9\n4 7 8 4 1 9 8 6 2\n",
"19\n4 19 2 2 2 2 19 2 2 3 2 2 2 2 2 2 2 2 2\n",
"35\n21 26 18 4 28 2 15 13 16 25 6 25 11 5 31 17 9 3 24 33 14 27 29 1 20 4 12 7 10 30 34 8 19 23 22\n",
"5\n0 1 2 1 5\n",
"9\n4 7 8 6 1 9 3 7 2\n",
"3\n2 2 0\n",
"19\n2 2 2 2 2 2 4 2 19 19 2 2 2 2 2 2 3 2 2\n",
"2\n2 0\n",
"19\n4 19 2 2 2 2 19 0 2 3 2 2 2 2 2 2 2 2 2\n",
"10\n3 7 1 2 6 6 4 10 9 10\n",
"4\n4 1 1 2\n"
],
"output": [
"-1\n",
"0 2 4 \n",
"13 15 17 19 21 \n",
"3 \n",
"3 5 \n",
"1 3 \n",
"2 \n",
"3 \n",
"0 \n",
"2 \n",
"2 4 \n",
"5 \n",
"1 \n",
"2 4 \n",
"2 \n",
"3 \n",
"2 \n",
"3 \n",
"4 6 \n",
"3 5 7 \n",
"3 \n",
"3 \n",
"1 3 \n",
"-1\n",
"6 \n",
"1 \n",
"4 6 \n",
"10 12 14 16 18 20 22 24 \n",
"5 \n",
"9 11 13 15 17 19 21 23 25 \n",
"6 8 10 12 14 16 18 20 22 24 26 28 \n",
"2 4 \n",
"3 5 7 \n",
"2 4 6 8 \n",
"16 18 \n",
"2 \n",
"0 2 \n",
"7 9 11 13 15 17 19 21 23 25 27 \n",
"13 15 17 19 21 \n",
"4 \n",
"3 5 \n",
"5 7 9 11 13 15 17 19 21 23 25 27 29 \n",
"4 6 8 \n",
"15 17 \n",
"0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 \n",
"-1\n",
"-1\n",
"1 \n",
"-1\n",
"4 6 \n",
"-1\n",
"1 3 \n",
"-1\n",
"-1\n",
"3 \n",
"-1\n",
"1 \n",
"-1\n",
"-1\n",
"3 \n",
"6 8 10 12 14 16 18 20 22 24 26 28 \n",
"-1\n",
"-1\n",
"2 \n",
"3 \n",
"-1\n",
"-1\n",
"-1\n",
"2 \n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Bob is an active user of the social network Faithbug. On this network, people are able to engage in a mutual friendship. That is, if a is a friend of b, then b is also a friend of a. Each user thus has a non-negative amount of friends.
This morning, somebody anonymously sent Bob the following link: [graph realization problem](https://en.wikipedia.org/wiki/Graph_realization_problem) and Bob wants to know who that was. In order to do that, he first needs to know how the social network looks like. He investigated the profile of every other person on the network and noted down the number of his friends. However, he neglected to note down the number of his friends. Help him find out how many friends he has. Since there may be many possible answers, print all of them.
Input
The first line contains one integer n (1 ≤ n ≤ 5 ⋅ 10^5), the number of people on the network excluding Bob.
The second line contains n numbers a_1,a_2, ..., a_n (0 ≤ a_i ≤ n), with a_i being the number of people that person i is a friend of.
Output
Print all possible values of a_{n+1} — the amount of people that Bob can be friend of, in increasing order.
If no solution exists, output -1.
Examples
Input
3
3 3 3
Output
3
Input
4
1 1 1 1
Output
0 2 4
Input
2
0 2
Output
-1
Input
35
21 26 18 4 28 2 15 13 16 25 6 32 11 5 31 17 9 3 24 33 14 27 29 1 20 4 12 7 10 30 34 8 19 23 22
Output
13 15 17 19 21
Note
In the first test case, the only solution is that everyone is friends with everyone. That is why Bob should have 3 friends.
In the second test case, there are three possible solutions (apart from symmetries):
* a is friend of b, c is friend of d, and Bob has no friends, or
* a is a friend of b and both c and d are friends with Bob, or
* Bob is friends of everyone.
The third case is impossible to solve, as the second person needs to be a friend with everybody, but the first one is a complete stranger.
### Input:
2
0 2
### Output:
-1
### Input:
4
1 1 1 1
### Output:
0 2 4
### Code:
def main():
n=int(input())
a=list(map(int,input().split()))
a.sort(reverse=True)
mod=sum(a)%2
counts=[0]*(n+1)
for guy in a:
counts[guy]+=1
cumcounts=[counts[0]]
for i in range(n):
cumcounts.append(cumcounts[-1]+counts[i+1])
partialsums=[0]
curr=0
for i in range(n):
curr+=(i+1)*counts[i+1]
partialsums.append(curr)
partialsums.append(0)
cumcounts.append(0)
sumi=0
diffs=[]
altdiffs=[]
for i in range(n):
sumi+=a[i]
rhs=i*(i+1)
if a[i]>i:
rhs+=partialsums[i]+(i+1)*(n-i-1-cumcounts[i])
else:
rhs+=partialsums[a[i]-1]+a[i]*(n-i-1-cumcounts[a[i]-1])
diffs.append(sumi-rhs)
rhs2=(i+1)*(i+2)
if a[i]>i+1:
rhs2+=partialsums[i+1]+(i+2)*(n-i-1-cumcounts[i+1])
else:
rhs2+=partialsums[a[i]-1]+a[i]*(n-i-1-cumcounts[a[i]-1])
altdiffs.append(sumi-rhs2)
mini=max(diffs)
maxi=-max(altdiffs)
mini=max(mini,0)
maxi=min(maxi,n)
out=""
if mini%2!=mod:
mini+=1
if maxi%2==mod:
maxi+=1
for guy in range(mini,maxi,2):
out+=str(guy)+" "
if mini>maxi:
print(-1)
else:
print(out)
main()
|
1110_C. Meaningless Operations_10471
|
Can the greatest common divisor and bitwise operations have anything in common? It is time to answer this question.
Suppose you are given a positive integer a. You want to choose some integer b from 1 to a - 1 inclusive in such a way that the [greatest common divisor (GCD)](https://en.wikipedia.org/wiki/Greatest_common_divisor) of integers a ⊕ b and a \> \& \> b is as large as possible. In other words, you'd like to compute the following function:
$$$f(a) = max_{0 < b < a}{gcd(a ⊕ b, a \> \& \> b)}.$$$
Here ⊕ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR), and \& denotes the [bitwise AND operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND).
The greatest common divisor of two integers x and y is the largest integer g such that both x and y are divided by g without remainder.
You are given q integers a_1, a_2, …, a_q. For each of these integers compute the largest possible value of the greatest common divisor (when b is chosen optimally).
Input
The first line contains an integer q (1 ≤ q ≤ 10^3) — the number of integers you need to compute the answer for.
After that q integers are given, one per line: a_1, a_2, …, a_q (2 ≤ a_i ≤ 2^{25} - 1) — the integers you need to compute the answer for.
Output
For each integer, print the answer in the same order as the integers are given in input.
Example
Input
3
2
3
5
Output
3
1
7
Note
For the first integer the optimal choice is b = 1, then a ⊕ b = 3, a \> \& \> b = 0, and the greatest common divisor of 3 and 0 is 3.
For the second integer one optimal choice is b = 2, then a ⊕ b = 1, a \> \& \> b = 2, and the greatest common divisor of 1 and 2 is 1.
For the third integer the optimal choice is b = 2, then a ⊕ b = 7, a \> \& \> b = 0, and the greatest common divisor of 7 and 0 is 7.
|
import math
from sys import stdin
q = int(input())
l = stdin.read().splitlines()
for i in l:
n = int(i)
k = int(math.log2(n + 1))
if (1 << k) < n + 1:
print((1 << (k + 1)) - 1)
continue
else:
found = False
for j in range(2, int(math.sqrt(n)) + 1):
if n % j == 0:
print(n // j)
found = True
break
if not found:
print(1)
|
{
"input": [
"3\n2\n3\n5\n",
"1\n228\n",
"9\n15\n7\n12\n122\n127\n99\n1999999\n255\n8388607\n",
"1\n88\n",
"9\n15\n7\n12\n122\n127\n99\n1984716\n255\n8388607\n",
"1\n11\n",
"9\n30\n7\n12\n122\n127\n99\n1984716\n255\n8388607\n",
"1\n19\n",
"9\n30\n7\n12\n122\n127\n99\n1984716\n204\n8388607\n",
"9\n30\n7\n12\n122\n127\n71\n1984716\n204\n14628115\n",
"1\n4\n",
"9\n30\n7\n4\n122\n127\n92\n1984716\n168\n14628115\n",
"1\n7\n",
"9\n30\n7\n4\n122\n226\n92\n1984716\n168\n14628115\n",
"9\n30\n7\n4\n122\n226\n170\n1984716\n168\n14628115\n",
"1\n245\n",
"9\n15\n7\n12\n122\n127\n99\n533847\n255\n8388607\n",
"9\n30\n4\n12\n122\n127\n99\n1984716\n255\n8388607\n",
"1\n32\n",
"9\n30\n7\n12\n122\n127\n99\n1984716\n104\n8388607\n",
"1\n15\n",
"9\n30\n7\n12\n122\n127\n134\n1984716\n204\n8388607\n",
"1\n63\n",
"9\n30\n7\n12\n122\n136\n92\n1984716\n204\n14628115\n",
"1\n2\n",
"9\n30\n7\n4\n122\n127\n17\n1984716\n168\n14628115\n",
"9\n30\n7\n4\n122\n226\n92\n1984716\n168\n1710958\n",
"9\n30\n6\n4\n122\n226\n170\n1984716\n168\n14628115\n",
"1\n259\n",
"9\n15\n4\n12\n99\n127\n99\n1999999\n255\n8388607\n",
"9\n30\n4\n21\n122\n127\n99\n1984716\n255\n8388607\n",
"9\n30\n5\n12\n122\n127\n99\n1984716\n104\n8388607\n",
"9\n30\n7\n12\n122\n175\n134\n1984716\n204\n8388607\n",
"9\n30\n7\n14\n122\n127\n71\n77725\n204\n14628115\n",
"9\n30\n7\n12\n122\n127\n92\n1984716\n168\n17916425\n",
"9\n30\n7\n4\n226\n127\n17\n1984716\n168\n14628115\n",
"9\n30\n6\n4\n122\n226\n170\n1984716\n100\n14628115\n",
"9\n15\n4\n12\n99\n127\n58\n1999999\n255\n8388607\n",
"9\n30\n4\n21\n122\n210\n99\n1984716\n255\n8388607\n",
"9\n30\n5\n12\n122\n127\n99\n1984716\n104\n660941\n",
"9\n30\n7\n12\n122\n45\n134\n1984716\n204\n8388607\n",
"9\n30\n7\n21\n122\n127\n71\n77725\n204\n14628115\n",
"9\n30\n7\n12\n122\n127\n92\n1984716\n168\n1700009\n",
"9\n30\n7\n4\n122\n327\n92\n1984716\n177\n1710958\n",
"9\n15\n4\n7\n99\n127\n58\n1999999\n255\n8388607\n",
"9\n15\n7\n12\n79\n127\n55\n805011\n255\n8388607\n",
"9\n30\n2\n21\n122\n210\n99\n1984716\n255\n8388607\n",
"9\n30\n5\n12\n122\n127\n99\n1984716\n104\n205715\n",
"9\n30\n7\n12\n122\n6\n134\n1984716\n204\n8388607\n",
"9\n30\n7\n12\n122\n171\n92\n1984716\n168\n1700009\n",
"9\n30\n6\n4\n122\n226\n383\n1984716\n100\n14628115\n",
"9\n28\n5\n4\n95\n226\n170\n1984716\n227\n7333744\n",
"9\n30\n2\n33\n122\n210\n99\n1984716\n255\n8388607\n",
"9\n30\n4\n14\n122\n127\n71\n77725\n166\n14628115\n",
"9\n30\n11\n12\n122\n136\n92\n1984716\n217\n14628115\n",
"9\n30\n7\n7\n122\n171\n92\n1984716\n168\n1700009\n",
"9\n30\n6\n4\n122\n226\n383\n3214896\n100\n14628115\n",
"9\n28\n5\n4\n168\n226\n170\n1984716\n227\n7333744\n",
"9\n15\n7\n12\n147\n3\n55\n805011\n255\n8388607\n",
"9\n30\n2\n33\n122\n281\n99\n1984716\n255\n8388607\n",
"1\n9\n",
"9\n30\n7\n12\n122\n127\n71\n1984716\n204\n8388607\n",
"1\n17\n",
"1\n10\n",
"9\n30\n7\n12\n122\n127\n92\n1984716\n204\n14628115\n",
"9\n30\n7\n12\n122\n127\n92\n1984716\n168\n14628115\n",
"1\n8\n",
"1\n6\n",
"1\n13\n",
"9\n30\n7\n4\n95\n226\n170\n1984716\n168\n14628115\n",
"9\n15\n7\n12\n99\n127\n99\n1999999\n255\n8388607\n",
"1\n97\n",
"1\n3\n",
"9\n30\n7\n14\n122\n127\n71\n1984716\n204\n14628115\n",
"9\n30\n7\n12\n122\n127\n92\n1984716\n168\n12775309\n",
"1\n12\n",
"1\n5\n",
"1\n20\n",
"9\n30\n7\n4\n95\n226\n170\n1984716\n227\n14628115\n",
"1\n33\n",
"9\n15\n7\n12\n79\n127\n99\n533847\n255\n8388607\n",
"1\n64\n",
"1\n29\n",
"1\n16\n",
"1\n51\n",
"9\n30\n7\n12\n122\n136\n92\n1984716\n169\n14628115\n",
"9\n30\n7\n4\n122\n226\n92\n1984716\n177\n1710958\n",
"1\n14\n",
"9\n30\n5\n4\n95\n226\n170\n1984716\n227\n14628115\n",
"1\n443\n",
"1\n43\n",
"9\n15\n7\n12\n79\n127\n99\n805011\n255\n8388607\n",
"1\n60\n",
"1\n24\n",
"1\n71\n",
"9\n30\n7\n12\n122\n136\n92\n1984716\n224\n14628115\n",
"9\n30\n6\n4\n122\n226\n228\n1984716\n100\n14628115\n",
"1\n22\n",
"9\n28\n5\n4\n95\n226\n170\n1984716\n227\n14628115\n",
"1\n273\n",
"1\n58\n",
"1\n89\n",
"1\n37\n"
],
"output": [
"3\n1\n7\n",
"255\n",
"5\n1\n15\n127\n1\n127\n2097151\n85\n178481\n",
"127\n",
"5\n1\n15\n127\n1\n127\n2097151\n85\n178481\n",
"15\n",
"31\n1\n15\n127\n1\n127\n2097151\n85\n178481\n",
"31\n",
"31\n1\n15\n127\n1\n127\n2097151\n255\n178481\n",
"31\n1\n15\n127\n1\n127\n2097151\n255\n16777215\n",
"7\n",
"31\n1\n7\n127\n1\n127\n2097151\n255\n16777215\n",
"1\n",
"31\n1\n7\n127\n255\n127\n2097151\n255\n16777215\n",
"31\n1\n7\n127\n255\n255\n2097151\n255\n16777215\n",
"255\n",
"5\n1\n15\n127\n1\n127\n1048575\n85\n178481\n",
"31\n7\n15\n127\n1\n127\n2097151\n85\n178481\n",
"63\n",
"31\n1\n15\n127\n1\n127\n2097151\n127\n178481\n",
"5\n",
"31\n1\n15\n127\n1\n255\n2097151\n255\n178481\n",
"21\n",
"31\n1\n15\n127\n255\n127\n2097151\n255\n16777215\n",
"3\n",
"31\n1\n7\n127\n1\n31\n2097151\n255\n16777215\n",
"31\n1\n7\n127\n255\n127\n2097151\n255\n2097151\n",
"31\n7\n7\n127\n255\n255\n2097151\n255\n16777215\n",
"511\n",
"5\n7\n15\n127\n1\n127\n2097151\n85\n178481\n",
"31\n7\n31\n127\n1\n127\n2097151\n85\n178481\n",
"31\n7\n15\n127\n1\n127\n2097151\n127\n178481\n",
"31\n1\n15\n127\n255\n255\n2097151\n255\n178481\n",
"31\n1\n15\n127\n1\n127\n131071\n255\n16777215\n",
"31\n1\n15\n127\n1\n127\n2097151\n255\n33554431\n",
"31\n1\n7\n255\n1\n31\n2097151\n255\n16777215\n",
"31\n7\n7\n127\n255\n255\n2097151\n127\n16777215\n",
"5\n7\n15\n127\n1\n63\n2097151\n85\n178481\n",
"31\n7\n31\n127\n255\n127\n2097151\n85\n178481\n",
"31\n7\n15\n127\n1\n127\n2097151\n127\n1048575\n",
"31\n1\n15\n127\n63\n255\n2097151\n255\n178481\n",
"31\n1\n31\n127\n1\n127\n131071\n255\n16777215\n",
"31\n1\n15\n127\n1\n127\n2097151\n255\n2097151\n",
"31\n1\n7\n127\n511\n127\n2097151\n255\n2097151\n",
"5\n7\n1\n127\n1\n63\n2097151\n85\n178481\n",
"5\n1\n15\n127\n1\n63\n1048575\n85\n178481\n",
"31\n3\n31\n127\n255\n127\n2097151\n85\n178481\n",
"31\n7\n15\n127\n1\n127\n2097151\n127\n262143\n",
"31\n1\n15\n127\n7\n255\n2097151\n255\n178481\n",
"31\n1\n15\n127\n255\n127\n2097151\n255\n2097151\n",
"31\n7\n7\n127\n255\n511\n2097151\n127\n16777215\n",
"31\n7\n7\n127\n255\n255\n2097151\n255\n8388607\n",
"31\n3\n63\n127\n255\n127\n2097151\n85\n178481\n",
"31\n7\n15\n127\n1\n127\n131071\n255\n16777215\n",
"31\n15\n15\n127\n255\n127\n2097151\n255\n16777215\n",
"31\n1\n1\n127\n255\n127\n2097151\n255\n2097151\n",
"31\n7\n7\n127\n255\n511\n4194303\n127\n16777215\n",
"31\n7\n7\n255\n255\n255\n2097151\n255\n8388607\n",
"5\n1\n15\n255\n1\n63\n1048575\n85\n178481\n",
"31\n3\n63\n127\n511\n127\n2097151\n85\n178481\n",
"15\n",
"31\n1\n15\n127\n1\n127\n2097151\n255\n178481\n",
"31\n",
"15\n",
"31\n1\n15\n127\n1\n127\n2097151\n255\n16777215\n",
"31\n1\n15\n127\n1\n127\n2097151\n255\n16777215\n",
"15\n",
"7\n",
"15\n",
"31\n1\n7\n127\n255\n255\n2097151\n255\n16777215\n",
"5\n1\n15\n127\n1\n127\n2097151\n85\n178481\n",
"127\n",
"1\n",
"31\n1\n15\n127\n1\n127\n2097151\n255\n16777215\n",
"31\n1\n15\n127\n1\n127\n2097151\n255\n16777215\n",
"15\n",
"7\n",
"31\n",
"31\n1\n7\n127\n255\n255\n2097151\n255\n16777215\n",
"63\n",
"5\n1\n15\n127\n1\n127\n1048575\n85\n178481\n",
"127\n",
"31\n",
"31\n",
"63\n",
"31\n1\n15\n127\n255\n127\n2097151\n255\n16777215\n",
"31\n1\n7\n127\n255\n127\n2097151\n255\n2097151\n",
"15\n",
"31\n7\n7\n127\n255\n255\n2097151\n255\n16777215\n",
"511\n",
"63\n",
"5\n1\n15\n127\n1\n127\n1048575\n85\n178481\n",
"63\n",
"31\n",
"127\n",
"31\n1\n15\n127\n255\n127\n2097151\n255\n16777215\n",
"31\n7\n7\n127\n255\n255\n2097151\n127\n16777215\n",
"31\n",
"31\n7\n7\n127\n255\n255\n2097151\n255\n16777215\n",
"511\n",
"63\n",
"127\n",
"63\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Can the greatest common divisor and bitwise operations have anything in common? It is time to answer this question.
Suppose you are given a positive integer a. You want to choose some integer b from 1 to a - 1 inclusive in such a way that the [greatest common divisor (GCD)](https://en.wikipedia.org/wiki/Greatest_common_divisor) of integers a ⊕ b and a \> \& \> b is as large as possible. In other words, you'd like to compute the following function:
$$$f(a) = max_{0 < b < a}{gcd(a ⊕ b, a \> \& \> b)}.$$$
Here ⊕ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation#XOR), and \& denotes the [bitwise AND operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND).
The greatest common divisor of two integers x and y is the largest integer g such that both x and y are divided by g without remainder.
You are given q integers a_1, a_2, …, a_q. For each of these integers compute the largest possible value of the greatest common divisor (when b is chosen optimally).
Input
The first line contains an integer q (1 ≤ q ≤ 10^3) — the number of integers you need to compute the answer for.
After that q integers are given, one per line: a_1, a_2, …, a_q (2 ≤ a_i ≤ 2^{25} - 1) — the integers you need to compute the answer for.
Output
For each integer, print the answer in the same order as the integers are given in input.
Example
Input
3
2
3
5
Output
3
1
7
Note
For the first integer the optimal choice is b = 1, then a ⊕ b = 3, a \> \& \> b = 0, and the greatest common divisor of 3 and 0 is 3.
For the second integer one optimal choice is b = 2, then a ⊕ b = 1, a \> \& \> b = 2, and the greatest common divisor of 1 and 2 is 1.
For the third integer the optimal choice is b = 2, then a ⊕ b = 7, a \> \& \> b = 0, and the greatest common divisor of 7 and 0 is 7.
### Input:
3
2
3
5
### Output:
3
1
7
### Input:
1
228
### Output:
255
### Code:
import math
from sys import stdin
q = int(input())
l = stdin.read().splitlines()
for i in l:
n = int(i)
k = int(math.log2(n + 1))
if (1 << k) < n + 1:
print((1 << (k + 1)) - 1)
continue
else:
found = False
for j in range(2, int(math.sqrt(n)) + 1):
if n % j == 0:
print(n // j)
found = True
break
if not found:
print(1)
|
1180_C. Valeriy and Deque_10481
|
Recently, on the course of algorithms and data structures, Valeriy learned how to use a deque. He built a deque filled with n elements. The i-th element is a_i (i = 1, 2, …, n). He gradually takes the first two leftmost elements from the deque (let's call them A and B, respectively), and then does the following: if A > B, he writes A to the beginning and writes B to the end of the deque, otherwise, he writes to the beginning B, and A writes to the end of the deque. We call this sequence of actions an operation.
For example, if deque was [2, 3, 4, 5, 1], on the operation he will write B=3 to the beginning and A=2 to the end, so he will get [3, 4, 5, 1, 2].
The teacher of the course, seeing Valeriy, who was passionate about his work, approached him and gave him q queries. Each query consists of the singular number m_j (j = 1, 2, …, q). It is required for each query to answer which two elements he will pull out on the m_j-th operation.
Note that the queries are independent and for each query the numbers A and B should be printed in the order in which they will be pulled out of the deque.
Deque is a data structure representing a list of elements where insertion of new elements or deletion of existing elements can be made from both sides.
Input
The first line contains two integers n and q (2 ≤ n ≤ 10^5, 0 ≤ q ≤ 3 ⋅ 10^5) — the number of elements in the deque and the number of queries. The second line contains n integers a_1, a_2, ..., a_n, where a_i (0 ≤ a_i ≤ 10^9) — the deque element in i-th position. The next q lines contain one number each, meaning m_j (1 ≤ m_j ≤ 10^{18}).
Output
For each teacher's query, output two numbers A and B — the numbers that Valeriy pulls out of the deque for the m_j-th operation.
Examples
Input
5 3
1 2 3 4 5
1
2
10
Output
1 2
2 3
5 2
Input
2 0
0 0
Output
Note
Consider all 10 steps for the first test in detail:
1. [1, 2, 3, 4, 5] — on the first operation, A and B are 1 and 2, respectively.
So, 2 we write to the beginning of the deque, and 1 — to the end.
We get the following status of the deque: [2, 3, 4, 5, 1].
2. [2, 3, 4, 5, 1] ⇒ A = 2, B = 3.
3. [3, 4, 5, 1, 2]
4. [4, 5, 1, 2, 3]
5. [5, 1, 2, 3, 4]
6. [5, 2, 3, 4, 1]
7. [5, 3, 4, 1, 2]
8. [5, 4, 1, 2, 3]
9. [5, 1, 2, 3, 4]
10. [5, 2, 3, 4, 1] ⇒ A = 5, B = 2.
|
import sys
n,q=list(map(int,input().split()))
a=list(map(int,input().split()))
mx1=max(a)
a1=[]
dp={}
for i in range(q):
a1.append(int(input()))
if a1==[]:
mx=0
else:
mx=max(a1)
count=0
while(1):
count+=1
val1=a[0]
val2=a[1]
if val1==mx1:
break
if val1>val2:
a.remove(val2)
a.append(val2)
else:
a.remove(val1)
a.append(val1)
dp[count]=(val1,val2)
#print(a)
for x in a1:
if x in dp:
print(dp[x][0],dp[x][1])
else:
xx=(x-count)%(n-1)
print(a[0],a[xx+1])
"""
12345 12
23451 23
34512 34
45123 45
51234 51
52341 52
53412 53
54123 54
51234 51
3 4 5 2 1
34521 34
45213 45
a=[5,2,1,3,4]
52134 52 xx=0 0,1
51342 51 xx=1 0,2
53421 53 xx=2 0,3
54213 54 xx=3 0,4
52134 52 xx=4 0,1
51342 51
53421 53
"""
|
{
"input": [
"5 3\n1 2 3 4 5\n1\n2\n10\n",
"2 0\n0 0\n",
"71 57\n9 26 80 10 65 60 63 1 15 85 71 1 58 27 41 97 42 15 42 56 87 22 10 28 34 90 13 70 71 56 65 21 0 78 47 96 56 77 32 83 28 16 10 41 0 18 78 12 27 58 4 67 21 41 99 20 21 52 74 10 83 45 43 65 2 15 1 63 46 97 72\n81\n21\n81\n81\n5\n9\n41\n76\n81\n92\n95\n94\n78\n93\n47\n30\n92\n3\n45\n81\n42\n88\n17\n3\n39\n9\n95\n19\n95\n1\n79\n21\n15\n57\n31\n21\n61\n53\n93\n56\n55\n91\n62\n16\n41\n65\n65\n1\n31\n12\n27\n61\n61\n81\n29\n56\n61\n",
"4 5\n1 2 5 5\n1\n2\n3\n4\n5\n",
"5 3\n5 1 2 3 4\n1\n316\n2\n",
"51 12\n52 59 4 82 16 80 52 81 0 36 70 25 0 66 24 58 70 34 81 71 53 87 45 12 97 73 72 35 51 55 66 43 8 20 89 48 48 53 32 87 17 13 43 80 70 84 16 87 8 18 25\n59\n31\n89\n77\n9\n78\n81\n29\n8\n41\n17\n59\n",
"5 10\n5728 41414 457879 94 1\n1\n100\n10000\n1000000\n100000000\n10000000000\n1000000000000\n100000000000000\n10000000000000000\n1000000000000000000\n",
"42 58\n70 65 58 27 24 10 88 81 83 30 29 98 42 97 61 59 48 2 69 22 43 48 94 27 92 70 94 87 69 42 72 79 57 23 62 32 39 86 95 16 11 42\n61\n74\n11\n13\n73\n29\n34\n87\n75\n27\n79\n37\n7\n31\n11\n42\n14\n18\n73\n13\n41\n42\n61\n45\n3\n21\n95\n51\n10\n45\n31\n55\n20\n13\n33\n65\n50\n56\n29\n5\n62\n61\n48\n85\n3\n91\n21\n97\n53\n80\n56\n65\n19\n24\n49\n89\n93\n94\n",
"51 15\n14 34 51 71 72 56 100 38 30 60 75 74 90 84 59 97 45 43 18 71 95 1 26 40 73 48 20 10 98 2 17 33 100 60 83 40 50 9 23 77 57 12 77 9 83 99 10 47 32 76 69\n81\n2\n82\n37\n21\n60\n9\n19\n85\n19\n1\n46\n16\n27\n21\n",
"66 31\n2 35 79 90 61 55 7 13 96 67 58 18 72 46 59 43 45 78 72 86 78 47 47 14 84 43 91 19 25 81 63 94 23 48 50 74 1 4 92 97 84 86 91 1 73 66 77 75 30 57 16 46 17 22 54 4 44 44 95 56 34 16 41 13 29 39\n95\n78\n48\n33\n97\n28\n83\n21\n93\n97\n9\n76\n13\n97\n44\n96\n85\n13\n45\n24\n57\n1\n73\n94\n89\n1\n39\n49\n49\n87\n81\n",
"49 55\n88 17 40 32 36 60 78 90 64 78 5 77 46 94 48 12 91 65 75 18 81 92 8 19 61 70 46 27 74 10 39 67 87 95 97 35 17 24 56 58 22 17 9 42 74 74 79 48 20\n89\n21\n5\n57\n46\n65\n76\n60\n76\n63\n34\n1\n98\n45\n77\n5\n61\n30\n77\n1\n21\n69\n74\n15\n91\n28\n18\n13\n100\n19\n51\n65\n8\n18\n17\n97\n81\n97\n21\n1\n100\n99\n31\n1\n69\n6\n81\n67\n81\n33\n81\n31\n26\n78\n1\n",
"3 2\n1000000 999999 999998\n98\n999999999999\n",
"2 1\n1 2\n1\n",
"71 57\n9 26 80 10 65 60 63 1 15 85 71 1 58 27 41 97 42 15 42 56 87 22 10 28 34 90 13 70 71 56 65 21 0 78 47 96 56 77 32 83 28 16 10 41 0 18 78 12 27 58 4 67 21 41 99 20 21 52 74 10 83 45 43 65 2 15 1 63 46 97 72\n81\n21\n81\n81\n5\n9\n41\n76\n81\n92\n95\n94\n78\n93\n47\n30\n92\n3\n45\n81\n42\n88\n17\n3\n39\n9\n95\n19\n95\n1\n79\n21\n15\n57\n31\n21\n61\n53\n12\n56\n55\n91\n62\n16\n41\n65\n65\n1\n31\n12\n27\n61\n61\n81\n29\n56\n61\n",
"4 5\n1 2 5 5\n1\n2\n3\n4\n10\n",
"5 3\n7 1 2 3 4\n1\n316\n2\n",
"51 12\n52 59 4 82 16 80 52 81 0 36 70 25 0 66 24 58 70 34 81 71 53 87 45 12 97 73 72 35 67 55 66 43 8 20 89 48 48 53 32 87 17 13 43 80 70 84 16 87 8 18 25\n59\n31\n89\n77\n9\n78\n81\n29\n8\n41\n17\n59\n",
"5 10\n5728 41414 457879 94 1\n1\n100\n10000\n1000000\n100000001\n10000000000\n1000000000000\n100000000000000\n10000000000000000\n1000000000000000000\n",
"42 58\n70 65 58 27 24 10 88 81 83 41 29 98 42 97 61 59 48 2 69 22 43 48 94 27 92 70 94 87 69 42 72 79 57 23 62 32 39 86 95 16 11 42\n61\n74\n11\n13\n73\n29\n34\n87\n75\n27\n79\n37\n7\n31\n11\n42\n14\n18\n73\n13\n41\n42\n61\n45\n3\n21\n95\n51\n10\n45\n31\n55\n20\n13\n33\n65\n50\n56\n29\n5\n62\n61\n48\n85\n3\n91\n21\n97\n53\n80\n56\n65\n19\n24\n49\n89\n93\n94\n",
"51 15\n14 34 51 71 72 56 100 38 21 60 75 74 90 84 59 97 45 43 18 71 95 1 26 40 73 48 20 10 98 2 17 33 100 60 83 40 50 9 23 77 57 12 77 9 83 99 10 47 32 76 69\n81\n2\n82\n37\n21\n60\n9\n19\n85\n19\n1\n46\n16\n27\n21\n",
"66 31\n2 35 79 90 61 55 7 13 96 67 58 18 72 46 59 43 45 78 72 137 78 47 47 14 84 43 91 19 25 81 63 94 23 48 50 74 1 4 92 97 84 86 91 1 73 66 77 75 30 57 16 46 17 22 54 4 44 44 95 56 34 16 41 13 29 39\n95\n78\n48\n33\n97\n28\n83\n21\n93\n97\n9\n76\n13\n97\n44\n96\n85\n13\n45\n24\n57\n1\n73\n94\n89\n1\n39\n49\n49\n87\n81\n",
"49 55\n88 17 40 32 57 60 78 90 64 78 5 77 46 94 48 12 91 65 75 18 81 92 8 19 61 70 46 27 74 10 39 67 87 95 97 35 17 24 56 58 22 17 9 42 74 74 79 48 20\n89\n21\n5\n57\n46\n65\n76\n60\n76\n63\n34\n1\n98\n45\n77\n5\n61\n30\n77\n1\n21\n69\n74\n15\n91\n28\n18\n13\n100\n19\n51\n65\n8\n18\n17\n97\n81\n97\n21\n1\n100\n99\n31\n1\n69\n6\n81\n67\n81\n33\n81\n31\n26\n78\n1\n",
"3 2\n1000000 999999 999998\n98\n2156209018\n",
"71 57\n9 26 80 10 65 60 63 1 15 85 71 1 58 27 41 97 42 15 42 56 87 22 10 28 34 90 13 70 71 56 65 21 0 78 47 96 56 77 32 83 28 16 10 41 0 18 78 12 27 58 4 67 21 41 99 20 21 52 74 10 83 45 43 65 2 15 1 63 46 97 72\n81\n21\n81\n81\n5\n9\n41\n76\n81\n92\n95\n94\n78\n93\n47\n30\n92\n3\n45\n81\n42\n88\n17\n3\n39\n9\n95\n19\n95\n1\n79\n21\n15\n57\n31\n21\n61\n53\n17\n56\n55\n91\n62\n16\n41\n65\n65\n1\n31\n12\n27\n61\n61\n81\n29\n56\n61\n",
"4 5\n1 0 5 5\n1\n2\n3\n4\n10\n",
"5 3\n7 1 2 3 4\n2\n316\n2\n",
"51 12\n52 59 4 82 16 80 52 81 0 36 70 25 0 66 24 58 70 34 144 71 53 87 45 12 97 73 72 35 67 55 66 43 8 20 89 48 48 53 32 87 17 13 43 80 70 84 16 87 8 18 25\n59\n31\n89\n77\n9\n78\n81\n29\n8\n41\n17\n59\n",
"42 58\n70 65 58 27 24 10 88 81 83 41 29 98 42 97 61 59 48 2 69 22 43 48 94 27 92 70 94 87 69 42 72 79 57 23 62 32 39 86 95 16 11 42\n61\n74\n11\n13\n111\n29\n34\n87\n75\n27\n79\n37\n7\n31\n11\n42\n14\n18\n73\n13\n41\n42\n61\n45\n3\n21\n95\n51\n10\n45\n31\n55\n20\n13\n33\n65\n50\n56\n29\n5\n62\n61\n48\n85\n3\n91\n21\n97\n53\n80\n56\n65\n19\n24\n49\n89\n93\n94\n",
"49 55\n88 17 40 32 57 60 78 90 64 78 5 77 46 94 48 12 91 65 75 18 81 92 8 19 61 70 46 27 74 10 39 67 87 95 97 35 17 24 56 58 22 17 9 42 74 74 79 48 20\n89\n21\n5\n57\n46\n65\n76\n60\n76\n63\n34\n1\n98\n45\n77\n5\n61\n30\n77\n1\n21\n69\n74\n15\n91\n28\n18\n13\n100\n19\n41\n65\n8\n18\n17\n97\n81\n97\n21\n1\n100\n99\n31\n1\n69\n6\n81\n67\n81\n33\n81\n31\n26\n78\n1\n",
"3 2\n1000000 999999 999998\n101\n2156209018\n",
"5 3\n7 1 2 3 4\n2\n316\n3\n",
"42 58\n70 65 58 27 24 10 88 81 83 41 29 98 42 97 61 59 48 2 69 22 43 48 94 27 92 70 94 87 69 42 72 79 57 23 62 32 39 86 95 16 11 42\n61\n74\n11\n13\n111\n29\n34\n87\n75\n27\n79\n37\n7\n31\n11\n42\n14\n18\n73\n13\n41\n42\n61\n45\n3\n21\n95\n51\n10\n45\n1\n55\n20\n13\n33\n65\n50\n56\n29\n5\n62\n61\n48\n85\n3\n91\n21\n97\n53\n80\n56\n65\n19\n24\n49\n89\n93\n94\n",
"51 15\n14 34 51 71 72 56 100 38 21 60 75 74 90 84 59 97 17 43 12 71 95 1 26 40 73 48 20 10 98 2 17 33 100 60 83 40 50 9 23 77 57 12 77 9 83 99 10 47 32 76 69\n81\n2\n82\n37\n21\n60\n9\n19\n85\n19\n1\n46\n16\n27\n21\n",
"71 57\n9 26 80 10 65 60 63 1 15 85 71 1 58 27 41 97 42 15 42 56 87 22 10 28 34 90 13 70 71 56 65 21 0 78 47 96 56 77 32 83 28 16 10 41 0 18 92 12 27 58 4 67 21 41 99 20 21 52 74 10 83 45 43 65 2 15 1 63 46 97 72\n150\n21\n81\n81\n5\n9\n41\n76\n81\n92\n95\n94\n78\n93\n47\n30\n92\n3\n45\n81\n42\n88\n17\n3\n39\n9\n95\n19\n95\n1\n79\n21\n15\n57\n31\n21\n61\n53\n17\n56\n55\n91\n62\n16\n41\n65\n65\n1\n31\n12\n27\n61\n61\n81\n29\n56\n61\n",
"42 58\n70 65 58 27 24 10 88 81 83 41 29 98 42 97 61 59 48 2 69 22 43 48 94 27 92 70 94 87 69 42 72 79 57 23 62 32 39 86 95 16 11 42\n61\n74\n11\n13\n111\n29\n34\n87\n75\n27\n79\n28\n7\n31\n11\n42\n14\n18\n73\n13\n41\n42\n61\n45\n3\n21\n95\n51\n10\n45\n1\n55\n20\n13\n33\n65\n50\n56\n29\n5\n62\n61\n48\n85\n3\n91\n21\n97\n53\n80\n56\n65\n19\n24\n49\n89\n93\n94\n",
"51 15\n14 34 51 71 72 56 100 38 21 60 75 74 90 84 59 97 17 43 12 71 95 1 26 40 73 48 20 10 98 2 17 33 100 60 83 40 50 9 23 77 57 12 77 9 83 99 10 47 32 76 69\n81\n2\n82\n37\n21\n41\n9\n19\n85\n19\n1\n46\n16\n27\n21\n",
"71 57\n9 26 80 10 65 60 63 1 15 85 71 1 58 27 41 97 42 15 42 56 87 22 10 28 34 90 13 70 71 56 65 21 0 78 47 191 56 77 32 83 28 16 10 41 0 18 92 12 27 58 4 67 21 41 99 20 21 52 74 10 83 45 43 65 2 15 1 63 46 97 72\n150\n21\n81\n81\n5\n9\n41\n76\n81\n92\n95\n94\n78\n93\n47\n30\n92\n3\n45\n81\n42\n88\n17\n3\n39\n9\n95\n19\n95\n1\n79\n21\n15\n57\n31\n21\n61\n53\n17\n56\n55\n91\n62\n16\n41\n65\n65\n1\n31\n12\n27\n61\n61\n81\n29\n56\n61\n",
"51 12\n52 59 4 82 16 80 52 81 0 36 70 25 0 36 24 58 70 34 144 71 53 97 45 12 97 73 72 35 67 105 66 43 8 20 89 48 48 53 32 87 17 13 43 80 70 84 16 87 8 18 25\n59\n31\n89\n77\n9\n78\n81\n29\n8\n41\n17\n59\n",
"42 58\n70 65 58 27 24 10 88 81 83 41 29 98 42 97 61 59 48 2 69 22 43 48 94 27 92 70 94 87 69 42 72 79 57 23 62 32 39 86 95 16 11 42\n61\n74\n11\n13\n111\n29\n34\n87\n75\n27\n79\n28\n7\n31\n11\n42\n14\n18\n73\n13\n41\n42\n61\n45\n3\n19\n95\n51\n10\n45\n1\n55\n20\n13\n33\n65\n50\n56\n29\n5\n62\n61\n48\n85\n3\n91\n21\n97\n53\n80\n56\n65\n19\n24\n49\n89\n93\n94\n",
"66 31\n2 35 79 90 61 55 7 13 114 67 58 18 72 46 59 43 45 78 72 137 78 47 47 14 84 43 91 19 25 81 63 94 23 48 50 74 0 4 92 97 84 86 91 1 73 66 77 75 30 57 16 46 17 22 54 4 44 44 95 56 34 8 41 13 57 39\n95\n78\n48\n33\n97\n28\n83\n21\n93\n97\n9\n76\n13\n97\n44\n96\n85\n13\n45\n24\n57\n1\n73\n94\n89\n1\n39\n49\n49\n87\n81\n",
"3 2\n1000000 999999 453800\n110\n2156209018\n",
"51 12\n52 59 4 141 16 80 52 81 0 36 70 25 0 36 24 58 70 34 144 71 53 97 45 12 97 73 72 35 67 105 66 43 8 20 89 48 48 53 32 87 17 13 43 80 70 84 16 87 8 18 25\n59\n31\n89\n77\n9\n78\n81\n29\n8\n41\n17\n59\n",
"42 58\n70 65 58 27 24 10 88 81 83 41 29 98 42 97 61 59 48 2 69 22 43 48 94 27 92 70 94 87 69 42 72 79 57 23 62 32 39 86 95 16 11 42\n61\n74\n11\n13\n111\n29\n34\n87\n75\n27\n79\n28\n7\n31\n11\n42\n14\n18\n129\n13\n41\n42\n61\n45\n3\n19\n95\n51\n10\n45\n1\n55\n20\n13\n33\n65\n50\n56\n29\n5\n62\n61\n48\n85\n3\n91\n21\n97\n53\n80\n56\n65\n19\n24\n49\n89\n93\n94\n",
"51 15\n14 34 51 71 72 56 100 13 21 60 75 74 90 84 59 97 17 43 12 71 95 1 26 40 73 48 20 10 98 2 17 33 100 60 83 40 50 9 23 77 114 12 77 9 83 99 10 47 32 76 69\n81\n2\n82\n37\n21\n41\n9\n19\n85\n19\n1\n46\n16\n27\n21\n",
"66 31\n2 35 79 90 61 55 7 13 114 67 58 18 72 46 59 43 45 78 72 137 78 47 47 14 84 43 91 19 25 81 63 94 23 48 50 74 0 4 92 97 84 86 91 1 73 66 77 75 30 57 16 46 17 22 54 4 44 44 95 56 34 8 41 13 57 39\n95\n78\n48\n33\n97\n28\n83\n21\n93\n97\n9\n115\n13\n97\n44\n96\n85\n13\n45\n24\n57\n1\n73\n94\n89\n1\n39\n49\n49\n87\n81\n",
"3 2\n1000000 999999 606166\n110\n2156209018\n",
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"66 31\n4 36 79 90 0 55 7 13 114 67 58 10 72 46 59 43 45 27 72 180 78 47 47 14 84 43 91 19 25 10 63 94 23 48 50 74 0 4 67 97 84 86 91 1 73 66 77 75 30 57 5 46 17 22 54 4 44 44 8 56 34 8 41 21 57 39\n95\n78\n48\n32\n97\n49\n83\n21\n93\n89\n9\n115\n13\n97\n44\n96\n85\n13\n45\n24\n57\n1\n73\n134\n89\n1\n39\n49\n40\n46\n15\n",
"71 57\n9 26 80 10 65 60 63 2 15 55 71 1 58 27 41 97 42 15 53 56 84 22 10 28 34 90 13 70 71 56 65 39 0 78 47 191 56 77 32 83 28 16 16 41 0 18 92 21 29 58 2 67 23 45 99 20 21 52 74 10 8 45 5 65 2 15 1 63 91 97 72\n107\n21\n81\n81\n5\n9\n41\n76\n81\n89\n114\n94\n78\n93\n47\n30\n92\n3\n45\n81\n42\n88\n26\n3\n39\n9\n95\n19\n95\n1\n79\n21\n15\n57\n31\n21\n48\n53\n16\n56\n55\n91\n62\n16\n41\n65\n114\n1\n31\n12\n27\n61\n61\n81\n29\n56\n61\n",
"66 31\n4 36 79 90 0 55 7 13 114 67 58 10 72 46 59 43 45 27 72 180 78 47 47 14 84 43 91 19 25 10 63 94 23 48 50 74 0 4 67 97 84 86 91 1 73 66 77 75 30 57 5 46 17 22 54 4 44 44 8 56 34 8 41 21 57 39\n23\n78\n48\n32\n97\n49\n83\n21\n93\n89\n9\n115\n13\n97\n44\n96\n85\n13\n45\n24\n57\n1\n73\n134\n89\n1\n39\n49\n40\n46\n15\n",
"71 57\n9 26 80 10 65 60 63 2 15 55 71 1 58 27 41 97 42 15 53 56 84 22 10 28 34 90 13 70 71 56 65 39 0 78 47 191 56 77 32 83 28 16 3 41 0 18 92 21 29 58 2 67 23 45 99 20 21 52 74 10 8 45 5 65 2 15 1 63 91 97 72\n107\n21\n81\n81\n5\n9\n41\n76\n81\n89\n114\n94\n78\n93\n47\n30\n92\n3\n45\n81\n42\n88\n26\n3\n39\n9\n95\n19\n95\n1\n79\n21\n15\n57\n31\n21\n48\n53\n16\n56\n55\n91\n62\n16\n41\n65\n114\n1\n31\n12\n27\n61\n61\n81\n29\n56\n61\n",
"71 57\n9 26 80 10 65 60 63 2 15 55 71 1 58 27 41 97 42 15 53 56 84 22 10 28 34 90 5 70 71 56 65 39 0 78 47 191 56 77 32 83 28 16 3 41 0 18 92 21 29 58 2 67 23 45 99 20 21 52 74 10 8 45 5 65 2 15 1 63 91 97 72\n107\n21\n81\n81\n5\n9\n41\n76\n81\n89\n114\n94\n78\n93\n47\n30\n92\n3\n45\n81\n42\n88\n26\n3\n39\n9\n95\n19\n95\n1\n79\n21\n15\n57\n31\n21\n48\n53\n16\n56\n55\n91\n62\n16\n41\n65\n114\n1\n31\n12\n27\n61\n61\n81\n29\n56\n61\n",
"66 31\n4 36 79 90 0 55 7 13 114 67 58 10 72 46 59 43 45 27 72 180 78 47 47 14 84 43 91 19 25 10 63 94 23 0 50 74 0 4 67 97 84 86 91 1 73 66 8 75 30 57 5 46 17 22 54 4 44 44 8 56 34 8 41 21 57 39\n23\n78\n48\n32\n97\n49\n83\n21\n93\n89\n9\n115\n13\n97\n44\n96\n85\n13\n45\n24\n57\n1\n73\n134\n89\n1\n39\n49\n40\n46\n15\n",
"71 57\n9 26 80 10 65 60 63 2 15 55 71 1 58 27 41 97 42 15 53 56 84 22 10 28 34 90 5 70 71 56 65 39 0 78 47 191 56 77 32 83 28 16 3 41 0 18 92 21 29 58 2 67 23 45 99 20 21 52 74 10 8 45 5 65 2 15 0 63 91 97 72\n107\n21\n81\n81\n5\n9\n41\n76\n81\n89\n114\n56\n78\n93\n47\n30\n92\n3\n45\n81\n42\n88\n26\n3\n39\n9\n95\n19\n95\n1\n79\n21\n15\n57\n31\n21\n48\n53\n16\n56\n55\n91\n62\n16\n41\n65\n114\n1\n31\n12\n27\n61\n61\n81\n29\n56\n61\n",
"66 31\n4 36 79 90 0 55 0 13 114 67 58 10 72 46 59 43 45 27 72 180 78 47 47 14 84 43 91 19 25 10 63 94 23 0 50 74 0 4 67 97 84 86 91 1 73 66 8 75 30 57 5 46 17 22 54 4 44 44 8 56 34 8 41 21 57 39\n23\n78\n48\n32\n97\n49\n83\n21\n93\n89\n9\n115\n13\n95\n44\n96\n85\n13\n45\n24\n57\n1\n73\n134\n89\n1\n39\n49\n40\n46\n15\n",
"66 31\n4 36 79 90 0 55 0 13 114 67 58 10 72 46 59 43 45 27 72 180 78 47 47 14 84 43 91 19 15 10 63 94 23 0 50 74 0 4 67 97 84 86 91 1 73 66 8 75 30 57 5 46 17 22 54 4 44 44 8 56 34 8 41 21 57 39\n23\n78\n48\n32\n97\n49\n83\n21\n93\n89\n9\n115\n13\n95\n44\n96\n85\n13\n45\n24\n57\n1\n73\n134\n89\n1\n39\n49\n40\n46\n15\n",
"71 57\n9 26 80 10 65 60 63 2 15 55 71 1 58 27 41 97 42 15 53 56 84 22 10 28 34 90 5 70 71 56 65 39 0 78 47 191 56 77 32 83 28 16 3 41 0 18 92 21 29 58 2 67 23 45 99 20 21 52 65 10 8 45 5 65 2 15 0 63 91 97 72\n107\n21\n81\n81\n5\n9\n41\n76\n81\n89\n114\n56\n78\n93\n47\n30\n92\n3\n45\n81\n42\n88\n26\n3\n39\n9\n95\n19\n30\n1\n79\n21\n15\n57\n31\n21\n48\n53\n16\n56\n55\n91\n62\n16\n41\n65\n114\n1\n31\n12\n27\n61\n61\n81\n29\n56\n61\n",
"66 31\n4 36 79 90 0 55 0 13 114 67 58 10 72 87 59 43 45 27 72 180 78 47 47 14 84 43 91 19 15 10 63 94 23 0 50 74 0 4 67 97 84 86 91 1 73 66 8 75 30 57 5 46 17 22 54 4 44 44 8 56 34 8 41 21 57 39\n23\n78\n48\n32\n97\n49\n83\n21\n93\n89\n9\n115\n13\n95\n44\n96\n85\n13\n45\n24\n57\n1\n73\n134\n89\n1\n39\n49\n40\n46\n15\n",
"71 57\n9 26 80 10 65 60 63 2 15 55 71 1 58 27 41 97 42 15 53 56 84 22 10 28 34 90 5 70 71 56 65 39 0 78 47 191 56 77 32 83 28 16 3 41 0 18 92 21 29 58 2 67 23 45 99 20 21 52 65 10 8 45 5 65 2 15 0 63 91 97 72\n107\n21\n81\n81\n5\n9\n41\n76\n81\n89\n114\n56\n78\n93\n47\n30\n92\n3\n45\n81\n42\n88\n26\n3\n39\n9\n95\n19\n30\n1\n79\n21\n15\n57\n31\n21\n48\n53\n15\n56\n55\n91\n62\n16\n41\n65\n114\n1\n31\n12\n27\n61\n61\n81\n29\n56\n61\n",
"66 31\n4 36 79 90 0 55 0 13 114 67 58 10 72 87 59 43 45 27 72 180 78 47 47 14 84 43 91 19 15 10 63 94 23 0 50 74 0 4 67 97 84 86 91 1 73 66 8 75 30 57 5 46 17 22 54 4 44 40 8 56 34 8 41 21 57 39\n23\n78\n48\n32\n97\n49\n83\n21\n93\n89\n9\n115\n13\n95\n44\n96\n85\n13\n45\n24\n57\n1\n73\n134\n89\n1\n39\n49\n40\n46\n15\n",
"71 57\n9 26 80 10 65 60 63 2 15 55 71 1 58 27 41 97 42 15 53 56 84 22 10 28 34 90 5 70 71 56 65 39 0 78 47 191 56 77 32 83 28 16 3 41 -1 18 92 21 29 58 2 67 23 45 99 20 21 52 65 10 8 45 5 65 2 15 0 63 91 97 72\n107\n21\n81\n81\n5\n9\n41\n76\n81\n89\n114\n56\n78\n93\n47\n30\n92\n3\n45\n81\n42\n88\n26\n3\n39\n9\n95\n19\n30\n1\n79\n21\n15\n57\n31\n21\n48\n53\n15\n56\n55\n91\n62\n16\n41\n65\n114\n1\n31\n12\n27\n61\n61\n81\n29\n56\n61\n",
"71 57\n9 26 80 10 65 60 63 2 15 55 71 1 58 27 41 97 42 15 53 56 84 22 10 28 34 90 5 70 71 56 65 39 0 78 47 191 56 77 32 83 28 16 3 41 -1 18 92 21 29 58 2 67 23 45 99 20 21 52 65 10 8 45 5 65 2 15 0 63 91 97 72\n107\n21\n81\n81\n5\n9\n41\n76\n81\n89\n114\n56\n78\n93\n47\n30\n92\n3\n45\n81\n42\n145\n26\n3\n39\n9\n95\n19\n30\n1\n79\n21\n15\n57\n31\n21\n48\n53\n15\n56\n55\n91\n62\n16\n41\n65\n114\n1\n31\n12\n27\n61\n61\n81\n29\n56\n61\n",
"66 31\n4 36 79 90 0 55 0 13 114 67 58 10 95 87 59 43 45 27 72 180 78 47 47 14 84 43 91 19 15 10 63 94 23 0 50 74 0 4 67 97 84 86 91 1 73 66 8 75 30 57 5 46 17 22 54 4 44 40 8 56 34 8 41 21 57 39\n23\n78\n48\n32\n97\n49\n83\n21\n174\n89\n9\n115\n13\n95\n44\n96\n85\n13\n45\n24\n57\n1\n73\n134\n89\n1\n39\n49\n40\n46\n15\n",
"71 57\n9 43 80 10 65 60 63 2 15 55 71 1 58 27 41 97 42 15 53 56 84 22 10 28 34 90 5 70 71 56 65 39 0 78 47 191 56 77 32 83 28 16 3 41 -1 18 92 21 29 58 2 67 23 45 99 20 21 52 65 10 8 45 5 65 2 15 0 63 91 97 72\n107\n21\n81\n81\n5\n9\n41\n76\n81\n89\n114\n56\n78\n93\n47\n30\n92\n3\n45\n81\n42\n145\n26\n3\n39\n9\n95\n19\n30\n1\n79\n21\n15\n57\n31\n21\n48\n53\n15\n56\n55\n91\n62\n16\n41\n65\n114\n1\n31\n12\n27\n61\n61\n81\n29\n56\n61\n",
"71 57\n9 26 80 10 65 60 63 1 15 85 71 1 58 27 41 97 42 15 42 56 87 22 10 28 34 90 13 70 71 56 65 21 0 78 47 96 56 77 32 83 28 16 10 41 0 18 78 12 27 58 4 67 21 41 99 20 21 52 74 10 83 45 43 65 2 15 1 63 46 97 72\n81\n21\n81\n81\n5\n9\n41\n76\n81\n92\n95\n94\n78\n93\n47\n30\n92\n3\n45\n89\n42\n88\n17\n3\n39\n9\n95\n19\n95\n1\n79\n21\n15\n57\n31\n21\n61\n53\n93\n56\n55\n91\n62\n16\n41\n65\n65\n1\n31\n12\n27\n61\n61\n81\n29\n56\n61\n",
"4 5\n1 2 5 5\n1\n4\n3\n4\n5\n",
"5 3\n5 1 2 3 4\n1\n212\n2\n",
"51 12\n52 59 4 82 16 80 52 81 0 36 70 25 0 66 24 58 70 34 81 71 53 87 45 12 97 73 72 35 51 55 66 43 8 20 89 48 48 53 32 87 17 13 43 80 70 84 16 66 8 18 25\n59\n31\n89\n77\n9\n78\n81\n29\n8\n41\n17\n59\n",
"5 10\n5728 41414 457879 94 1\n1\n100\n10001\n1000000\n100000000\n10000000000\n1000000000000\n100000000000000\n10000000000000000\n1000000000000000000\n"
],
"output": [
"1 2\n2 3\n5 2\n",
"\n",
"99 1\n97 22\n99 1\n99 1\n80 60\n80 85\n97 16\n99 63\n99 1\n99 10\n99 90\n99 34\n99 15\n99 28\n97 12\n97 65\n99 10\n80 10\n97 18\n99 1\n97 10\n99 42\n97 15\n80 10\n97 83\n80 85\n99 90\n97 56\n99 90\n9 26\n99 80\n97 22\n85 97\n99 52\n97 21\n97 22\n99 45\n97 41\n99 28\n99 21\n99 20\n99 22\n99 43\n97 42\n97 16\n99 15\n99 15\n9 26\n97 21\n85 58\n97 70\n99 45\n99 45\n99 1\n97 56\n99 21\n99 45\n",
"1 2\n2 5\n5 5\n5 1\n5 2\n",
"5 1\n5 4\n5 2\n",
"97 36\n97 43\n97 87\n97 35\n82 36\n97 51\n97 43\n97 55\n82 0\n97 13\n82 34\n97 36\n",
"5728 41414\n457879 1\n457879 1\n457879 1\n457879 1\n457879 1\n457879 1\n457879 1\n457879 1\n457879 1\n",
"98 43\n98 23\n88 98\n98 97\n98 57\n98 42\n98 62\n98 10\n98 62\n98 87\n98 95\n98 86\n88 81\n98 79\n88 98\n98 65\n98 61\n98 69\n98 57\n98 97\n98 42\n98 65\n98 43\n98 24\n70 27\n98 48\n98 97\n98 29\n88 29\n98 24\n98 79\n98 61\n98 43\n98 97\n98 23\n98 92\n98 30\n98 59\n98 42\n70 10\n98 48\n98 43\n98 81\n98 27\n70 27\n98 30\n98 48\n98 59\n98 42\n98 16\n98 59\n98 92\n98 22\n98 92\n98 83\n98 81\n98 88\n98 42\n",
"100 33\n34 51\n100 100\n100 9\n100 1\n100 75\n100 60\n100 71\n100 40\n100 71\n14 34\n100 10\n100 45\n100 10\n100 1\n",
"97 63\n97 46\n97 30\n96 48\n97 23\n96 25\n97 72\n96 47\n97 25\n97 23\n96 67\n97 18\n96 46\n97 23\n97 73\n97 94\n97 78\n96 46\n97 66\n96 84\n97 44\n2 35\n97 90\n97 81\n97 84\n2 35\n96 97\n97 57\n97 57\n97 47\n97 45\n",
"97 17\n94 92\n88 60\n97 78\n97 79\n97 65\n97 74\n97 46\n97 74\n97 12\n95 97\n88 17\n97 40\n97 74\n97 10\n88 60\n97 90\n94 39\n97 10\n88 17\n94 92\n97 92\n97 46\n94 12\n97 42\n94 74\n94 75\n90 94\n97 36\n94 18\n97 32\n97 65\n90 64\n94 75\n94 65\n97 17\n97 94\n97 17\n94 92\n88 17\n97 36\n97 32\n94 67\n88 17\n97 92\n88 78\n97 94\n97 18\n97 94\n94 95\n97 94\n94 67\n94 46\n97 39\n88 17\n",
"1000000 999998\n1000000 999999\n",
"1 2\n",
"\n99 1\n97 22\n99 1\n99 1\n80 60\n80 85\n97 16\n99 63\n99 1\n99 10\n99 90\n99 34\n99 15\n99 28\n97 12\n97 65\n99 10\n80 10\n97 18\n99 1\n97 10\n99 42\n97 15\n80 10\n97 83\n80 85\n99 90\n97 56\n99 90\n9 26\n99 80\n97 22\n85 97\n99 52\n97 21\n97 22\n99 45\n97 41\n85 58\n99 21\n99 20\n99 22\n99 43\n97 42\n97 16\n99 15\n99 15\n9 26\n97 21\n85 58\n97 70\n99 45\n99 45\n99 1\n97 56\n99 21\n99 45\n",
"\n1 2\n2 5\n5 5\n5 1\n5 1\n",
"\n7 1\n7 4\n7 2\n",
"\n97 36\n97 43\n97 87\n97 35\n82 36\n97 67\n97 43\n97 55\n82 0\n97 13\n82 34\n97 36\n",
"\n5728 41414\n457879 1\n457879 1\n457879 1\n457879 5728\n457879 1\n457879 1\n457879 1\n457879 1\n457879 1\n",
"\n98 43\n98 23\n88 98\n98 97\n98 57\n98 42\n98 62\n98 10\n98 62\n98 87\n98 95\n98 86\n88 81\n98 79\n88 98\n98 65\n98 61\n98 69\n98 57\n98 97\n98 42\n98 65\n98 43\n98 24\n70 27\n98 48\n98 97\n98 29\n88 29\n98 24\n98 79\n98 61\n98 43\n98 97\n98 23\n98 92\n98 41\n98 59\n98 42\n70 10\n98 48\n98 43\n98 81\n98 27\n70 27\n98 41\n98 48\n98 59\n98 42\n98 16\n98 59\n98 92\n98 22\n98 92\n98 83\n98 81\n98 88\n98 42\n",
"\n100 33\n34 51\n100 100\n100 9\n100 1\n100 75\n100 60\n100 71\n100 40\n100 71\n14 34\n100 10\n100 45\n100 10\n100 1\n",
"\n137 63\n137 46\n137 30\n137 48\n137 23\n137 25\n137 72\n137 47\n137 25\n137 23\n96 67\n137 18\n96 46\n137 23\n137 73\n137 94\n137 78\n96 46\n137 66\n137 84\n137 44\n2 35\n137 90\n137 81\n137 84\n2 35\n137 97\n137 57\n137 57\n137 47\n137 45\n",
"\n97 17\n94 92\n88 60\n97 78\n97 79\n97 65\n97 74\n97 46\n97 74\n97 12\n95 97\n88 17\n97 40\n97 74\n97 10\n88 60\n97 90\n94 39\n97 10\n88 17\n94 92\n97 92\n97 46\n94 12\n97 42\n94 74\n94 75\n90 94\n97 57\n94 18\n97 32\n97 65\n90 64\n94 75\n94 65\n97 17\n97 94\n97 17\n94 92\n88 17\n97 57\n97 32\n94 67\n88 17\n97 92\n88 78\n97 94\n97 18\n97 94\n94 95\n97 94\n94 67\n94 46\n97 39\n88 17\n",
"\n1000000 999998\n1000000 999998\n",
"\n99 1\n97 22\n99 1\n99 1\n80 60\n80 85\n97 16\n99 63\n99 1\n99 10\n99 90\n99 34\n99 15\n99 28\n97 12\n97 65\n99 10\n80 10\n97 18\n99 1\n97 10\n99 42\n97 15\n80 10\n97 83\n80 85\n99 90\n97 56\n99 90\n9 26\n99 80\n97 22\n85 97\n99 52\n97 21\n97 22\n99 45\n97 41\n97 15\n99 21\n99 20\n99 22\n99 43\n97 42\n97 16\n99 15\n99 15\n9 26\n97 21\n85 58\n97 70\n99 45\n99 45\n99 1\n97 56\n99 21\n99 45\n",
"\n1 0\n1 5\n5 5\n5 0\n5 0\n",
"\n7 2\n7 4\n7 2\n",
"\n144 36\n144 43\n144 87\n144 35\n82 36\n144 67\n144 43\n144 55\n82 0\n144 13\n82 34\n144 36\n",
"\n98 43\n98 23\n88 98\n98 97\n98 42\n98 42\n98 62\n98 10\n98 62\n98 87\n98 95\n98 86\n88 81\n98 79\n88 98\n98 65\n98 61\n98 69\n98 57\n98 97\n98 42\n98 65\n98 43\n98 24\n70 27\n98 48\n98 97\n98 29\n88 29\n98 24\n98 79\n98 61\n98 43\n98 97\n98 23\n98 92\n98 41\n98 59\n98 42\n70 10\n98 48\n98 43\n98 81\n98 27\n70 27\n98 41\n98 48\n98 59\n98 42\n98 16\n98 59\n98 92\n98 22\n98 92\n98 83\n98 81\n98 88\n98 42\n",
"\n97 17\n94 92\n88 60\n97 78\n97 79\n97 65\n97 74\n97 46\n97 74\n97 12\n95 97\n88 17\n97 40\n97 74\n97 10\n88 60\n97 90\n94 39\n97 10\n88 17\n94 92\n97 92\n97 46\n94 12\n97 42\n94 74\n94 75\n90 94\n97 57\n94 18\n97 17\n97 65\n90 64\n94 75\n94 65\n97 17\n97 94\n97 17\n94 92\n88 17\n97 57\n97 32\n94 67\n88 17\n97 92\n88 78\n97 94\n97 18\n97 94\n94 95\n97 94\n94 67\n94 46\n97 39\n88 17\n",
"\n1000000 999999\n1000000 999998\n",
"\n7 2\n7 4\n7 3\n",
"\n98 43\n98 23\n88 98\n98 97\n98 42\n98 42\n98 62\n98 10\n98 62\n98 87\n98 95\n98 86\n88 81\n98 79\n88 98\n98 65\n98 61\n98 69\n98 57\n98 97\n98 42\n98 65\n98 43\n98 24\n70 27\n98 48\n98 97\n98 29\n88 29\n98 24\n70 65\n98 61\n98 43\n98 97\n98 23\n98 92\n98 41\n98 59\n98 42\n70 10\n98 48\n98 43\n98 81\n98 27\n70 27\n98 41\n98 48\n98 59\n98 42\n98 16\n98 59\n98 92\n98 22\n98 92\n98 83\n98 81\n98 88\n98 42\n",
"\n100 33\n34 51\n100 100\n100 9\n100 1\n100 75\n100 60\n100 71\n100 40\n100 71\n14 34\n100 10\n100 17\n100 10\n100 1\n",
"\n99 71\n97 22\n99 1\n99 1\n80 60\n80 85\n97 16\n99 63\n99 1\n99 10\n99 90\n99 34\n99 15\n99 28\n97 12\n97 65\n99 10\n80 10\n97 18\n99 1\n97 10\n99 42\n97 15\n80 10\n97 83\n80 85\n99 90\n97 56\n99 90\n9 26\n99 80\n97 22\n85 97\n99 52\n97 21\n97 22\n99 45\n97 41\n97 15\n99 21\n99 20\n99 22\n99 43\n97 42\n97 16\n99 15\n99 15\n9 26\n97 21\n85 58\n97 70\n99 45\n99 45\n99 1\n97 56\n99 21\n99 45\n",
"\n98 43\n98 23\n88 98\n98 97\n98 42\n98 42\n98 62\n98 10\n98 62\n98 87\n98 95\n98 69\n88 81\n98 79\n88 98\n98 65\n98 61\n98 69\n98 57\n98 97\n98 42\n98 65\n98 43\n98 24\n70 27\n98 48\n98 97\n98 29\n88 29\n98 24\n70 65\n98 61\n98 43\n98 97\n98 23\n98 92\n98 41\n98 59\n98 42\n70 10\n98 48\n98 43\n98 81\n98 27\n70 27\n98 41\n98 48\n98 59\n98 42\n98 16\n98 59\n98 92\n98 22\n98 92\n98 83\n98 81\n98 88\n98 42\n",
"\n100 33\n34 51\n100 100\n100 9\n100 1\n100 12\n100 60\n100 71\n100 40\n100 71\n14 34\n100 10\n100 17\n100 10\n100 1\n",
"\n191 71\n97 22\n191 1\n191 1\n80 60\n80 85\n191 16\n191 63\n191 1\n191 10\n191 90\n191 34\n191 15\n191 28\n191 12\n97 65\n191 10\n80 10\n191 18\n191 1\n191 10\n191 42\n97 15\n80 10\n191 83\n80 85\n191 90\n97 56\n191 90\n9 26\n191 80\n97 22\n85 97\n191 52\n97 21\n97 22\n191 45\n191 41\n97 15\n191 21\n191 20\n191 22\n191 43\n97 42\n191 16\n191 15\n191 15\n9 26\n97 21\n85 58\n97 70\n191 45\n191 45\n191 1\n97 56\n191 21\n191 45\n",
"\n144 36\n144 43\n144 87\n144 35\n82 36\n144 67\n144 43\n144 105\n82 0\n144 13\n82 34\n144 36\n",
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"\n1000000 453800\n1000000 453800\n",
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"\n1000000 606166\n1000000 606166\n",
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"\n191 99\n97 22\n191 1\n191 1\n80 60\n80 55\n191 16\n191 63\n191 1\n191 56\n191 0\n191 34\n191 15\n191 28\n191 21\n97 65\n191 10\n80 10\n191 18\n191 1\n191 16\n191 42\n97 13\n80 10\n191 83\n80 55\n191 90\n97 56\n191 90\n9 26\n191 55\n97 22\n80 97\n191 52\n97 39\n97 22\n191 29\n191 45\n97 15\n191 21\n191 20\n191 22\n191 43\n97 42\n191 16\n191 15\n191 0\n9 26\n97 39\n80 58\n97 70\n191 45\n191 45\n191 1\n97 56\n191 21\n191 45\n",
"\n144 36\n144 43\n144 87\n144 35\n141 36\n144 67\n144 43\n141 36\n141 0\n144 13\n141 23\n144 36\n",
"\n171 33\n59 51\n171 100\n171 9\n171 2\n171 24\n100 171\n171 71\n171 98\n171 71\n20 59\n171 8\n171 17\n171 10\n171 2\n",
"\n191 99\n97 22\n191 1\n191 1\n80 60\n80 55\n191 16\n191 63\n191 1\n191 56\n191 0\n191 34\n191 15\n191 28\n191 21\n97 65\n191 10\n80 10\n191 18\n191 1\n191 16\n191 53\n97 13\n80 10\n191 83\n80 55\n191 90\n97 56\n191 90\n9 26\n191 55\n97 22\n80 97\n191 52\n97 39\n97 22\n191 29\n191 45\n97 15\n191 21\n191 20\n191 22\n191 43\n97 42\n191 16\n191 15\n191 0\n9 26\n97 39\n80 58\n97 70\n191 45\n191 45\n191 1\n97 56\n191 21\n191 45\n",
"\n144 4\n144 43\n144 87\n144 35\n141 36\n144 67\n144 43\n141 36\n141 0\n144 13\n141 23\n144 36\n",
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"\n191 77\n97 22\n191 1\n191 1\n80 60\n80 55\n191 16\n191 63\n191 1\n191 56\n191 0\n191 34\n191 15\n191 28\n191 21\n97 65\n191 10\n80 10\n191 18\n191 1\n191 16\n191 53\n97 13\n80 10\n191 83\n80 55\n191 90\n97 56\n191 90\n9 26\n191 55\n97 22\n80 97\n191 52\n97 39\n97 22\n191 29\n191 45\n97 15\n191 21\n191 20\n191 22\n191 43\n97 42\n191 16\n191 15\n191 0\n9 26\n97 39\n80 58\n97 70\n191 45\n191 45\n191 1\n97 56\n191 21\n191 45\n",
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"\n180 63\n180 46\n180 30\n180 23\n180 23\n180 57\n180 72\n180 47\n180 25\n180 84\n114 67\n180 5\n114 46\n180 23\n180 73\n180 94\n180 78\n114 46\n180 66\n180 84\n180 44\n2 36\n180 90\n180 0\n180 84\n2 36\n180 97\n180 57\n180 84\n180 77\n114 43\n",
"\n171 33\n59 51\n171 100\n171 9\n171 2\n171 24\n100 171\n171 71\n71 72\n171 71\n20 59\n171 8\n171 3\n171 10\n171 2\n",
"\n191 77\n97 22\n191 1\n191 1\n80 60\n80 55\n191 16\n191 63\n191 1\n191 56\n191 0\n191 34\n191 15\n191 28\n191 21\n97 65\n191 10\n80 10\n191 18\n191 1\n191 16\n191 53\n97 13\n80 10\n191 83\n80 55\n191 90\n97 56\n191 90\n9 26\n191 55\n97 22\n80 97\n191 52\n97 39\n97 22\n191 29\n191 45\n97 15\n191 21\n191 20\n191 22\n191 5\n97 42\n191 16\n191 15\n191 0\n9 26\n97 39\n80 58\n97 70\n191 45\n191 45\n191 1\n97 56\n191 21\n191 45\n",
"\n180 63\n180 46\n180 30\n180 23\n180 23\n180 57\n180 72\n180 47\n180 25\n180 84\n114 67\n180 5\n114 46\n180 23\n180 73\n180 94\n180 78\n114 46\n180 66\n180 84\n180 44\n4 36\n180 90\n180 0\n180 84\n4 36\n180 97\n180 57\n180 84\n180 77\n114 43\n",
"\n191 77\n97 22\n191 1\n191 1\n80 60\n80 55\n191 16\n191 63\n191 1\n191 56\n191 0\n191 34\n191 15\n191 28\n191 21\n97 65\n191 10\n80 10\n191 18\n191 1\n191 16\n191 53\n97 13\n80 10\n191 83\n80 55\n191 90\n97 56\n191 90\n9 26\n191 55\n97 22\n80 97\n191 52\n97 39\n97 22\n191 29\n191 45\n97 42\n191 21\n191 20\n191 22\n191 5\n97 42\n191 16\n191 15\n191 0\n9 26\n97 39\n80 58\n97 70\n191 45\n191 45\n191 1\n97 56\n191 21\n191 45\n",
"\n180 14\n180 46\n180 30\n180 23\n180 23\n180 57\n180 72\n180 47\n180 25\n180 84\n114 67\n180 5\n114 46\n180 23\n180 73\n180 94\n180 78\n114 46\n180 66\n180 84\n180 44\n4 36\n180 90\n180 0\n180 84\n4 36\n180 97\n180 57\n180 84\n180 77\n114 43\n",
"\n191 77\n97 22\n191 1\n191 1\n80 60\n80 55\n191 16\n191 63\n191 1\n191 56\n191 0\n191 34\n191 15\n191 28\n191 21\n97 65\n191 10\n80 10\n191 18\n191 1\n191 3\n191 53\n97 13\n80 10\n191 83\n80 55\n191 90\n97 56\n191 90\n9 26\n191 55\n97 22\n80 97\n191 52\n97 39\n97 22\n191 29\n191 45\n97 42\n191 21\n191 20\n191 22\n191 5\n97 42\n191 16\n191 15\n191 0\n9 26\n97 39\n80 58\n97 70\n191 45\n191 45\n191 1\n97 56\n191 21\n191 45\n",
"\n191 77\n97 22\n191 1\n191 1\n80 60\n80 55\n191 16\n191 63\n191 1\n191 56\n191 0\n191 34\n191 15\n191 28\n191 21\n97 65\n191 10\n80 10\n191 18\n191 1\n191 3\n191 53\n97 5\n80 10\n191 83\n80 55\n191 90\n97 56\n191 90\n9 26\n191 55\n97 22\n80 97\n191 52\n97 39\n97 22\n191 29\n191 45\n97 42\n191 21\n191 20\n191 22\n191 5\n97 42\n191 16\n191 15\n191 0\n9 26\n97 39\n80 58\n97 70\n191 45\n191 45\n191 1\n97 56\n191 21\n191 45\n",
"\n180 14\n180 46\n180 30\n180 23\n180 23\n180 57\n180 72\n180 47\n180 25\n180 84\n114 67\n180 5\n114 46\n180 23\n180 73\n180 94\n180 78\n114 46\n180 66\n180 84\n180 44\n4 36\n180 90\n180 0\n180 84\n4 36\n180 97\n180 57\n180 84\n180 8\n114 43\n",
"\n191 77\n97 22\n191 1\n191 1\n80 60\n80 55\n191 16\n191 63\n191 1\n191 56\n191 0\n191 21\n191 15\n191 28\n191 21\n97 65\n191 10\n80 10\n191 18\n191 1\n191 3\n191 53\n97 5\n80 10\n191 83\n80 55\n191 90\n97 56\n191 90\n9 26\n191 55\n97 22\n80 97\n191 52\n97 39\n97 22\n191 29\n191 45\n97 42\n191 21\n191 20\n191 22\n191 5\n97 42\n191 16\n191 15\n191 0\n9 26\n97 39\n80 58\n97 70\n191 45\n191 45\n191 1\n97 56\n191 21\n191 45\n",
"\n180 14\n180 46\n180 30\n180 23\n180 23\n180 57\n180 72\n180 47\n180 25\n180 84\n114 67\n180 5\n114 46\n180 63\n180 73\n180 94\n180 78\n114 46\n180 66\n180 84\n180 44\n4 36\n180 90\n180 0\n180 84\n4 36\n180 97\n180 57\n180 84\n180 8\n114 43\n",
"\n180 14\n180 46\n180 30\n180 23\n180 23\n180 57\n180 72\n180 47\n180 15\n180 84\n114 67\n180 5\n114 46\n180 63\n180 73\n180 94\n180 78\n114 46\n180 66\n180 84\n180 44\n4 36\n180 90\n180 0\n180 84\n4 36\n180 97\n180 57\n180 84\n180 8\n114 43\n",
"\n191 77\n97 22\n191 1\n191 1\n80 60\n80 55\n191 16\n191 63\n191 1\n191 56\n191 0\n191 21\n191 15\n191 28\n191 21\n97 65\n191 10\n80 10\n191 18\n191 1\n191 3\n191 53\n97 5\n80 10\n191 83\n80 55\n191 90\n97 56\n97 65\n9 26\n191 55\n97 22\n80 97\n191 52\n97 39\n97 22\n191 29\n191 45\n97 42\n191 21\n191 20\n191 22\n191 5\n97 42\n191 16\n191 15\n191 0\n9 26\n97 39\n80 58\n97 70\n191 45\n191 45\n191 1\n97 56\n191 21\n191 45\n",
"\n180 14\n180 87\n180 30\n180 23\n180 23\n180 57\n180 72\n180 47\n180 15\n180 84\n114 67\n180 5\n114 87\n180 63\n180 73\n180 94\n180 78\n114 87\n180 66\n180 84\n180 44\n4 36\n180 90\n180 0\n180 84\n4 36\n180 97\n180 57\n180 84\n180 8\n114 43\n",
"\n191 77\n97 22\n191 1\n191 1\n80 60\n80 55\n191 16\n191 63\n191 1\n191 56\n191 0\n191 21\n191 15\n191 28\n191 21\n97 65\n191 10\n80 10\n191 18\n191 1\n191 3\n191 53\n97 5\n80 10\n191 83\n80 55\n191 90\n97 56\n97 65\n9 26\n191 55\n97 22\n80 97\n191 52\n97 39\n97 22\n191 29\n191 45\n80 97\n191 21\n191 20\n191 22\n191 5\n97 42\n191 16\n191 15\n191 0\n9 26\n97 39\n80 58\n97 70\n191 45\n191 45\n191 1\n97 56\n191 21\n191 45\n",
"\n180 14\n180 87\n180 30\n180 23\n180 23\n180 57\n180 72\n180 47\n180 15\n180 84\n114 67\n180 5\n114 87\n180 63\n180 73\n180 94\n180 78\n114 87\n180 66\n180 84\n180 40\n4 36\n180 90\n180 0\n180 84\n4 36\n180 97\n180 57\n180 84\n180 8\n114 43\n",
"\n191 77\n97 22\n191 1\n191 1\n80 60\n80 55\n191 16\n191 63\n191 1\n191 56\n191 -1\n191 21\n191 15\n191 28\n191 21\n97 65\n191 10\n80 10\n191 18\n191 1\n191 3\n191 53\n97 5\n80 10\n191 83\n80 55\n191 90\n97 56\n97 65\n9 26\n191 55\n97 22\n80 97\n191 52\n97 39\n97 22\n191 29\n191 45\n80 97\n191 21\n191 20\n191 22\n191 5\n97 42\n191 16\n191 15\n191 -1\n9 26\n97 39\n80 58\n97 70\n191 45\n191 45\n191 1\n97 56\n191 21\n191 45\n",
"\n191 77\n97 22\n191 1\n191 1\n80 60\n80 55\n191 16\n191 63\n191 1\n191 56\n191 -1\n191 21\n191 15\n191 28\n191 21\n97 65\n191 10\n80 10\n191 18\n191 1\n191 3\n191 60\n97 5\n80 10\n191 83\n80 55\n191 90\n97 56\n97 65\n9 26\n191 55\n97 22\n80 97\n191 52\n97 39\n97 22\n191 29\n191 45\n80 97\n191 21\n191 20\n191 22\n191 5\n97 42\n191 16\n191 15\n191 -1\n9 26\n97 39\n80 58\n97 70\n191 45\n191 45\n191 1\n97 56\n191 21\n191 45\n",
"\n180 14\n180 87\n180 30\n180 23\n180 23\n180 57\n180 72\n180 47\n180 73\n180 84\n114 67\n180 5\n114 87\n180 63\n180 73\n180 94\n180 78\n114 87\n180 66\n180 84\n180 40\n4 36\n180 90\n180 0\n180 84\n4 36\n180 97\n180 57\n180 84\n180 8\n114 43\n",
"\n191 77\n97 22\n191 1\n191 1\n80 60\n80 55\n191 16\n191 63\n191 1\n191 56\n191 -1\n191 21\n191 15\n191 28\n191 21\n97 65\n191 10\n80 10\n191 18\n191 1\n191 3\n191 60\n97 5\n80 10\n191 83\n80 55\n191 90\n97 56\n97 65\n9 43\n191 55\n97 22\n80 97\n191 52\n97 39\n97 22\n191 29\n191 45\n80 97\n191 21\n191 20\n191 22\n191 5\n97 42\n191 16\n191 15\n191 -1\n9 43\n97 39\n80 58\n97 70\n191 45\n191 45\n191 1\n97 56\n191 21\n191 45\n",
"\n99 1\n97 22\n99 1\n99 1\n80 60\n80 85\n97 16\n99 63\n99 1\n99 10\n99 90\n99 34\n99 15\n99 28\n97 12\n97 65\n99 10\n80 10\n97 18\n99 56\n97 10\n99 42\n97 15\n80 10\n97 83\n80 85\n99 90\n97 56\n99 90\n9 26\n99 80\n97 22\n85 97\n99 52\n97 21\n97 22\n99 45\n97 41\n99 28\n99 21\n99 20\n99 22\n99 43\n97 42\n97 16\n99 15\n99 15\n9 26\n97 21\n85 58\n97 70\n99 45\n99 45\n99 1\n97 56\n99 21\n99 45\n",
"\n1 2\n5 1\n5 5\n5 1\n5 2\n",
"\n5 1\n5 4\n5 2\n",
"\n97 36\n97 43\n97 87\n97 35\n82 36\n97 51\n97 43\n97 55\n82 0\n97 13\n82 34\n97 36\n",
"\n5728 41414\n457879 1\n457879 5728\n457879 1\n457879 1\n457879 1\n457879 1\n457879 1\n457879 1\n457879 1\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Recently, on the course of algorithms and data structures, Valeriy learned how to use a deque. He built a deque filled with n elements. The i-th element is a_i (i = 1, 2, …, n). He gradually takes the first two leftmost elements from the deque (let's call them A and B, respectively), and then does the following: if A > B, he writes A to the beginning and writes B to the end of the deque, otherwise, he writes to the beginning B, and A writes to the end of the deque. We call this sequence of actions an operation.
For example, if deque was [2, 3, 4, 5, 1], on the operation he will write B=3 to the beginning and A=2 to the end, so he will get [3, 4, 5, 1, 2].
The teacher of the course, seeing Valeriy, who was passionate about his work, approached him and gave him q queries. Each query consists of the singular number m_j (j = 1, 2, …, q). It is required for each query to answer which two elements he will pull out on the m_j-th operation.
Note that the queries are independent and for each query the numbers A and B should be printed in the order in which they will be pulled out of the deque.
Deque is a data structure representing a list of elements where insertion of new elements or deletion of existing elements can be made from both sides.
Input
The first line contains two integers n and q (2 ≤ n ≤ 10^5, 0 ≤ q ≤ 3 ⋅ 10^5) — the number of elements in the deque and the number of queries. The second line contains n integers a_1, a_2, ..., a_n, where a_i (0 ≤ a_i ≤ 10^9) — the deque element in i-th position. The next q lines contain one number each, meaning m_j (1 ≤ m_j ≤ 10^{18}).
Output
For each teacher's query, output two numbers A and B — the numbers that Valeriy pulls out of the deque for the m_j-th operation.
Examples
Input
5 3
1 2 3 4 5
1
2
10
Output
1 2
2 3
5 2
Input
2 0
0 0
Output
Note
Consider all 10 steps for the first test in detail:
1. [1, 2, 3, 4, 5] — on the first operation, A and B are 1 and 2, respectively.
So, 2 we write to the beginning of the deque, and 1 — to the end.
We get the following status of the deque: [2, 3, 4, 5, 1].
2. [2, 3, 4, 5, 1] ⇒ A = 2, B = 3.
3. [3, 4, 5, 1, 2]
4. [4, 5, 1, 2, 3]
5. [5, 1, 2, 3, 4]
6. [5, 2, 3, 4, 1]
7. [5, 3, 4, 1, 2]
8. [5, 4, 1, 2, 3]
9. [5, 1, 2, 3, 4]
10. [5, 2, 3, 4, 1] ⇒ A = 5, B = 2.
### Input:
5 3
1 2 3 4 5
1
2
10
### Output:
1 2
2 3
5 2
### Input:
2 0
0 0
### Output:
### Code:
import sys
n,q=list(map(int,input().split()))
a=list(map(int,input().split()))
mx1=max(a)
a1=[]
dp={}
for i in range(q):
a1.append(int(input()))
if a1==[]:
mx=0
else:
mx=max(a1)
count=0
while(1):
count+=1
val1=a[0]
val2=a[1]
if val1==mx1:
break
if val1>val2:
a.remove(val2)
a.append(val2)
else:
a.remove(val1)
a.append(val1)
dp[count]=(val1,val2)
#print(a)
for x in a1:
if x in dp:
print(dp[x][0],dp[x][1])
else:
xx=(x-count)%(n-1)
print(a[0],a[xx+1])
"""
12345 12
23451 23
34512 34
45123 45
51234 51
52341 52
53412 53
54123 54
51234 51
3 4 5 2 1
34521 34
45213 45
a=[5,2,1,3,4]
52134 52 xx=0 0,1
51342 51 xx=1 0,2
53421 53 xx=2 0,3
54213 54 xx=3 0,4
52134 52 xx=4 0,1
51342 51
53421 53
"""
|
1199_C. MP3_10485
|
One common way of digitalizing sound is to record sound intensity at particular time moments. For each time moment intensity is recorded as a non-negative integer. Thus we can represent a sound file as an array of n non-negative integers.
If there are exactly K distinct values in the array, then we need k = ⌈ log_{2} K ⌉ bits to store each value. It then takes nk bits to store the whole file.
To reduce the memory consumption we need to apply some compression. One common way is to reduce the number of possible intensity values. We choose two integers l ≤ r, and after that all intensity values are changed in the following way: if the intensity value is within the range [l;r], we don't change it. If it is less than l, we change it to l; if it is greater than r, we change it to r. You can see that we lose some low and some high intensities.
Your task is to apply this compression in such a way that the file fits onto a disk of size I bytes, and the number of changed elements in the array is minimal possible.
We remind you that 1 byte contains 8 bits.
k = ⌈ log_{2} K ⌉ is the smallest integer such that K ≤ 2^{k}. In particular, if K = 1, then k = 0.
Input
The first line contains two integers n and I (1 ≤ n ≤ 4 ⋅ 10^{5}, 1 ≤ I ≤ 10^{8}) — the length of the array and the size of the disk in bytes, respectively.
The next line contains n integers a_{i} (0 ≤ a_{i} ≤ 10^{9}) — the array denoting the sound file.
Output
Print a single integer — the minimal possible number of changed elements.
Examples
Input
6 1
2 1 2 3 4 3
Output
2
Input
6 2
2 1 2 3 4 3
Output
0
Input
6 1
1 1 2 2 3 3
Output
2
Note
In the first example we can choose l=2, r=3. The array becomes 2 2 2 3 3 3, the number of distinct elements is K=2, and the sound file fits onto the disk. Only two values are changed.
In the second example the disk is larger, so the initial file fits it and no changes are required.
In the third example we have to change both 1s or both 3s.
|
from collections import *
from math import *
n,k = map(int,input().split())
a = list(map(int,input().split()))
d = Counter(a)
a.sort()
val = [0 for i in range(400005)]
a = list(set(a))
a.sort()
n1 = len(a)
val[0] = d[a[0]]
for i in range(1,n1):
val[i] = val[i-1] + d[a[i]]
m = n1
#print(n1)
for m in range(n1,0,-1):
s = ceil(log2(m))
if s*n <= 8*k:
break
#print(m,val[:10])
m1 = val[m-1]
for i in range(m,n1):
m1 = max(m1,val[i]-val[i-m])
print(n-m1)
|
{
"input": [
"6 2\n2 1 2 3 4 3\n",
"6 1\n1 1 2 2 3 3\n",
"6 1\n2 1 2 3 4 3\n",
"4 2\n2 2 2 1\n",
"40 1\n296861916 110348711 213599874 304979682 902720247 958794999 445626005 29685036 968749742 772121742 50110079 72399009 347194050 322418543 594963355 407238845 847251668 210179965 293944170 300817194 842872332 82882809 446438478 304657690 343250734 567326942 47727237 662711343 59995716 812214268 994315801 193163726 656281454 249432773 772706196 977253852 342331261 182317828 550599535 3939813\n",
"3 11\n1 2 3\n",
"20 8\n1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2\n",
"50 20\n592183311 362557946 154127088 616872926 395353745 675069471 509655682 79915471 356656666 937992998 304422065 724106263 472338455 792258113 796069631 663370025 201799298 566151622 722278085 508905399 703159587 690854023 925377265 11010958 69791159 990158269 535460930 167415727 999216963 237203826 693974848 530462137 555061429 744123832 887168514 479773974 575345653 282142246 899762676 446274594 338501746 168668673 408947684 226311538 645441958 258972430 216333311 338561078 123733185 539429791\n",
"10 1\n589934963 440265648 161048053 196789927 951616256 63404428 660569162 779938975 237139603 31052281\n",
"64 40\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
"2 1\n1 3\n",
"1 1\n1\n",
"8 30\n1 2 3 4 5 6 7 8\n",
"9 1\n1 2 1 2 1 2 1 2 1000000000\n",
"5 100000000\n1 2 3 4 5\n",
"6 1213\n1 1 2 2 3 3\n",
"5 100000\n1 2 3 3 4\n",
"3 120\n1 2 3\n",
"10 500\n1 2 3 4 5 6 7 8 9 10\n",
"6 100000000\n2 1 2 3 4 3\n",
"9 100000000\n1 2 3 4 5 6 7 8 9\n",
"2 100000\n2 3\n",
"8 10000000\n1 2 3 4 5 6 7 8\n",
"2 64\n1 2\n",
"10 100\n1 2 3 4 5 6 7 8 9 10\n",
"5 100000000\n1 1 2 2 5\n",
"2 40000000\n3 9\n",
"8 65\n1 2 3 4 5 6 7 8\n",
"2 30000000\n2 5\n",
"3 288383\n2 2 2\n",
"5 100000\n1 2 3 4 5\n",
"2 1000000\n1 1\n",
"100 800\n1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10\n",
"6 100000\n2 1 2 3 4 3\n",
"100 1000\n1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10\n",
"8 31\n2 8 5 1 10 5 9 9\n",
"81 800\n2 8 5 1 10 5 9 9 3 5 6 6 2 8 2 2 6 3 8 7 2 5 3 4 3 3 2 7 9 6 8 7 2 9 10 3 8 10 6 5 4 2 3 4 4 5 2 2 4 9 8 5 3 8 8 10 4 2 10 9 7 6 1 3 9 7 1 3 5 9 7 6 1 10 1 1 7 2 4 9 10\n",
"3 10000000\n1 2 3\n",
"8 32\n1 2 3 4 5 6 7 8\n",
"100 1000\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
"5 70\n1 2 3 4 5\n",
"5 100000\n1 2 2 3 4\n",
"5 1000000\n1 2 3 3 4\n",
"1 10000000\n1\n",
"8 64\n1 1 1 1 1 1 1 1\n",
"6 48\n2 1 2 3 4 3\n",
"3 100000000\n1 1 2\n",
"2 30000000\n1 3\n",
"10 1000000\n1 2 3 4 5 6 7 8 9 10\n",
"2 100000000\n1 2\n",
"8 33\n1 2 3 4 5 6 7 8\n",
"2 64\n2 3\n",
"8 31\n1 1 2 2 3 3 4 4\n",
"10 100\n1 1 2 2 2 3 3 3 3 4\n",
"5 100\n1 2 3 4 5\n",
"8 63\n1 2 3 4 5 6 7 8\n",
"7 999992\n1 2 3 4 5 6 7\n",
"100 1249\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100\n",
"2 8\n1 2\n",
"50 400\n0 30 60 90 120 150 180 210 240 270 300 330 360 390 420 450 480 510 540 570 600 630 660 690 720 750 780 810 840 870 900 930 960 990 1020 1050 1080 1110 1140 1170 1200 1230 1260 1290 1320 1350 1380 1410 1440 1470\n",
"5 1234567\n1 2 3 4 5\n",
"2 1000\n1 2\n",
"1 100000000\n69\n",
"1 4\n1\n",
"8 31\n1 2 3 4 5 6 7 8\n",
"2 10000\n1 2\n",
"8 64\n1 2 3 4 5 6 7 8\n",
"8 31\n1 1 1 1 1 1 1 1\n",
"1 100000000\n1\n",
"4 2\n2 2 2 2\n",
"40 1\n296861916 110348711 213599874 304979682 902720247 958794999 445626005 29685036 1006613858 772121742 50110079 72399009 347194050 322418543 594963355 407238845 847251668 210179965 293944170 300817194 842872332 82882809 446438478 304657690 343250734 567326942 47727237 662711343 59995716 812214268 994315801 193163726 656281454 249432773 772706196 977253852 342331261 182317828 550599535 3939813\n",
"50 20\n592183311 362557946 154127088 616872926 395353745 675069471 509655682 79915471 356656666 937992998 304422065 724106263 472338455 792258113 796069631 663370025 201799298 566151622 722278085 827802227 703159587 690854023 925377265 11010958 69791159 990158269 535460930 167415727 999216963 237203826 693974848 530462137 555061429 744123832 887168514 479773974 575345653 282142246 899762676 446274594 338501746 168668673 408947684 226311538 645441958 258972430 216333311 338561078 123733185 539429791\n",
"10 1\n589934963 440265648 161048053 196789927 951616256 63404428 660569162 779938975 122275696 31052281\n",
"9 1\n1 2 1 2 2 2 1 2 1000000000\n",
"2 00000\n1 2\n",
"3 11\n1 2 1\n",
"20 8\n1 1 0 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2\n",
"64 40\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
"1 1\n0\n",
"8 30\n1 2 3 4 5 6 13 8\n",
"5 100000000\n1 3 3 4 5\n",
"6 1213\n0 1 2 2 3 3\n",
"5 100000\n1 2 6 3 4\n",
"3 25\n1 2 3\n",
"10 500\n1 2 3 4 5 6 7 9 9 10\n",
"6 100000000\n2 2 2 3 4 3\n",
"9 100000000\n1 2 3 4 5 1 7 8 9\n",
"2 100000\n2 0\n",
"8 10000000\n2 2 3 4 5 6 7 8\n",
"2 64\n1 3\n",
"10 100\n1 2 3 4 5 6 7 8 1 10\n",
"8 28\n1 2 3 4 5 6 7 8\n",
"2 30000000\n0 5\n",
"5 100000\n0 2 3 4 5\n",
"2 1000010\n1 1\n",
"100 800\n1 2 3 4 5 12 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10\n",
"6 100000\n2 1 2 3 5 3\n",
"100 1000\n1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 2 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10\n",
"8 31\n2 16 5 1 10 5 9 9\n",
"81 800\n2 8 5 1 10 5 9 9 3 5 6 6 2 8 2 2 6 3 8 7 2 5 3 4 3 3 2 7 9 6 8 7 2 9 10 3 8 10 6 5 4 2 3 4 4 5 2 2 4 9 8 5 3 12 8 10 4 2 10 9 7 6 1 3 9 7 1 3 5 9 7 6 1 10 1 1 7 2 4 9 10\n",
"3 10000000\n0 2 3\n",
"100 1000\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1\n",
"5 70\n1 1 3 4 5\n",
"5 100000\n1 2 2 3 8\n",
"5 1000000\n2 2 3 3 4\n",
"8 57\n1 1 1 1 1 1 1 1\n",
"6 48\n2 1 1 3 4 3\n",
"10 1000000\n1 2 3 4 5 6 8 8 9 10\n",
"2 101000000\n1 2\n",
"8 33\n1 2 3 4 8 6 7 8\n",
"2 54\n1 3\n",
"8 31\n0 1 2 2 3 3 4 4\n",
"10 100\n1 1 2 2 1 3 3 3 3 4\n",
"5 100\n1 0 3 4 5\n",
"8 63\n1 2 3 4 5 9 7 8\n",
"7 999992\n1 2 4 4 5 6 7\n",
"100 1249\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 23 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100\n",
"2 6\n1 2\n",
"50 400\n0 22 60 90 120 150 180 210 240 270 300 330 360 390 420 450 480 510 540 570 600 630 660 690 720 750 780 810 840 870 900 930 960 990 1020 1050 1080 1110 1140 1170 1200 1230 1260 1290 1320 1350 1380 1410 1440 1470\n",
"5 1234567\n1 2 3 4 2\n",
"2 1100\n1 2\n",
"1 100000000\n48\n",
"1 6\n1\n",
"8 31\n1 2 3 4 5 6 7 13\n",
"8 64\n1 2 3 4 5 6 13 8\n",
"8 16\n1 1 1 1 1 1 1 1\n",
"1 100000010\n1\n",
"4 2\n2 1 2 2\n",
"40 1\n296861916 171061080 213599874 304979682 902720247 958794999 445626005 29685036 1006613858 772121742 50110079 72399009 347194050 322418543 594963355 407238845 847251668 210179965 293944170 300817194 842872332 82882809 446438478 304657690 343250734 567326942 47727237 662711343 59995716 812214268 994315801 193163726 656281454 249432773 772706196 977253852 342331261 182317828 550599535 3939813\n",
"3 11\n2 2 1\n",
"20 8\n1 1 0 1 1 1 1 1 2 1 1 2 2 2 2 2 2 2 2 2\n",
"50 20\n592183311 362557946 154127088 616872926 395353745 675069471 509655682 79915471 356656666 937992998 304422065 724106263 472338455 792258113 796069631 1325917135 201799298 566151622 722278085 827802227 703159587 690854023 925377265 11010958 69791159 990158269 535460930 167415727 999216963 237203826 693974848 530462137 555061429 744123832 887168514 479773974 575345653 282142246 899762676 446274594 338501746 168668673 408947684 226311538 645441958 258972430 216333311 338561078 123733185 539429791\n",
"10 1\n589934963 440265648 161048053 281428778 951616256 63404428 660569162 779938975 122275696 31052281\n",
"64 40\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
"1 2\n1\n",
"8 30\n1 3 3 4 5 6 13 8\n"
],
"output": [
"0",
"2",
"2\n",
"0",
"39",
"0",
"0",
"42",
"9",
"0",
"0",
"0",
"0",
"5",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0",
"0\n",
"39\n",
"42\n",
"9\n",
"4\n",
"1\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"39\n",
"0\n",
"0\n",
"42\n",
"9\n",
"0\n",
"0\n",
"0\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
One common way of digitalizing sound is to record sound intensity at particular time moments. For each time moment intensity is recorded as a non-negative integer. Thus we can represent a sound file as an array of n non-negative integers.
If there are exactly K distinct values in the array, then we need k = ⌈ log_{2} K ⌉ bits to store each value. It then takes nk bits to store the whole file.
To reduce the memory consumption we need to apply some compression. One common way is to reduce the number of possible intensity values. We choose two integers l ≤ r, and after that all intensity values are changed in the following way: if the intensity value is within the range [l;r], we don't change it. If it is less than l, we change it to l; if it is greater than r, we change it to r. You can see that we lose some low and some high intensities.
Your task is to apply this compression in such a way that the file fits onto a disk of size I bytes, and the number of changed elements in the array is minimal possible.
We remind you that 1 byte contains 8 bits.
k = ⌈ log_{2} K ⌉ is the smallest integer such that K ≤ 2^{k}. In particular, if K = 1, then k = 0.
Input
The first line contains two integers n and I (1 ≤ n ≤ 4 ⋅ 10^{5}, 1 ≤ I ≤ 10^{8}) — the length of the array and the size of the disk in bytes, respectively.
The next line contains n integers a_{i} (0 ≤ a_{i} ≤ 10^{9}) — the array denoting the sound file.
Output
Print a single integer — the minimal possible number of changed elements.
Examples
Input
6 1
2 1 2 3 4 3
Output
2
Input
6 2
2 1 2 3 4 3
Output
0
Input
6 1
1 1 2 2 3 3
Output
2
Note
In the first example we can choose l=2, r=3. The array becomes 2 2 2 3 3 3, the number of distinct elements is K=2, and the sound file fits onto the disk. Only two values are changed.
In the second example the disk is larger, so the initial file fits it and no changes are required.
In the third example we have to change both 1s or both 3s.
### Input:
6 2
2 1 2 3 4 3
### Output:
0
### Input:
6 1
1 1 2 2 3 3
### Output:
2
### Code:
from collections import *
from math import *
n,k = map(int,input().split())
a = list(map(int,input().split()))
d = Counter(a)
a.sort()
val = [0 for i in range(400005)]
a = list(set(a))
a.sort()
n1 = len(a)
val[0] = d[a[0]]
for i in range(1,n1):
val[i] = val[i-1] + d[a[i]]
m = n1
#print(n1)
for m in range(n1,0,-1):
s = ceil(log2(m))
if s*n <= 8*k:
break
#print(m,val[:10])
m1 = val[m-1]
for i in range(m,n1):
m1 = max(m1,val[i]-val[i-m])
print(n-m1)
|
1216_B. Shooting_10489
|
Recently Vasya decided to improve his pistol shooting skills. Today his coach offered him the following exercise. He placed n cans in a row on a table. Cans are numbered from left to right from 1 to n. Vasya has to knock down each can exactly once to finish the exercise. He is allowed to choose the order in which he will knock the cans down.
Vasya knows that the durability of the i-th can is a_i. It means that if Vasya has already knocked x cans down and is now about to start shooting the i-th one, he will need (a_i ⋅ x + 1) shots to knock it down. You can assume that if Vasya starts shooting the i-th can, he will be shooting it until he knocks it down.
Your task is to choose such an order of shooting so that the number of shots required to knock each of the n given cans down exactly once is minimum possible.
Input
The first line of the input contains one integer n (2 ≤ n ≤ 1 000) — the number of cans.
The second line of the input contains the sequence a_1, a_2, ..., a_n (1 ≤ a_i ≤ 1 000), where a_i is the durability of the i-th can.
Output
In the first line print the minimum number of shots required to knock each of the n given cans down exactly once.
In the second line print the sequence consisting of n distinct integers from 1 to n — the order of indices of cans that minimizes the number of shots required. If there are several answers, you can print any of them.
Examples
Input
3
20 10 20
Output
43
1 3 2
Input
4
10 10 10 10
Output
64
2 1 4 3
Input
6
5 4 5 4 4 5
Output
69
6 1 3 5 2 4
Input
2
1 4
Output
3
2 1
Note
In the first example Vasya can start shooting from the first can. He knocks it down with the first shot because he haven't knocked any other cans down before. After that he has to shoot the third can. To knock it down he shoots 20 ⋅ 1 + 1 = 21 times. After that only second can remains. To knock it down Vasya shoots 10 ⋅ 2 + 1 = 21 times. So the total number of shots is 1 + 21 + 21 = 43.
In the second example the order of shooting does not matter because all cans have the same durability.
|
n = map(int, input().split())
A = list(map(int, input().split()))
la = []
ind = 1
for a in A:
la.append((a, ind))
ind += 1
la.sort(key=lambda x: x[0], reverse=True)
# print(la)
x = 0
sm = 0
li = []
for tp in la:
a = tp[0]
sm += (a * x + 1)
x += 1
li.append(tp[1])
print(sm)
print(" ".join(str(i) for i in li))
|
{
"input": [
"3\n20 10 20\n",
"2\n1 4\n",
"4\n10 10 10 10\n",
"6\n5 4 5 4 4 5\n",
"5\n13 16 20 18 11\n",
"5\n13 16 20 33 11\n",
"3\n8 10 20\n",
"2\n0 4\n",
"6\n5 1 5 4 4 5\n",
"5\n13 16 20 33 15\n",
"6\n5 1 5 2 4 5\n",
"2\n-1 5\n",
"6\n5 1 7 2 4 5\n",
"3\n8 17 49\n",
"6\n5 2 7 2 4 5\n",
"3\n8 21 49\n",
"6\n5 2 7 2 3 5\n",
"3\n12 21 49\n",
"6\n5 2 7 3 3 5\n",
"3\n12 29 49\n",
"6\n5 2 7 3 3 6\n",
"3\n12 49 49\n",
"2\n1 9\n",
"6\n5 2 7 2 3 6\n",
"3\n12 49 34\n",
"3\n12 49 1\n",
"3\n5 45 1\n",
"2\n2 12\n",
"3\n6 45 1\n",
"3\n4 45 1\n",
"3\n8 88 1\n",
"3\n8 15 2\n",
"2\n2 0\n",
"2\n2 1\n",
"3\n14 23 2\n",
"3\n0 23 2\n",
"3\n0 23 4\n",
"3\n0 29 6\n",
"3\n0 29 9\n",
"3\n0 29 11\n",
"3\n0 29 5\n",
"2\n-2 0\n",
"2\n-4 0\n",
"3\n0 42 8\n",
"2\n-3 0\n",
"3\n-1 46 0\n",
"3\n-1 25 1\n",
"3\n-1 0 0\n",
"5\n13 9 20 18 11\n",
"3\n20 11 20\n",
"4\n10 10 10 11\n",
"5\n15 16 20 33 11\n",
"3\n8 2 20\n",
"5\n13 3 20 33 15\n",
"3\n8 19 35\n",
"6\n5 0 5 2 4 5\n",
"3\n8 18 49\n",
"6\n5 1 7 2 4 0\n",
"3\n4 17 49\n",
"3\n8 10 35\n",
"2\n0 5\n",
"3\n8 10 49\n",
"2\n-1 4\n",
"2\n-1 8\n",
"2\n0 8\n",
"2\n0 9\n",
"2\n1 8\n",
"2\n1 15\n",
"3\n12 45 1\n",
"2\n1 12\n",
"2\n2 7\n",
"2\n2 5\n",
"3\n4 88 1\n",
"2\n2 9\n",
"2\n2 18\n",
"3\n8 15 1\n",
"2\n2 15\n",
"3\n8 23 2\n",
"2\n2 2\n",
"2\n0 1\n",
"2\n0 2\n",
"3\n0 46 4\n",
"2\n-1 2\n",
"3\n0 29 4\n",
"2\n1 2\n",
"2\n1 1\n",
"2\n0 0\n",
"2\n-1 1\n",
"2\n-1 0\n",
"3\n0 42 5\n",
"3\n0 42 9\n",
"3\n-1 42 8\n",
"2\n-3 1\n",
"3\n-1 46 8\n",
"2\n-3 2\n",
"2\n-4 1\n",
"3\n-1 25 0\n",
"2\n2 4\n",
"2\n0 3\n",
"2\n0 6\n"
],
"output": [
"43\n1 3 2\n",
"3\n2 1\n",
"64\n1 2 3 4\n",
"69\n1 3 6 2 4 5\n",
"138\n3 4 2 1 5\n",
"140\n4 3 2 1 5\n",
"29\n3 2 1\n",
"2\n2 1\n",
"54\n6 3 1 5 4 2\n",
"154\n4 3 2 5 1\n",
"46\n6 3 1 5 4 2\n",
"1\n2 1\n",
"46\n3 6 1 5 4 2\n",
"36\n3 2 1\n",
"51\n3 6 1 5 4 2\n",
"40\n3 2 1\n",
"48\n3 6 1 5 4 2\n",
"48\n3 2 1\n",
"52\n3 6 1 5 4 2\n",
"56\n3 2 1\n",
"53\n3 6 1 5 4 2\n",
"76\n3 2 1\n",
"3\n2 1\n",
"49\n3 6 1 5 4 2\n",
"61\n2 3 1\n",
"17\n2 1 3\n",
"10\n2 1 3\n",
"4\n2 1\n",
"11\n2 1 3\n",
"9\n2 1 3\n",
"13\n2 1 3\n",
"15\n2 1 3\n",
"2\n1 2\n",
"3\n1 2\n",
"21\n2 1 3\n",
"5\n2 3 1\n",
"7\n2 3 1\n",
"9\n2 3 1\n",
"12\n2 3 1\n",
"14\n2 3 1\n",
"8\n2 3 1\n",
"0\n2 1\n",
"-2\n2 1\n",
"11\n2 3 1\n",
"-1\n2 1\n",
"1\n2 3 1\n",
"2\n2 3 1\n",
"1\n3 2 1\n",
"118\n3 4 1 5 2\n",
"45\n3 1 2\n",
"64\n4 3 2 1\n",
"146\n4 3 2 1 5\n",
"15\n3 1 2\n",
"106\n4 3 5 1 2\n",
"38\n3 2 1\n",
"41\n6 3 1 5 4 2\n",
"37\n3 2 1\n",
"29\n3 1 5 4 2 6\n",
"28\n3 2 1\n",
"29\n3 2 1\n",
"2\n2 1\n",
"29\n3 2 1\n",
"1\n2 1\n",
"1\n2 1\n",
"2\n2 1\n",
"2\n2 1\n",
"3\n2 1\n",
"3\n2 1\n",
"17\n2 1 3\n",
"3\n2 1\n",
"4\n2 1\n",
"4\n2 1\n",
"9\n2 1 3\n",
"4\n2 1\n",
"4\n2 1\n",
"13\n2 1 3\n",
"4\n2 1\n",
"15\n2 1 3\n",
"4\n2 1\n",
"2\n2 1\n",
"2\n2 1\n",
"7\n2 3 1\n",
"1\n2 1\n",
"7\n2 3 1\n",
"3\n2 1\n",
"3\n2 1\n",
"2\n2 1\n",
"1\n2 1\n",
"1\n2 1\n",
"8\n2 3 1\n",
"12\n2 3 1\n",
"9\n2 3 1\n",
"-1\n2 1\n",
"9\n2 3 1\n",
"-1\n2 1\n",
"-2\n2 1\n",
"1\n2 3 1\n",
"4\n2 1\n",
"2\n2 1\n",
"2\n2 1\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Recently Vasya decided to improve his pistol shooting skills. Today his coach offered him the following exercise. He placed n cans in a row on a table. Cans are numbered from left to right from 1 to n. Vasya has to knock down each can exactly once to finish the exercise. He is allowed to choose the order in which he will knock the cans down.
Vasya knows that the durability of the i-th can is a_i. It means that if Vasya has already knocked x cans down and is now about to start shooting the i-th one, he will need (a_i ⋅ x + 1) shots to knock it down. You can assume that if Vasya starts shooting the i-th can, he will be shooting it until he knocks it down.
Your task is to choose such an order of shooting so that the number of shots required to knock each of the n given cans down exactly once is minimum possible.
Input
The first line of the input contains one integer n (2 ≤ n ≤ 1 000) — the number of cans.
The second line of the input contains the sequence a_1, a_2, ..., a_n (1 ≤ a_i ≤ 1 000), where a_i is the durability of the i-th can.
Output
In the first line print the minimum number of shots required to knock each of the n given cans down exactly once.
In the second line print the sequence consisting of n distinct integers from 1 to n — the order of indices of cans that minimizes the number of shots required. If there are several answers, you can print any of them.
Examples
Input
3
20 10 20
Output
43
1 3 2
Input
4
10 10 10 10
Output
64
2 1 4 3
Input
6
5 4 5 4 4 5
Output
69
6 1 3 5 2 4
Input
2
1 4
Output
3
2 1
Note
In the first example Vasya can start shooting from the first can. He knocks it down with the first shot because he haven't knocked any other cans down before. After that he has to shoot the third can. To knock it down he shoots 20 ⋅ 1 + 1 = 21 times. After that only second can remains. To knock it down Vasya shoots 10 ⋅ 2 + 1 = 21 times. So the total number of shots is 1 + 21 + 21 = 43.
In the second example the order of shooting does not matter because all cans have the same durability.
### Input:
3
20 10 20
### Output:
43
1 3 2
### Input:
2
1 4
### Output:
3
2 1
### Code:
n = map(int, input().split())
A = list(map(int, input().split()))
la = []
ind = 1
for a in A:
la.append((a, ind))
ind += 1
la.sort(key=lambda x: x[0], reverse=True)
# print(la)
x = 0
sm = 0
li = []
for tp in la:
a = tp[0]
sm += (a * x + 1)
x += 1
li.append(tp[1])
print(sm)
print(" ".join(str(i) for i in li))
|
1239_C. Queue in the Train_10493
|
There are n seats in the train's car and there is exactly one passenger occupying every seat. The seats are numbered from 1 to n from left to right. The trip is long, so each passenger will become hungry at some moment of time and will go to take boiled water for his noodles. The person at seat i (1 ≤ i ≤ n) will decide to go for boiled water at minute t_i.
Tank with a boiled water is located to the left of the 1-st seat. In case too many passengers will go for boiled water simultaneously, they will form a queue, since there can be only one passenger using the tank at each particular moment of time. Each passenger uses the tank for exactly p minutes. We assume that the time it takes passengers to go from their seat to the tank is negligibly small.
Nobody likes to stand in a queue. So when the passenger occupying the i-th seat wants to go for a boiled water, he will first take a look on all seats from 1 to i - 1. In case at least one of those seats is empty, he assumes that those people are standing in a queue right now, so he would be better seating for the time being. However, at the very first moment he observes that all seats with numbers smaller than i are busy, he will go to the tank.
There is an unspoken rule, that in case at some moment several people can go to the tank, than only the leftmost of them (that is, seating on the seat with smallest number) will go to the tank, while all others will wait for the next moment.
Your goal is to find for each passenger, when he will receive the boiled water for his noodles.
Input
The first line contains integers n and p (1 ≤ n ≤ 100 000, 1 ≤ p ≤ 10^9) — the number of people and the amount of time one person uses the tank.
The second line contains n integers t_1, t_2, ..., t_n (0 ≤ t_i ≤ 10^9) — the moments when the corresponding passenger will go for the boiled water.
Output
Print n integers, where i-th of them is the time moment the passenger on i-th seat will receive his boiled water.
Example
Input
5 314
0 310 942 628 0
Output
314 628 1256 942 1570
Note
Consider the example.
At the 0-th minute there were two passengers willing to go for a water, passenger 1 and 5, so the first passenger has gone first, and returned at the 314-th minute. At this moment the passenger 2 was already willing to go for the water, so the passenger 2 has gone next, and so on. In the end, 5-th passenger was last to receive the boiled water.
|
import sys
reader = (s.rstrip() for s in sys.stdin)
input = reader.__next__
from heapq import heappop, heappush, heapify
from collections import deque
class SWAG_Stack():
def __init__(self, F):
self.stack1 = deque()
self.stack2 = deque()
self.F = F
self.len = 0
def push(self, x):
if self.stack2:
self.stack2.append((x, self.F(self.stack2[-1][1], x)))
else:
self.stack2.append((x, x))
self.len += 1
def pop(self):
if not self.stack1:
while self.stack2:
x, _ = self.stack2.pop()
if self.stack1:
self.stack1.appendleft((x, self.F(x, self.stack1[0][1])))
else:
self.stack1.appendleft((x, x))
x, _ = self.stack1.popleft()
self.len -= 1
return x
def sum_all(self):
if self.stack1 and self.stack2:
return self.F(self.stack1[0][1], self.stack2[-1][1])
elif self.stack1:
return self.stack1[0][1]
elif self.stack2:
return self.stack2[-1][1]
else:
return float("inf")
n,p = map(int, input().split())
t = list((j, i) for i,j in enumerate(map(int, input().split())))
heapify(t)
stack = SWAG_Stack(min)
heap = []
cur = 0
ans = [-1]*n
hoge = 0
# 今追加できるやつで最も小さいものを追加
# ここでなにもなかったら？
# 時間を変更する
# 次の時間までに追加できるものを追加
# 清算
while hoge != n:
if heap and stack.sum_all() > heap[0]:
j = heappop(heap)
stack.push(j)
if stack.len==0 and t:
cur = max(cur, t[0][0])
while t and t[0][0] <= cur+p:
ti, i = heappop(t)
if ti == cur+p:
# 後回し
heappush(heap, i)
else:
# いま追加できるか確認
if stack.sum_all() > i:
stack.push(i)
else:
# 後回し
heappush(heap, i)
if stack.len:
j = stack.pop()
cur += p
ans[j] = cur
hoge += 1
print(*ans)
|
{
"input": [
"5 314\n0 310 942 628 0\n",
"100 1000000000\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
"1 1\n1\n",
"100 1000000000\n12 803 439 918 435 300 497 520 718 573 782 523 328 88 275 159 128 389 920 869 503 80 490 289 22 889 353 799 29 131 587 123 405 221 727 135 248 348 299 833 19 943 471 410 635 626 784 712 213 724 550 661 860 536 718 173 406 832 520 748 512 29 466 982 574 848 11 693 915 965 177 479 63 498 484 190 404 149 664 614 817 179 103 938 167 66 165 319 694 432 754 598 929 33 228 719 54 213 330 625\n",
"100 100981\n558 354 667 283 78 604 578 91 880 892 370 546 16 601 43 831 593 93 281 801 448 199 579 207 703 328 678 319 308 145 65 176 287 476 511 727 200 47 16 246 718 989 479 384 761 412 885 583 185 759 285 247 444 341 542 568 44 816 332 183 239 608 152 517 445 606 699 303 366 193 975 644 201 732 270 555 390 454 601 554 69 816 242 96 565 299 90 164 558 255 876 963 743 949 936 854 825 15 409 449\n",
"100 101209\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
"1 1000000000\n999999999\n",
"100 1000000000\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
"1 2\n1\n",
"100 1000000000\n12 803 439 918 435 300 497 520 718 573 782 523 328 88 275 159 128 389 920 869 503 80 490 289 22 889 353 799 29 131 587 123 405 221 727 135 248 348 299 833 19 943 471 410 635 626 784 712 213 724 550 661 860 536 718 173 406 832 520 748 512 29 466 982 574 848 11 693 915 965 177 479 63 498 484 190 404 149 664 614 817 179 103 938 167 66 165 319 694 432 754 598 929 33 228 240 54 213 330 625\n",
"100 100981\n558 354 667 283 78 604 578 91 880 892 370 546 16 601 43 831 593 93 281 801 448 199 579 207 703 328 678 319 308 145 65 176 287 476 511 727 200 47 16 246 718 989 479 384 761 412 885 583 185 759 285 247 444 341 542 568 37 816 332 183 239 608 152 517 445 606 699 303 366 193 975 644 201 732 270 555 390 454 601 554 69 816 242 96 565 299 90 164 558 255 876 963 743 949 936 854 825 15 409 449\n",
"100 101209\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
"1 1000000000\n1714525343\n",
"5 314\n0 310 1802 628 0\n",
"100 1000000000\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
"1 2\n0\n",
"5 314\n0 310 18 628 0\n",
"5 314\n0 365 18 628 0\n",
"1 3\n1\n",
"100 1000000000\n12 803 439 918 435 300 497 520 718 573 782 523 328 88 275 159 128 389 920 869 503 80 490 289 22 889 353 799 29 131 587 123 405 221 727 135 248 348 359 833 19 943 471 410 635 626 784 712 213 724 550 661 860 536 718 173 406 832 520 748 512 29 466 982 574 848 0 693 915 965 177 479 63 498 484 190 404 149 664 614 817 179 103 1083 167 66 165 319 694 432 754 598 929 33 228 240 54 213 330 625\n",
"100 101209\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1\n",
"5 314\n0 365 18 1117 0\n",
"100 1000000000\n1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
"100 101209\n1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1\n",
"100 1000000000\n12 803 439 918 435 300 497 520 718 573 782 523 328 88 275 159 128 389 920 869 503 80 490 289 22 889 353 799 29 131 587 123 405 221 727 135 248 348 299 833 19 943 471 410 635 626 784 712 213 724 550 661 860 536 718 173 406 832 520 748 512 29 466 982 574 848 11 693 915 965 177 479 63 498 484 190 404 149 664 614 817 179 103 1083 167 66 165 319 694 432 754 598 929 33 228 240 54 213 330 625\n",
"100 100981\n558 354 667 283 78 604 578 91 880 892 370 546 16 601 43 831 593 93 281 801 448 199 579 207 703 328 678 319 308 145 65 176 287 476 511 727 200 47 16 246 718 989 519 384 761 412 885 583 185 759 285 247 444 341 542 568 37 816 332 183 239 608 152 517 445 606 699 303 366 193 975 644 201 732 270 555 390 454 601 554 69 816 242 96 565 299 90 164 558 255 876 963 743 949 936 854 825 15 409 449\n",
"100 101209\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
"100 1000000000\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
"1 3\n0\n",
"100 1000000000\n12 803 439 918 435 300 497 520 718 573 782 523 328 88 275 159 128 389 920 869 503 80 490 289 22 889 353 799 29 131 587 123 405 221 727 135 248 348 359 833 19 943 471 410 635 626 784 712 213 724 550 661 860 536 718 173 406 832 520 748 512 29 466 982 574 848 11 693 915 965 177 479 63 498 484 190 404 149 664 614 817 179 103 1083 167 66 165 319 694 432 754 598 929 33 228 240 54 213 330 625\n",
"100 100981\n558 354 667 283 78 604 578 91 880 892 370 546 16 601 43 831 593 93 281 801 448 199 579 207 703 328 678 319 308 145 65 176 287 476 511 727 200 47 16 246 718 989 519 384 761 412 885 583 185 759 23 247 444 341 542 568 37 816 332 183 239 608 152 517 445 606 699 303 366 193 975 644 201 732 270 555 390 454 601 554 69 816 242 96 565 299 90 164 558 255 876 963 743 949 936 854 825 15 409 449\n",
"100 101209\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1\n",
"100 1000000000\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
"100 100981\n558 354 667 283 78 604 578 91 880 892 370 546 16 601 43 831 593 93 281 801 448 199 579 207 703 328 678 319 308 145 65 176 287 476 511 727 200 47 16 246 718 989 519 384 761 412 885 583 185 759 23 247 444 341 542 568 37 816 332 183 239 608 152 517 445 606 699 303 366 193 975 644 201 732 270 555 390 454 1046 554 69 816 242 96 565 299 90 164 558 255 876 963 743 949 936 854 825 15 409 449\n",
"100 1000000000\n12 803 439 918 435 300 497 520 718 573 782 523 328 88 275 159 128 389 920 869 503 80 490 289 22 889 353 799 29 131 587 123 405 221 727 135 248 348 359 833 20 943 471 410 635 626 784 712 213 724 550 661 860 536 718 173 406 832 520 748 512 29 466 982 574 848 0 693 915 965 177 479 63 498 484 190 404 149 664 614 817 179 103 1083 167 66 165 319 694 432 754 598 929 33 228 240 54 213 330 625\n",
"100 100981\n558 354 667 283 78 604 578 91 880 892 370 546 16 601 43 831 593 93 281 801 448 199 579 207 703 328 678 319 308 145 65 176 287 476 511 727 200 47 16 246 718 989 519 384 761 412 885 583 185 759 23 247 444 341 542 568 37 816 332 183 239 608 228 517 445 606 699 303 366 193 975 644 201 732 270 555 390 454 1046 554 69 816 242 96 565 299 90 164 558 255 876 963 743 949 936 854 825 15 409 449\n",
"100 101209\n1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1\n",
"100 1000000000\n1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
"100 1000000000\n12 803 439 918 435 300 497 520 718 573 782 523 328 88 275 159 128 389 920 869 503 80 490 289 22 889 353 799 29 131 587 123 405 221 727 135 248 348 359 833 20 943 471 410 635 626 784 712 213 724 550 661 860 536 718 173 406 832 520 748 512 29 466 982 574 848 0 693 915 965 177 479 63 498 484 190 404 149 664 614 817 179 103 1083 167 66 165 319 694 432 754 598 929 33 228 240 54 213 188 625\n",
"100 100981\n558 354 667 283 78 604 578 91 880 576 370 546 16 601 43 831 593 93 281 801 448 199 579 207 703 328 678 319 308 145 65 176 287 476 511 727 200 47 16 246 718 989 519 384 761 412 885 583 185 759 23 247 444 341 542 568 37 816 332 183 239 608 228 517 445 606 699 303 366 193 975 644 201 732 270 555 390 454 1046 554 69 816 242 96 565 299 90 164 558 255 876 963 743 949 936 854 825 15 409 449\n",
"100 101209\n1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1\n",
"100 1000000000\n1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
"100 1000000000\n12 803 439 918 435 300 497 520 718 573 782 523 328 88 275 159 128 389 920 869 503 80 490 289 22 889 353 799 29 131 587 123 405 221 727 135 248 348 359 833 20 943 471 410 635 626 784 712 213 724 550 661 860 536 718 173 406 832 520 748 512 29 466 982 574 848 0 693 915 965 177 479 63 498 484 287 404 149 664 614 817 179 103 1083 167 66 165 319 694 432 754 598 929 33 228 240 54 213 188 625\n",
"100 100981\n558 354 667 283 78 604 578 91 880 576 370 546 16 601 43 831 593 93 281 801 448 199 579 207 703 328 678 319 308 145 65 176 287 476 511 727 200 47 16 246 718 989 519 384 761 412 885 583 185 759 23 247 444 341 542 568 37 816 332 183 239 608 228 517 445 606 699 303 366 193 975 644 201 732 270 555 390 454 1046 554 69 816 242 96 565 299 90 164 609 255 876 963 743 949 936 854 825 15 409 449\n",
"100 101209\n1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1\n",
"100 1000000000\n1 1 0 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 2 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
"100 1000000000\n12 803 439 918 435 300 497 520 718 573 782 523 328 88 275 159 128 389 920 869 503 80 490 289 22 889 353 799 29 131 587 123 405 221 727 135 248 348 359 833 20 943 471 410 635 626 784 712 213 724 550 661 860 536 718 173 406 832 520 748 512 29 466 982 574 848 0 693 915 409 177 479 63 498 484 287 404 149 664 614 817 179 103 1083 167 66 165 319 694 432 754 598 929 33 228 240 54 213 188 625\n",
"100 100981\n558 354 667 283 78 604 578 91 880 576 370 546 16 601 43 831 593 93 281 801 448 199 579 207 703 328 678 319 308 145 65 176 287 476 511 727 200 47 16 246 718 989 519 384 761 412 885 583 185 759 23 247 444 341 542 568 37 816 332 183 239 608 228 517 445 606 699 303 366 193 975 644 201 732 270 555 390 454 1046 554 69 816 242 96 565 299 90 164 609 255 876 963 743 949 936 142 825 15 409 449\n",
"100 1000000000\n1 1 0 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 2 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 0 1 1 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
"100 1000000000\n12 803 439 918 435 300 497 520 718 573 782 94 328 88 275 159 128 389 920 869 503 80 490 289 22 889 353 799 29 131 587 123 405 221 727 135 248 348 359 833 20 943 471 410 635 626 784 712 213 724 550 661 860 536 718 173 406 832 520 748 512 29 466 982 574 848 0 693 915 409 177 479 63 498 484 287 404 149 664 614 817 179 103 1083 167 66 165 319 694 432 754 598 929 33 228 240 54 213 188 625\n",
"100 100981\n558 354 667 283 78 604 578 91 880 576 370 546 16 601 43 831 593 93 281 801 448 199 579 207 703 328 678 319 308 145 65 176 287 476 511 727 200 47 16 246 718 989 519 384 761 412 885 583 185 759 23 247 444 341 542 568 37 816 332 183 239 608 228 517 445 606 699 303 366 193 975 644 201 732 270 555 390 454 1046 554 69 816 242 96 565 299 90 164 609 255 876 963 743 949 936 189 825 15 409 449\n"
],
"output": [
"314 628 1256 942 1570 \n",
"1000000001 2000000001 3000000001 4000000001 5000000001 6000000001 7000000001 8000000001 9000000001 10000000001 11000000001 12000000001 13000000001 14000000001 15000000001 16000000001 17000000001 18000000001 19000000001 20000000001 21000000001 22000000001 23000000001 24000000001 25000000001 26000000001 27000000001 28000000001 29000000001 30000000001 31000000001 32000000001 33000000001 34000000001 35000000001 36000000001 37000000001 38000000001 39000000001 40000000001 41000000001 42000000001 43000000001 44000000001 45000000001 46000000001 47000000001 48000000001 49000000001 50000000001 51000000001 52000000001 53000000001 54000000001 55000000001 56000000001 57000000001 58000000001 59000000001 60000000001 61000000001 62000000001 63000000001 64000000001 65000000001 66000000001 67000000001 68000000001 69000000001 70000000001 71000000001 72000000001 73000000001 74000000001 75000000001 76000000001 77000000001 78000000001 79000000001 80000000001 81000000001 82000000001 83000000001 84000000001 85000000001 86000000001 87000000001 88000000001 89000000001 90000000001 91000000001 92000000001 93000000001 94000000001 95000000001 96000000001 97000000001 98000000001 99000000001 100000000001 \n",
"2 \n",
"2000000011 3000000011 4000000011 5000000011 6000000011 7000000011 8000000011 9000000011 10000000011 11000000011 12000000011 13000000011 14000000011 15000000011 16000000011 17000000011 18000000011 19000000011 20000000011 21000000011 22000000011 23000000011 24000000011 25000000011 26000000011 27000000011 28000000011 29000000011 30000000011 31000000011 32000000011 33000000011 34000000011 35000000011 36000000011 37000000011 38000000011 39000000011 40000000011 41000000011 42000000011 43000000011 44000000011 45000000011 46000000011 47000000011 48000000011 49000000011 50000000011 51000000011 52000000011 53000000011 54000000011 55000000011 56000000011 57000000011 58000000011 59000000011 60000000011 61000000011 62000000011 63000000011 64000000011 65000000011 66000000011 67000000011 1000000011 68000000011 69000000011 70000000011 71000000011 72000000011 73000000011 74000000011 75000000011 76000000011 77000000011 78000000011 79000000011 80000000011 81000000011 82000000011 83000000011 84000000011 85000000011 86000000011 87000000011 88000000011 89000000011 90000000011 91000000011 92000000011 93000000011 94000000011 95000000011 96000000011 97000000011 98000000011 99000000011 100000000011 \n",
"605901 504920 706882 403939 302958 807863 908844 1009825 1110806 1211787 1312768 1413749 201977 1514730 1615711 1716692 1817673 1918654 2019635 2120616 2221597 2322578 2423559 2524540 2625521 2726502 2827483 2928464 3029445 3130426 3231407 3332388 3433369 3534350 3635331 3736312 3837293 3938274 4039255 4140236 4241217 4342198 4443179 4544160 4645141 4746122 4847103 4948084 5049065 5150046 5251027 5352008 5452989 5553970 5654951 5755932 5856913 5957894 6058875 6159856 6260837 6361818 6462799 6563780 6664761 6765742 6866723 6967704 7068685 7169666 7270647 7371628 7472609 7573590 7674571 7775552 7876533 7977514 8078495 8179476 8280457 8381438 8482419 8583400 8684381 8785362 8886343 8987324 9088305 9189286 9290267 9391248 9492229 9593210 9694191 9795172 9896153 100996 9997134 10098115 \n",
"101210 202419 303628 404837 506046 607255 708464 809673 910882 1012091 1113300 1214509 1315718 1416927 1518136 1619345 1720554 1821763 1922972 2024181 2125390 2226599 2327808 2429017 2530226 2631435 2732644 2833853 2935062 3036271 3137480 3238689 3339898 3441107 3542316 3643525 3744734 3845943 3947152 4048361 4149570 4250779 4351988 4453197 4554406 4655615 4756824 4858033 4959242 5060451 5161660 5262869 5364078 5465287 5566496 5667705 5768914 5870123 5971332 6072541 6173750 6274959 6376168 6477377 6578586 6679795 6781004 6882213 6983422 7084631 7185840 7287049 7388258 7489467 7590676 7691885 7793094 7894303 7995512 8096721 8197930 8299139 8400348 8501557 8602766 8703975 8805184 8906393 9007602 9108811 9210020 9311229 9412438 9513647 9614856 9716065 9817274 9918483 10019692 10120901 \n",
"1999999999 \n",
"2000000000 3000000000 4000000000 5000000000 6000000000 7000000000 8000000000 9000000000 10000000000 11000000000 12000000000 13000000000 14000000000 15000000000 16000000000 17000000000 18000000000 19000000000 20000000000 21000000000 22000000000 23000000000 24000000000 25000000000 26000000000 27000000000 28000000000 29000000000 30000000000 31000000000 32000000000 33000000000 34000000000 35000000000 36000000000 37000000000 38000000000 39000000000 40000000000 41000000000 42000000000 43000000000 44000000000 45000000000 46000000000 47000000000 48000000000 49000000000 50000000000 51000000000 52000000000 53000000000 54000000000 55000000000 56000000000 57000000000 58000000000 59000000000 60000000000 61000000000 62000000000 63000000000 64000000000 65000000000 66000000000 67000000000 68000000000 69000000000 70000000000 71000000000 72000000000 73000000000 74000000000 75000000000 76000000000 77000000000 1000000000 78000000000 79000000000 80000000000 81000000000 82000000000 83000000000 84000000000 85000000000 86000000000 87000000000 88000000000 89000000000 90000000000 91000000000 92000000000 93000000000 94000000000 95000000000 96000000000 97000000000 98000000000 99000000000 100000000000 ",
"3 ",
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"605901 504920 706882 403939 302958 807863 908844 1009825 1110806 1211787 1312768 1413749 201977 1514730 1615711 1716692 1817673 1918654 2019635 2120616 2221597 2322578 2423559 2524540 2625521 2726502 2827483 2928464 3029445 3130426 3231407 3332388 3433369 3534350 3635331 3736312 3837293 3938274 4039255 4140236 4241217 4342198 4443179 4544160 4645141 4746122 4847103 4948084 5049065 5150046 5251027 5352008 5452989 5553970 5654951 5755932 5856913 5957894 6058875 6159856 6260837 6361818 6462799 6563780 6664761 6765742 6866723 6967704 7068685 7169666 7270647 7371628 7472609 7573590 7674571 7775552 7876533 7977514 8078495 8179476 8280457 8381438 8482419 8583400 8684381 8785362 8886343 8987324 9088305 9189286 9290267 9391248 9492229 9593210 9694191 9795172 9896153 100996 9997134 10098115 ",
"202418 303627 404836 506045 607254 708463 809672 910881 1012090 1113299 1214508 1315717 1416926 1518135 1619344 1720553 1821762 1922971 2024180 2125389 2226598 2327807 2429016 2530225 2631434 2732643 2833852 2935061 3036270 3137479 3238688 3339897 3441106 3542315 3643524 3744733 3845942 3947151 4048360 4149569 4250778 4351987 4453196 4554405 4655614 4756823 4858032 4959241 5060450 5161659 5262868 5364077 101209 5465286 5566495 5667704 5768913 5870122 5971331 6072540 6173749 6274958 6376167 6477376 6578585 6679794 6781003 6882212 6983421 7084630 7185839 7287048 7388257 7489466 7590675 7691884 7793093 7894302 7995511 8096720 8197929 8299138 8400347 8501556 8602765 8703974 8805183 8906392 9007601 9108810 9210019 9311228 9412437 9513646 9614855 9716064 9817273 9918482 10019691 10120900 ",
"2000000000 3000000000 1000000000 4000000000 5000000000 6000000000 7000000000 8000000000 9000000000 10000000000 11000000000 12000000000 13000000000 14000000000 15000000000 16000000000 17000000000 18000000000 19000000000 20000000000 21000000000 22000000000 23000000000 24000000000 25000000000 26000000000 27000000000 28000000000 29000000000 30000000000 31000000000 32000000000 33000000000 34000000000 35000000000 36000000000 37000000000 38000000000 39000000000 40000000000 41000000000 42000000000 43000000000 44000000000 45000000000 46000000000 47000000000 48000000000 49000000000 50000000000 51000000000 52000000000 53000000000 54000000000 55000000000 56000000000 57000000000 58000000000 59000000000 60000000000 61000000000 62000000000 63000000000 64000000000 65000000000 66000000000 67000000000 68000000000 69000000000 70000000000 71000000000 72000000000 73000000000 74000000000 75000000000 76000000000 77000000000 78000000000 79000000000 80000000000 81000000000 82000000000 83000000000 84000000000 85000000000 86000000000 87000000000 88000000000 89000000000 90000000000 91000000000 92000000000 93000000000 94000000000 95000000000 96000000000 97000000000 98000000000 99000000000 100000000000 ",
"2000000000 3000000000 4000000000 5000000000 6000000000 7000000000 8000000000 9000000000 10000000000 11000000000 12000000000 13000000000 14000000000 15000000000 16000000000 17000000000 18000000000 19000000000 20000000000 21000000000 22000000000 23000000000 24000000000 25000000000 26000000000 27000000000 28000000000 29000000000 30000000000 31000000000 32000000000 33000000000 34000000000 35000000000 36000000000 37000000000 38000000000 39000000000 40000000000 41000000000 42000000000 43000000000 44000000000 45000000000 46000000000 47000000000 48000000000 49000000000 50000000000 51000000000 52000000000 53000000000 54000000000 55000000000 56000000000 57000000000 58000000000 59000000000 60000000000 61000000000 62000000000 63000000000 64000000000 65000000000 66000000000 67000000000 1000000000 68000000000 69000000000 70000000000 71000000000 72000000000 73000000000 74000000000 75000000000 76000000000 77000000000 78000000000 79000000000 80000000000 81000000000 82000000000 83000000000 84000000000 85000000000 86000000000 87000000000 88000000000 89000000000 90000000000 91000000000 92000000000 93000000000 94000000000 95000000000 96000000000 97000000000 98000000000 99000000000 100000000000 ",
"605901 504920 706882 403939 302958 807863 908844 1009825 1110806 1211787 1312768 1413749 201977 1514730 1615711 1716692 1817673 1918654 2019635 2120616 2221597 2322578 2423559 2524540 2625521 2726502 2827483 2928464 3029445 3130426 3231407 3332388 3433369 3534350 3635331 3736312 3837293 3938274 4039255 4140236 4241217 4342198 4443179 4544160 4645141 4746122 4847103 4948084 5049065 5150046 5251027 5352008 5452989 5553970 5654951 5755932 5856913 5957894 6058875 6159856 6260837 6361818 6462799 6563780 6664761 6765742 6866723 6967704 7068685 7169666 7270647 7371628 7472609 7573590 7674571 7775552 7876533 7977514 8078495 8179476 8280457 8381438 8482419 8583400 8684381 8785362 8886343 8987324 9088305 9189286 9290267 9391248 9492229 9593210 9694191 9795172 9896153 100996 9997134 10098115 ",
"2000000000 3000000000 1000000000 4000000000 5000000000 6000000000 7000000000 8000000000 9000000000 10000000000 11000000000 12000000000 13000000000 14000000000 15000000000 16000000000 17000000000 18000000000 19000000000 20000000000 21000000000 22000000000 23000000000 24000000000 25000000000 26000000000 27000000000 28000000000 29000000000 30000000000 31000000000 32000000000 33000000000 34000000000 35000000000 36000000000 37000000000 38000000000 39000000000 40000000000 41000000000 42000000000 43000000000 44000000000 45000000000 46000000000 47000000000 48000000000 49000000000 50000000000 51000000000 52000000000 53000000000 54000000000 55000000000 56000000000 57000000000 58000000000 59000000000 60000000000 61000000000 62000000000 63000000000 64000000000 65000000000 66000000000 67000000000 68000000000 69000000000 70000000000 71000000000 72000000000 73000000000 74000000000 75000000000 76000000000 77000000000 78000000000 79000000000 80000000000 81000000000 82000000000 83000000000 84000000000 85000000000 86000000000 87000000000 88000000000 89000000000 90000000000 91000000000 92000000000 93000000000 94000000000 95000000000 96000000000 97000000000 98000000000 99000000000 100000000000 ",
"2000000000 3000000000 4000000000 5000000000 6000000000 7000000000 8000000000 9000000000 10000000000 11000000000 12000000000 13000000000 14000000000 15000000000 16000000000 17000000000 18000000000 19000000000 20000000000 21000000000 22000000000 23000000000 24000000000 25000000000 26000000000 27000000000 28000000000 29000000000 30000000000 31000000000 32000000000 33000000000 34000000000 35000000000 36000000000 37000000000 38000000000 39000000000 40000000000 41000000000 42000000000 43000000000 44000000000 45000000000 46000000000 47000000000 48000000000 49000000000 50000000000 51000000000 52000000000 53000000000 54000000000 55000000000 56000000000 57000000000 58000000000 59000000000 60000000000 61000000000 62000000000 63000000000 64000000000 65000000000 66000000000 67000000000 1000000000 68000000000 69000000000 70000000000 71000000000 72000000000 73000000000 74000000000 75000000000 76000000000 77000000000 78000000000 79000000000 80000000000 81000000000 82000000000 83000000000 84000000000 85000000000 86000000000 87000000000 88000000000 89000000000 90000000000 91000000000 92000000000 93000000000 94000000000 95000000000 96000000000 97000000000 98000000000 99000000000 100000000000 ",
"605901 504920 706882 403939 302958 807863 908844 1009825 1110806 1211787 1312768 1413749 201977 1514730 1615711 1716692 1817673 1918654 2019635 2120616 2221597 2322578 2423559 2524540 2625521 2726502 2827483 2928464 3029445 3130426 3231407 3332388 3433369 3534350 3635331 3736312 3837293 3938274 4039255 4140236 4241217 4342198 4443179 4544160 4645141 4746122 4847103 4948084 5049065 5150046 5251027 5352008 5452989 5553970 5654951 5755932 5856913 5957894 6058875 6159856 6260837 6361818 6462799 6563780 6664761 6765742 6866723 6967704 7068685 7169666 7270647 7371628 7472609 7573590 7674571 7775552 7876533 7977514 8078495 8179476 8280457 8381438 8482419 8583400 8684381 8785362 8886343 8987324 9088305 9189286 9290267 9391248 9492229 9593210 9694191 9795172 9896153 100996 9997134 10098115 "
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
There are n seats in the train's car and there is exactly one passenger occupying every seat. The seats are numbered from 1 to n from left to right. The trip is long, so each passenger will become hungry at some moment of time and will go to take boiled water for his noodles. The person at seat i (1 ≤ i ≤ n) will decide to go for boiled water at minute t_i.
Tank with a boiled water is located to the left of the 1-st seat. In case too many passengers will go for boiled water simultaneously, they will form a queue, since there can be only one passenger using the tank at each particular moment of time. Each passenger uses the tank for exactly p minutes. We assume that the time it takes passengers to go from their seat to the tank is negligibly small.
Nobody likes to stand in a queue. So when the passenger occupying the i-th seat wants to go for a boiled water, he will first take a look on all seats from 1 to i - 1. In case at least one of those seats is empty, he assumes that those people are standing in a queue right now, so he would be better seating for the time being. However, at the very first moment he observes that all seats with numbers smaller than i are busy, he will go to the tank.
There is an unspoken rule, that in case at some moment several people can go to the tank, than only the leftmost of them (that is, seating on the seat with smallest number) will go to the tank, while all others will wait for the next moment.
Your goal is to find for each passenger, when he will receive the boiled water for his noodles.
Input
The first line contains integers n and p (1 ≤ n ≤ 100 000, 1 ≤ p ≤ 10^9) — the number of people and the amount of time one person uses the tank.
The second line contains n integers t_1, t_2, ..., t_n (0 ≤ t_i ≤ 10^9) — the moments when the corresponding passenger will go for the boiled water.
Output
Print n integers, where i-th of them is the time moment the passenger on i-th seat will receive his boiled water.
Example
Input
5 314
0 310 942 628 0
Output
314 628 1256 942 1570
Note
Consider the example.
At the 0-th minute there were two passengers willing to go for a water, passenger 1 and 5, so the first passenger has gone first, and returned at the 314-th minute. At this moment the passenger 2 was already willing to go for the water, so the passenger 2 has gone next, and so on. In the end, 5-th passenger was last to receive the boiled water.
### Input:
5 314
0 310 942 628 0
### Output:
314 628 1256 942 1570
### Input:
100 1000000000
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
### Output:
1000000001 2000000001 3000000001 4000000001 5000000001 6000000001 7000000001 8000000001 9000000001 10000000001 11000000001 12000000001 13000000001 14000000001 15000000001 16000000001 17000000001 18000000001 19000000001 20000000001 21000000001 22000000001 23000000001 24000000001 25000000001 26000000001 27000000001 28000000001 29000000001 30000000001 31000000001 32000000001 33000000001 34000000001 35000000001 36000000001 37000000001 38000000001 39000000001 40000000001 41000000001 42000000001 43000000001 44000000001 45000000001 46000000001 47000000001 48000000001 49000000001 50000000001 51000000001 52000000001 53000000001 54000000001 55000000001 56000000001 57000000001 58000000001 59000000001 60000000001 61000000001 62000000001 63000000001 64000000001 65000000001 66000000001 67000000001 68000000001 69000000001 70000000001 71000000001 72000000001 73000000001 74000000001 75000000001 76000000001 77000000001 78000000001 79000000001 80000000001 81000000001 82000000001 83000000001 84000000001 85000000001 86000000001 87000000001 88000000001 89000000001 90000000001 91000000001 92000000001 93000000001 94000000001 95000000001 96000000001 97000000001 98000000001 99000000001 100000000001
### Code:
import sys
reader = (s.rstrip() for s in sys.stdin)
input = reader.__next__
from heapq import heappop, heappush, heapify
from collections import deque
class SWAG_Stack():
def __init__(self, F):
self.stack1 = deque()
self.stack2 = deque()
self.F = F
self.len = 0
def push(self, x):
if self.stack2:
self.stack2.append((x, self.F(self.stack2[-1][1], x)))
else:
self.stack2.append((x, x))
self.len += 1
def pop(self):
if not self.stack1:
while self.stack2:
x, _ = self.stack2.pop()
if self.stack1:
self.stack1.appendleft((x, self.F(x, self.stack1[0][1])))
else:
self.stack1.appendleft((x, x))
x, _ = self.stack1.popleft()
self.len -= 1
return x
def sum_all(self):
if self.stack1 and self.stack2:
return self.F(self.stack1[0][1], self.stack2[-1][1])
elif self.stack1:
return self.stack1[0][1]
elif self.stack2:
return self.stack2[-1][1]
else:
return float("inf")
n,p = map(int, input().split())
t = list((j, i) for i,j in enumerate(map(int, input().split())))
heapify(t)
stack = SWAG_Stack(min)
heap = []
cur = 0
ans = [-1]*n
hoge = 0
# 今追加できるやつで最も小さいものを追加
# ここでなにもなかったら？
# 時間を変更する
# 次の時間までに追加できるものを追加
# 清算
while hoge != n:
if heap and stack.sum_all() > heap[0]:
j = heappop(heap)
stack.push(j)
if stack.len==0 and t:
cur = max(cur, t[0][0])
while t and t[0][0] <= cur+p:
ti, i = heappop(t)
if ti == cur+p:
# 後回し
heappush(heap, i)
else:
# いま追加できるか確認
if stack.sum_all() > i:
stack.push(i)
else:
# 後回し
heappush(heap, i)
if stack.len:
j = stack.pop()
cur += p
ans[j] = cur
hoge += 1
print(*ans)
|
1257_E. The Contest_10497
|
A team of three programmers is going to play a contest. The contest consists of n problems, numbered from 1 to n. Each problem is printed on a separate sheet of paper. The participants have decided to divide the problem statements into three parts: the first programmer took some prefix of the statements (some number of first paper sheets), the third contestant took some suffix of the statements (some number of last paper sheets), and the second contestant took all remaining problems. But something went wrong — the statements were printed in the wrong order, so the contestants have received the problems in some random order.
The first contestant has received problems a_{1, 1}, a_{1, 2}, ..., a_{1, k_1}. The second one has received problems a_{2, 1}, a_{2, 2}, ..., a_{2, k_2}. The third one has received all remaining problems (a_{3, 1}, a_{3, 2}, ..., a_{3, k_3}).
The contestants don't want to play the contest before they redistribute the statements. They want to redistribute them so that the first contestant receives some prefix of the problemset, the third contestant receives some suffix of the problemset, and the second contestant receives all the remaining problems.
During one move, some contestant may give one of their problems to other contestant. What is the minimum number of moves required to redistribute the problems?
It is possible that after redistribution some participant (or even two of them) will not have any problems.
Input
The first line contains three integers k_1, k_2 and k_3 (1 ≤ k_1, k_2, k_3 ≤ 2 ⋅ 10^5, k_1 + k_2 + k_3 ≤ 2 ⋅ 10^5) — the number of problems initially taken by the first, the second and the third participant, respectively.
The second line contains k_1 integers a_{1, 1}, a_{1, 2}, ..., a_{1, k_1} — the problems initially taken by the first participant.
The third line contains k_2 integers a_{2, 1}, a_{2, 2}, ..., a_{2, k_2} — the problems initially taken by the second participant.
The fourth line contains k_3 integers a_{3, 1}, a_{3, 2}, ..., a_{3, k_3} — the problems initially taken by the third participant.
It is guaranteed that no problem has been taken by two (or three) participants, and each integer a_{i, j} meets the condition 1 ≤ a_{i, j} ≤ n, where n = k_1 + k_2 + k_3.
Output
Print one integer — the minimum number of moves required to redistribute the problems so that the first participant gets the prefix of the problemset, the third participant gets the suffix of the problemset, and the second participant gets all of the remaining problems.
Examples
Input
2 1 2
3 1
4
2 5
Output
1
Input
3 2 1
3 2 1
5 4
6
Output
0
Input
2 1 3
5 6
4
1 2 3
Output
3
Input
1 5 1
6
5 1 2 4 7
3
Output
2
Note
In the first example the third contestant should give the problem 2 to the first contestant, so the first contestant has 3 first problems, the third contestant has 1 last problem, and the second contestant has 1 remaining problem.
In the second example the distribution of problems is already valid: the first contestant has 3 first problems, the third contestant has 1 last problem, and the second contestant has 2 remaining problems.
The best course of action in the third example is to give all problems to the third contestant.
The best course of action in the fourth example is to give all problems to the second contestant.
|
x,y,z=map(int,input().split())
d=[[],[],[]]
d[0]=list(map(int,input().split()))
d[1]=list(map(int,input().split()))
d[2]=list(map(int,input().split()))
dicto=[dict(),dict(),dict()]
dp=[[float("inf")]*(x+y+z+1) for i in range(3)]
for i in range(3):
for j in d[i]:
dicto[i][j]=1
dp[0][0]=0
mini=9999999999999
for i in range(1,x+y+z+1):
mini=999999999999
for j in range(3):
for k in range(j+1):
mini=min(mini,dp[k][i-1])
if i not in dicto[j]:
dp[j][i]=mini+1
else:
dp[j][i]=mini
for i in range(3):
mini=min(dp[0][x+y+z],dp[1][x+y+z],dp[2][x+y+z])
print(mini)
|
{
"input": [
"2 1 2\n3 1\n4\n2 5\n",
"1 5 1\n6\n5 1 2 4 7\n3\n",
"3 2 1\n3 2 1\n5 4\n6\n",
"2 1 3\n5 6\n4\n1 2 3\n",
"5 10 6\n14 3 6 12 21\n7 1 5 8 10 11 13 17 18 20\n9 2 4 15 16 19\n",
"11 7 9\n4 8 9 12 14 16 19 21 22 23 27\n1 2 3 11 17 18 26\n5 6 7 10 13 15 20 24 25\n",
"1 1 1\n3\n1\n2\n",
"1 1 1\n3\n2\n1\n",
"2 1 2\n2 1\n4\n3 5\n",
"2 1 2\n3 1\n2\n4 5\n"
],
"output": [
"1",
"2",
"0",
"3",
"11",
"15",
"1",
"2\n",
"1\n",
"1\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
A team of three programmers is going to play a contest. The contest consists of n problems, numbered from 1 to n. Each problem is printed on a separate sheet of paper. The participants have decided to divide the problem statements into three parts: the first programmer took some prefix of the statements (some number of first paper sheets), the third contestant took some suffix of the statements (some number of last paper sheets), and the second contestant took all remaining problems. But something went wrong — the statements were printed in the wrong order, so the contestants have received the problems in some random order.
The first contestant has received problems a_{1, 1}, a_{1, 2}, ..., a_{1, k_1}. The second one has received problems a_{2, 1}, a_{2, 2}, ..., a_{2, k_2}. The third one has received all remaining problems (a_{3, 1}, a_{3, 2}, ..., a_{3, k_3}).
The contestants don't want to play the contest before they redistribute the statements. They want to redistribute them so that the first contestant receives some prefix of the problemset, the third contestant receives some suffix of the problemset, and the second contestant receives all the remaining problems.
During one move, some contestant may give one of their problems to other contestant. What is the minimum number of moves required to redistribute the problems?
It is possible that after redistribution some participant (or even two of them) will not have any problems.
Input
The first line contains three integers k_1, k_2 and k_3 (1 ≤ k_1, k_2, k_3 ≤ 2 ⋅ 10^5, k_1 + k_2 + k_3 ≤ 2 ⋅ 10^5) — the number of problems initially taken by the first, the second and the third participant, respectively.
The second line contains k_1 integers a_{1, 1}, a_{1, 2}, ..., a_{1, k_1} — the problems initially taken by the first participant.
The third line contains k_2 integers a_{2, 1}, a_{2, 2}, ..., a_{2, k_2} — the problems initially taken by the second participant.
The fourth line contains k_3 integers a_{3, 1}, a_{3, 2}, ..., a_{3, k_3} — the problems initially taken by the third participant.
It is guaranteed that no problem has been taken by two (or three) participants, and each integer a_{i, j} meets the condition 1 ≤ a_{i, j} ≤ n, where n = k_1 + k_2 + k_3.
Output
Print one integer — the minimum number of moves required to redistribute the problems so that the first participant gets the prefix of the problemset, the third participant gets the suffix of the problemset, and the second participant gets all of the remaining problems.
Examples
Input
2 1 2
3 1
4
2 5
Output
1
Input
3 2 1
3 2 1
5 4
6
Output
0
Input
2 1 3
5 6
4
1 2 3
Output
3
Input
1 5 1
6
5 1 2 4 7
3
Output
2
Note
In the first example the third contestant should give the problem 2 to the first contestant, so the first contestant has 3 first problems, the third contestant has 1 last problem, and the second contestant has 1 remaining problem.
In the second example the distribution of problems is already valid: the first contestant has 3 first problems, the third contestant has 1 last problem, and the second contestant has 2 remaining problems.
The best course of action in the third example is to give all problems to the third contestant.
The best course of action in the fourth example is to give all problems to the second contestant.
### Input:
2 1 2
3 1
4
2 5
### Output:
1
### Input:
1 5 1
6
5 1 2 4 7
3
### Output:
2
### Code:
x,y,z=map(int,input().split())
d=[[],[],[]]
d[0]=list(map(int,input().split()))
d[1]=list(map(int,input().split()))
d[2]=list(map(int,input().split()))
dicto=[dict(),dict(),dict()]
dp=[[float("inf")]*(x+y+z+1) for i in range(3)]
for i in range(3):
for j in d[i]:
dicto[i][j]=1
dp[0][0]=0
mini=9999999999999
for i in range(1,x+y+z+1):
mini=999999999999
for j in range(3):
for k in range(j+1):
mini=min(mini,dp[k][i-1])
if i not in dicto[j]:
dp[j][i]=mini+1
else:
dp[j][i]=mini
for i in range(3):
mini=min(dp[0][x+y+z],dp[1][x+y+z],dp[2][x+y+z])
print(mini)
|
1280_F. Intergalactic Sliding Puzzle_10500
|
You are an intergalactic surgeon and you have an alien patient. For the purposes of this problem, we can and we will model this patient's body using a 2 × (2k + 1) rectangular grid. The alien has 4k + 1 distinct organs, numbered 1 to 4k + 1.
In healthy such aliens, the organs are arranged in a particular way. For example, here is how the organs of a healthy such alien would be positioned, when viewed from the top, for k = 4:
<image>
Here, the E represents empty space.
In general, the first row contains organs 1 to 2k + 1 (in that order from left to right), and the second row contains organs 2k + 2 to 4k + 1 (in that order from left to right) and then empty space right after.
Your patient's organs are complete, and inside their body, but they somehow got shuffled around! Your job, as an intergalactic surgeon, is to put everything back in its correct position. All organs of the alien must be in its body during the entire procedure. This means that at any point during the procedure, there is exactly one cell (in the grid) that is empty. In addition, you can only move organs around by doing one of the following things:
* You can switch the positions of the empty space E with any organ to its immediate left or to its immediate right (if they exist). In reality, you do this by sliding the organ in question to the empty space;
* You can switch the positions of the empty space E with any organ to its immediate top or its immediate bottom (if they exist) only if the empty space is on the leftmost column, rightmost column or in the centermost column. Again, you do this by sliding the organ in question to the empty space.
Your job is to figure out a sequence of moves you must do during the surgical procedure in order to place back all 4k + 1 internal organs of your patient in the correct cells. If it is impossible to do so, you must say so.
Input
The first line of input contains a single integer t (1 ≤ t ≤ 4) denoting the number of test cases. The next lines contain descriptions of the test cases.
Each test case consists of three lines. The first line contains a single integer k (1 ≤ k ≤ 15) which determines the size of the grid. Then two lines follow. Each of them contains 2k + 1 space-separated integers or the letter E. They describe the first and second rows of organs, respectively. It is guaranteed that all 4k + 1 organs are present and there is exactly one E.
Output
For each test case, first, print a single line containing either:
* SURGERY COMPLETE if it is possible to place back all internal organs in the correct locations;
* SURGERY FAILED if it is impossible.
If it is impossible, then this is the only line of output for the test case. However, if it is possible, output a few more lines describing the sequence of moves to place the organs in the correct locations.
The sequence of moves will be a (possibly empty) string of letters u, d, l or r, representing sliding the organ that's directly above, below, to the left or to the right of the empty space, respectively, into the empty space. Print the sequence of moves in the following line, as such a string.
For convenience, you may use shortcuts to reduce the size of your output. You may use uppercase letters as shortcuts for sequences of moves. For example, you could choose T to represent the string lddrr. These shortcuts may also include other shortcuts on their own! For example, you could choose E to represent TruT, etc.
You may use any number of uppercase letters (including none) as shortcuts. The only requirements are the following:
* The total length of all strings in your output for a single case is at most 10^4;
* There must be no cycles involving the shortcuts that are reachable from the main sequence;
* The resulting sequence of moves is finite, after expanding all shortcuts. Note that the final sequence of moves (after expanding) may be much longer than 10^4; the only requirement is that it's finite.
As an example, if T = lddrr, E = TruT and R = rrr, then TurTlER expands to:
* TurTlER
* lddrrurTlER
* lddrrurlddrrlER
* lddrrurlddrrlTruTR
* lddrrurlddrrllddrrruTR
* lddrrurlddrrllddrrrulddrrR
* lddrrurlddrrllddrrrulddrrrrr
To use shortcuts, print each one of them in a single line as the uppercase letter, then space, and then the string that this shortcut represents. They may be printed in any order. At the end of all of those, print a single line containing DONE.
Note: You still need to print DONE even if you don't plan on using shortcuts.
Your sequence does not need to be the shortest. Any valid sequence of moves (satisfying the requirements above) will be accepted.
Example
Input
2
3
1 2 3 5 6 E 7
8 9 10 4 11 12 13
11
34 45 6 22 16 43 38 44 5 4 41 14 7 29 28 19 9 18 42 8 17 33 1
E 15 40 36 31 24 10 2 21 11 32 23 30 27 35 25 13 12 39 37 26 20 3
Output
SURGERY COMPLETE
IR
R SrS
S rr
I lldll
DONE
SURGERY FAILED
Note
There are three shortcuts defined in the first sample output:
* R = SrS
* S = rr
* I = lldll
The sequence of moves is IR and it expands to:
* IR
* lldllR
* lldllSrS
* lldllrrrS
* lldllrrrrr
|
def solve(k, grid):
seek = *range(2*k + 2), *range(4*k + 1, 2*k + 1, -1)
flat = [seek[v] for v in grid[0] + grid[1][::-1] if v]
m = {
'L': 'l'*2*k + 'u' + 'r'*2*k + 'd',
'R': 'u' + 'l'*2*k + 'd' + 'r'*2*k,
'C': 'l'*k + 'u' + 'r'*k + 'd',
'D': 'CC' + 'R'*(2*k + 1) + 'CC' + 'R'*(2*k + 2),
'F': 'R'*(k - 1) + 'DD' + 'R'*(2*k + 1) + 'D' + 'L'*2*k + 'DD' + 'L'*k,
'G': 'FF',
}
[(i, j)] = [(i, j) for i in range(2) for j in range(2*k + 1) if grid[i][j] == 0]
st = 'r'*(2*k - j) + 'd'*(1 - i)
for v in range(2, 4*k + 2):
ct = flat.index(v)
if ct >= 2:
st += 'L'*(ct - 2) + 'GR'*(ct - 2) + 'G'
flat = flat[ct - 1: ct + 1] + flat[:ct - 1] + flat[ct + 1:]
if ct >= 1:
st += 'G'
flat = flat[1:3] + flat[:1] + flat[3:]
st += 'L'
flat = flat[1:] + flat[:1]
if flat[0] == 1: return st, m
def main():
def get_line():
return [0 if x == 'E' else int(x) for x in input().split()]
for cas in range(int(input())):
res = solve(int(input()), [get_line() for i in range(2)])
if res is None:
print('SURGERY FAILED')
else:
print('SURGERY COMPLETE')
st, m = res
print(st)
for shortcut in m.items(): print(*shortcut)
print('DONE')
main()
|
{
"input": [
"2\n3\n1 2 3 5 6 E 7\n8 9 10 4 11 12 13\n11\n34 45 6 22 16 43 38 44 5 4 41 14 7 29 28 19 9 18 42 8 17 33 1\nE 15 40 36 31 24 10 2 21 11 32 23 30 27 35 25 13 12 39 37 26 20 3\n",
"2\n3\n1 2 3 5 6 E 7\n8 9 10 4 11 12 13\n11\n34 45 6 22 16 43 38 44 5 4 41 14 7 29 28 19 9 18 42 8 17 33 1\nE 15 40 36 31 24 10 2 21 11 32 23 30 27 35 25 13 12 39 37 26 20 3\n",
"4\n3\n1 5 3 4 13 7 6\nE 2 12 11 10 9 8\n2\n1 7 E 3 4\n9 8 2 6 5\n2\n1 7 6 4 9\nE 5 8 2 3\n3\n1 8 10 E 4 5 6\n13 12 11 3 9 2 7\n",
"4\n3\n7 1 E 2 6 4 11\n3 8 5 12 9 10 13\n3\n4 9 6 13 5 12 1\n10 8 E 11 7 2 3\n3\nE 13 2 1 8 12 7\n11 6 5 4 10 3 9\n2\n6 E 2 9 8\n7 4 3 1 5\n",
"4\n3\n1 2 3 4 5 6 7\n13 12 11 10 9 8 E\n4\n1 2 3 4 5 6 7 15 9\n8 13 17 14 16 12 11 10 E\n11\n1 2 3 4 5 6 7 44 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\n45 8 43 42 41 40 39 38 37 36 25 34 33 E 32 31 30 29 28 27 26 35 24\n3\n1 2 3 4 5 6 9\n13 E 12 11 10 7 8\n",
"1\n8\n11 1 8 17 33 24 16 32 28 20 25 31 E 23 22 13 26\n21 14 27 18 2 10 5 4 3 19 9 6 7 15 30 29 12\n",
"4\n13\n22 8 9 35 39 23 19 41 2 46 48 21 50 32 26 52 E 36 16 6 37 27 53 33 47 40 20\n24 42 15 18 31 11 25 1 12 3 49 44 29 10 51 4 13 5 38 14 28 34 17 45 7 43 30\n11\n24 9 7 21 23 20 34 11 15 33 18 E 13 12 1 43 29 26 22 36 19 41 37\n16 2 38 40 42 39 44 8 35 31 28 17 45 14 4 3 6 25 30 5 27 10 32\n10\n11 6 9 41 24 16 12 33 4 20 15 17 1 8 13 19 23 34 38 32 7\n31 3 5 35 14 26 18 2 21 39 29 22 28 40 10 27 37 30 E 25 36\n4\nE 5 3 6 9 15 2 12 13\n16 4 1 11 8 10 14 17 7\n",
"4\n12\n28 11 40 E 42 47 33 32 1 13 4 49 21 44 9 45 15 31 22 34 8 18 43 5 16\n37 38 26 30 24 12 14 27 3 41 2 36 23 7 6 39 19 25 10 29 35 48 46 17 20\n6\n17 4 1 15 24 13 12 8 3 E 10 6 23\n19 21 9 11 5 18 16 20 14 25 7 2 22\n15\n45 44 16 48 31 54 34 47 9 32 4 27 41 3 26 40 59 12 60 42 5 29 21 37 22 55 57 7 56 38 36\n50 18 8 28 15 52 13 17 51 23 58 35 25 19 E 20 30 14 33 1 43 2 61 24 46 39 11 49 6 53 10\n6\n24 7 6 4 17 22 1 13 E 5 25 2 11\n14 23 9 12 21 18 8 15 3 19 10 20 16\n",
"4\n6\n23 1 16 5 E 17 21 11 8 9 4 20 12\n18 3 24 25 2 6 13 15 22 14 10 7 19\n7\n23 27 14 15 22 24 10 16 25 17 9 5 20 E 29\n18 12 4 13 11 7 26 8 28 1 2 19 6 21 3\n7\n20 3 11 9 19 13 21 29 25 27 16 5 8 1 2\n18 4 10 14 28 26 6 12 23 24 15 7 E 22 17\n6\n23 7 1 11 3 15 2 20 24 16 12 18 25\n8 10 E 14 13 6 19 5 22 17 4 21 9\n",
"4\n2\n1 2 3 4 5\nE 6 7 8 9\n15\n1 2 3 4 5 E 6 7 8 9 10 31 12 13 14 15 16 17 18 19 20 21 22 23 24 25 44 27 28 29 30\n61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 26 43 42 41 40 39 34 37 36 35 38 33 32 11\n3\n1 2 3 4 5 E 6\n13 12 11 10 9 8 7\n2\n1 2 3 4 5\nE 9 8 7 6\n",
"4\n3\nE 1 2 3 10 5 6\n13 12 9 4 11 8 7\n1\nE 1 2\n4 5 3\n1\nE 1 2\n5 4 3\n1\nE 1 2\n5 4 3\n",
"4\n1\n4 1 5\n3 2 E\n1\n1 2 3\nE 5 4\n1\n2 1 3\nE 5 4\n1\n2 3 5\n4 E 1\n",
"4\n2\nE 6 7 8 9\n1 2 3 4 5\n2\nE 8 2 3 4\n9 1 7 6 5\n3\nE 8 9 10 11 12 13\n1 2 3 4 5 6 7\n2\nE 9 8 7 6\n1 2 3 4 5\n",
"4\n3\n1 2 3 10 5 13 6\nE 12 11 9 4 8 7\n3\n1 2 3 11 5 6 7\n13 12 4 8 10 9 E\n15\n1 2 3 15 5 6 7 8 9 10 11 12 13 14 4 16 17 18 19 20 21 22 23 24 25 26 27 56 29 50 31\nE 61 60 59 58 57 28 55 54 53 52 51 30 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32\n11\n1 2 3 18 5 6 7 8 9 25 11 12 13 14 26 16 17 4 19 20 21 22 23\n45 44 43 42 41 40 E 39 38 37 36 35 34 33 32 31 30 29 28 27 15 10 24\n",
"4\n4\n2 10 14 3 16 17 9 7 8\n1 5 12 E 6 15 13 11 4\n3\n2 12 E 13 11 4 9\n10 8 7 6 1 3 5\n6\n2 20 9 12 19 25 23 8 3 18 6 13 21\n4 E 7 10 11 16 22 5 15 17 1 24 14\n1\n3 E 2\n5 4 1\n",
"4\n2\nE 1 2 9 4\n3 8 7 6 5\n5\nE 1 15 3 4 5 6 7 8 9 10\n21 20 19 18 17 16 2 14 13 12 11\n1\nE 2 1\n5 3 4\n1\nE 2 1\n5 4 3\n",
"2\n6\n24 20 1 8 11 22 2 E 23 19 10 6 9\n21 4 12 7 17 15 16 5 3 25 13 14 18\n4\n5 E 13 4 14 17 2 9 3\n12 1 10 6 7 16 11 8 15\n",
"4\n2\n8 1 E 5 4\n9 6 7 2 3\n4\n10 11 16 14 13 7 6 9 3\n4 17 1 2 E 15 8 12 5\n2\n6 3 1 8 5\n2 7 4 9 E\n2\n9 E 1 8 7\n5 3 2 6 4\n",
"4\n14\nE 1 2 3 4 5 22 7 44 25 10 11 12 13 14 15 16 17 18 19 20 21 6 23 24 9 26 27 28\n57 56 55 54 53 52 51 50 49 48 47 46 45 8 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29\n2\nE 1 2 3 4\n6 7 8 9 5\n2\nE 1 2 3 4\n9 8 7 6 5\n2\nE 1 2 3 4\n9 8 7 6 5\n",
"4\n2\n1 2 7 3 4\n9 8 E 5 6\n3\n1 2 12 4 5 3 7\nE 13 6 11 10 9 8\n14\n1 2 13 4 5 6 7 8 9 10 11 12 E 3 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28\n57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 33 41 40 39 38 37 36 35 34 42 32 31 30 29\n1\n1 4 5\nE 2 3\n",
"4\n2\n1 2 3 4 5\nE 9 8 7 6\n3\n1 2 3 4 5 6 7\nE 8 9 10 11 12 13\n3\n1 2 3 4 5 6 7\nE 9 8 10 13 12 11\n3\n1 2 3 4 5 6 7\nE 13 12 11 10 9 8\n",
"4\n3\n1 3 9 2 13 4 10\n6 7 E 11 12 5 8\n3\n5 7 8 1 6 11 4\nE 2 13 3 12 9 10\n2\n1 4 6 3 8\n2 5 E 7 9\n4\n9 3 2 13 7 8 16 12 17\n11 5 4 10 6 15 14 1 E\n",
"4\n2\n3 1 2 9 4\nE 8 7 6 5\n2\n3 2 1 7 4\n9 8 E 6 5\n1\n3 5 1\nE 4 2\n14\n3 17 57 56 27 20 39 44 12 41 37 16 24 31 53 15 43 9 19 26 28 36 33 29 8 21 55 38 50\n42 51 49 5 13 40 7 34 35 22 2 E 23 18 48 52 6 30 1 46 25 10 54 14 45 4 32 11 47\n",
"4\n3\n7 11 E 6 8 2 3\n9 10 4 12 13 1 5\n3\n2 6 11 12 3 7 13\n8 9 5 1 4 E 10\n3\n2 10 9 12 7 4 E\n1 6 5 3 8 13 11\n3\n9 11 1 6 E 4 2\n13 12 3 7 8 10 5\n",
"4\n1\nE 2 3\n1 5 4\n1\nE 2 5\n3 4 1\n1\nE 3 2\n4 5 1\n1\nE 4 3\n5 1 2\n",
"4\n2\n9 8 7 6 5\nE 1 2 3 4\n4\n11 6 7 13 12 15 16 1 5\n8 9 E 2 17 3 10 4 14\n3\n13 2 E 3 4 5 8\n1 12 11 10 9 6 7\n3\n13 4 6 5 1 11 E\n3 9 2 7 8 10 12\n",
"1\n9\n36 21 27 E 24 22 16 6 3 9 34 8 32 23 31 28 10 26 17\n25 12 7 30 29 13 15 4 33 2 14 11 5 19 37 35 20 1 18\n",
"4\n3\n6 7 12 4 5 1 11\nE 13 3 9 10 8 2\n4\n2 15 5 E 10 11 12 9 3\n16 7 6 1 4 13 17 14 8\n3\n6 5 11 8 13 4 1\n10 2 3 12 7 9 E\n3\n4 1 13 7 2 9 3\n8 E 10 11 12 5 6\n",
"4\n3\n1 2 3 4 7 6 5\n13 12 E 11 10 9 8\n3\n1 2 3 4 7 6 5\n13 12 11 10 E 9 8\n15\n1 2 3 4 16 6 54 8 9 10 11 12 13 E 14 15 5 17 18 19 20 21 22 23 24 25 26 27 28 29 30\n61 60 59 58 57 56 55 7 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31\n15\n1 2 3 4 51 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31\n61 60 59 58 57 56 55 54 53 52 5 50 49 48 47 46 45 44 43 42 41 40 E 39 38 37 36 35 34 33 32\n",
"4\n3\n13 12 11 10 8 9 7\n1 2 6 E 4 5 3\n3\n13 12 11 10 9 2 7\n1 8 3 4 5 E 6\n3\n13 12 11 10 9 8 7\nE 1 2 3 4 5 6\n15\n14 39 5 10 35 6 52 26 58 54 8 25 16 19 31 56 42 41 33 23 27 44 2 57 36 20 E 29 3 21 46\n9 4 43 49 45 48 28 61 47 60 53 55 1 51 32 13 18 30 38 34 22 17 12 37 7 24 40 11 50 15 59\n",
"1\n15\n61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31\nE 1 2 3 4 5 6 7 8 9 10 14 12 13 11 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30\n",
"4\n15\n1 2 3 4 5 6 7 8 9 39 11 12 13 14 15 16 17 18 19 20 E 21 22 23 24 25 26 27 28 29 30\n61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 10 38 37 36 35 34 33 32 31\n3\n1 2 3 4 5 6 7\n13 E 12 11 10 9 8\n3\n1 2 3 4 5 6 7\n13 12 10 8 9 11 E\n3\n1 2 3 4 5 6 7\n13 12 11 10 E 9 8\n",
"4\n5\n18 19 17 7 3 21 5 10 1 15 4\nE 6 16 2 11 14 12 8 9 13 20\n8\n21 18 27 2 32 4 17 25 29 19 14 E 23 1 24 7 26\n15 28 22 31 16 12 33 13 8 20 10 9 5 11 6 30 3\n15\n21 33 59 58 57 56 55 54 53 52 51 50 49 48 47 E 46 45 44 43 42 41 40 39 38 37 36 35 34 60 32\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 61 22 23 24 30 26 27 28 29 25 31\n13\n23 34 21 22 20 42 13 11 16 44 2 45 E 10 3 43 37 49 50 30 24 1 53 25 4 18 51\n12 15 29 38 27 19 8 41 14 47 40 35 26 33 28 6 39 31 36 17 7 48 5 32 46 52 9\n",
"3\n15\n61 11 56 42 50 30 52 17 25 58 34 10 33 55 32 19 46 38 3 35 1 18 9 57 47 12 45 20 51 39 49\n6 24 16 14 22 21 8 48 29 31 36 43 26 27 E 44 13 59 15 2 40 53 5 23 60 28 4 54 41 7 37\n7\n19 5 2 13 12 9 4 1 20 7 8 26 29 15 27\n17 3 28 6 24 11 E 18 22 25 23 16 14 10 21\n12\n5 39 3 41 9 4 27 36 31 30 46 20 48 33 18 28 2 19 29 40 23 26 45 42 43\n34 44 21 32 10 E 6 47 37 12 35 13 8 17 11 15 25 16 24 38 7 1 49 14 22\n",
"4\n5\n15 12 5 13 20 14 18 21 E 19 9\n16 10 8 7 2 11 17 6 3 1 4\n7\n16 13 2 E 9 19 3 18 22 27 17 7 20 11 8\n26 24 28 6 29 5 14 10 23 21 15 1 25 12 4\n8\n3 22 16 33 28 11 1 4 23 17 E 7 15 14 24 9 32\n31 26 13 5 29 10 25 18 20 27 21 2 30 19 12 8 6\n7\n15 13 5 29 28 19 12 9 6 22 14 23 3 1 26\n27 4 11 10 17 8 16 21 E 18 25 20 2 7 24\n",
"4\n1\n5 E 2\n4 3 1\n2\n4 1 2 6 5\n3 7 E 8 9\n2\n1 4 E 3 9\n7 2 6 8 5\n2\n1 9 8 2 6\nE 3 5 7 4\n",
"4\n3\n1 9 3 4 5 6 7\nE 13 12 11 10 2 8\n2\n1 9 6 3 4\nE 8 7 2 5\n15\n1 12 3 4 5 6 7 17 9 10 11 2 13 14 15 16 8 18 36 20 21 22 23 24 25 26 27 28 29 30 31\n61 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 E 44 43 42 41 40 39 38 37 19 35 34 33 32\n14\n1 13 3 4 5 6 7 8 9 10 11 12 2 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29\n57 56 E 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30\n",
"4\n3\n1 E 2 3 4 5 6\n13 12 11 10 9 8 7\n1\n1 E 2\n4 5 3\n1\n1 E 2\n5 4 3\n2\n1 E 3 4 5\n9 8 7 6 2\n",
"4\n6\n22 18 11 20 14 24 17 5 15 6 2 12 8\n4 E 25 16 13 7 23 9 10 3 21 19 1\n12\n29 3 47 30 39 2 14 26 49 10 44 31 25 22 12 45 8 5 16 6 32 18 15 37 36\n43 35 20 42 7 13 4 17 46 34 48 33 1 27 24 41 E 21 9 38 11 28 40 23 19\n9\n24 6 14 13 37 11 18 31 28 19 5 25 17 36 34 35 23 E 12\n9 27 4 32 3 21 8 10 1 26 33 29 7 15 22 2 20 30 16\n12\nE 25 20 40 6 36 24 37 3 49 19 34 2 16 7 23 17 27 21 38 14 15 29 33 41\n31 43 5 9 1 30 26 22 11 12 47 39 28 10 8 46 32 35 18 13 48 42 45 44 4\n",
"3\n15\n41 60 15 5 6 45 37 38 28 24 44 46 11 58 51 59 55 57 E 22 26 21 25 1 33 35 2 23 56 53 43\n30 27 13 7 14 34 42 52 61 49 39 36 32 10 12 48 4 3 16 40 20 18 50 17 29 9 19 47 8 54 31\n6\n21 9 7 E 12 6 13 22 2 25 16 19 4\n5 11 18 14 15 17 20 10 24 1 23 8 3\n9\n10 11 3 32 18 24 31 16 1 28 12 6 5 4 8 23 E 33 22\n27 34 19 21 30 17 9 36 14 20 25 2 35 29 37 26 15 13 7\n",
"4\n3\n8 9 10 11 12 13 7\nE 1 2 3 4 5 6\n6\n8 14 3 6 22 4 15 2 21 20 13 11 E\n1 24 7 25 23 5 18 12 9 10 16 19 17\n9\n8 30 14 29 32 2 10 18 34 36 37 28 20 17 22 5 16 9 6\nE 35 12 13 23 27 19 33 21 25 24 4 1 26 3 31 15 7 11\n3\n9 6 11 7 5 10 E\n13 8 12 1 3 4 2\n",
"4\n1\n1 2 3\nE 5 4\n1\n1 2 3\nE 5 4\n15\n1 2 3 4 E 5 6 7 8 9 45 11 12 13 14 15 16 17 59 19 20 21 22 23 24 25 26 27 28 29 30\n61 60 18 58 57 56 55 54 53 52 51 50 49 48 47 46 10 44 43 42 40 41 39 38 37 36 35 34 33 32 31\n2\n1 2 3 4 E\n9 8 7 6 5\n",
"4\n3\n4 1 2 3 E 5 6\n13 12 11 10 9 8 7\n1\n4 1 2\n5 E 3\n2\n4 2 3 1 5\n6 9 8 7 E\n1\n4 5 1\n2 E 3\n",
"4\n10\n5 39 27 32 10 34 3 35 20 23 1 24 22 7 E 29 12 13 19 26 17\n9 21 16 31 30 6 40 11 18 14 33 25 41 2 28 36 15 37 38 4 8\n3\n6 1 13 3 4 8 E\n2 12 11 10 9 5 7\n3\n6 2 3 4 8 1 7\n13 12 11 10 E 9 5\n2\n6 7 8 9 5\nE 1 2 3 4\n",
"4\n1\n1 2 3\n5 E 4\n1\n1 2 3\n5 4 E\n2\n1 2 3 8 E\n9 4 7 6 5\n2\n1 2 3 9 5\n4 8 E 7 6\n",
"4\n1\n4 5 3\nE 1 2\n13\n4 25 18 43 19 47 37 3 13 6 51 29 35 7 53 15 30 26 2 20 41 49 12 48 28 10 52\n21 50 5 31 22 34 23 8 44 33 27 24 14 42 E 40 1 46 9 11 39 38 36 16 32 45 17\n2\n5 2 3 4 7\n9 6 8 1 E\n1\n5 4 3\nE 1 2\n",
"4\n3\n1 2 E 3 4 12 6\n13 5 11 10 9 8 7\n1\n1 2 E\n5 4 3\n1\n1 2 3\nE 4 5\n1\n1 2 3\nE 5 4\n",
"4\n13\n8 31 22 14 5 25 1 13 17 12 29 52 26 44 10 41 46 4 43 20 16 E 6 18 15 28 51\n50 53 34 33 32 36 37 49 38 45 11 24 48 35 21 42 19 30 47 39 27 3 23 9 2 7 40\n3\n12 8 6 5 10 13 9\nE 11 1 2 7 3 4\n7\n14 1 13 16 7 19 29 3 11 2 E 26 15 9 24\n17 6 10 12 8 25 20 5 28 23 4 18 27 22 21\n11\n32 2 9 7 44 40 45 12 10 13 20 14 8 17 42 6 18 36 29 39 21 16 37\n43 38 26 33 27 24 19 4 22 34 11 28 30 31 E 1 25 5 41 15 35 23 3\n",
"4\n7\n6 19 22 26 1 14 13 27 11 17 23 8 28 25 16\n9 4 E 10 21 5 15 12 18 20 3 2 7 24 29\n2\n7 2 E 3 1\n4 9 6 8 5\n11\n7 2 3 4 5 6 1 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\n45 44 43 42 E 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24\n2\n7 2 3 8 5\n9 4 1 6 E\n",
"4\n3\nE 13 12 11 10 9 8\n1 2 3 4 5 6 7\n5\nE 18 21 7 1 3 15 12 8 11 4\n20 14 16 17 6 5 13 2 19 9 10\n11\nE 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23\n7\nE 27 19 21 22 4 3 18 8 12 28 29 26 15 23\n14 25 1 13 5 6 11 10 16 24 2 17 7 9 20\n",
"4\n3\nE 1 2 3 4 5 6\n8 9 10 11 12 13 7\n3\nE 1 2 3 4 5 6\n13 12 11 10 9 8 7\n3\nE 1 2 3 4 5 6\n13 12 11 10 9 8 7\n14\nE 1 2 3 4 5 6 47 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28\n57 56 55 54 53 52 51 50 49 48 7 46 45 44 43 42 40 41 39 38 37 36 35 34 33 32 31 30 29\n",
"4\n3\n1 2 4 6 13 3 7\n5 E 12 11 10 9 8\n1\n1 2 5\nE 4 3\n2\n1 2 6 4 E\n9 5 7 3 8\n2\n1 2 6 4 5\nE 9 8 7 3\n",
"4\n1\nE 4 5\n1 2 3\n1\nE 5 2\n1 4 3\n1\nE 5 4\n1 2 3\n2\nE 6 3 1 4\n9 8 7 2 5\n",
"4\n2\n1 2 3 4 5\n9 8 E 7 6\n2\n1 2 3 4 5\n9 8 7 E 6\n2\n1 2 3 4 5\n9 8 7 6 E\n3\n1 2 3 4 7 5 E\n13 12 11 10 6 8 9\n",
"4\n1\n2 1 3\nE 4 5\n1\n2 1 5\n3 4 E\n1\n2 4 E\n5 3 1\n2\n2 6 E 7 9\n8 1 5 4 3\n",
"4\n14\n1 2 3 4 5 6 7 8 9 10 11 12 13 46 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29\nE 57 56 55 54 35 52 51 50 49 48 47 14 45 44 43 42 41 40 39 38 37 36 53 34 33 32 31 30\n15\n1 2 3 4 5 6 7 8 9 10 11 12 19 14 15 16 17 18 13 20 21 22 23 24 25 26 27 28 29 30 31\nE 61 60 59 58 57 56 55 54 53 35 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 52 34 33 32\n5\n1 2 3 4 5 6 7 8 9 10 11\n12 20 19 18 17 16 15 14 13 21 E\n4\n1 2 3 4 5 6 7 8 9\n17 16 15 14 13 12 11 10 E\n",
"4\n2\n7 9 3 1 4\n8 6 5 2 E\n3\n7 13 6 2 E 1 3\n9 12 4 11 10 5 8\n2\n8 1 E 3 4\n2 6 5 7 9\n2\n8 9 3 4 E\n5 1 7 6 2\n",
"4\n3\nE 1 2 3 10 5 6\n13 12 9 4 11 8 7\n1\nE 1 2\n4 5 3\n1\nE 2 2\n5 4 3\n1\nE 1 2\n5 4 3\n",
"4\n2\nE 1 2 9 4\n3 8 7 6 5\n5\nE 2 15 3 4 5 6 7 8 9 10\n21 20 19 18 17 16 2 14 13 12 11\n1\nE 2 1\n5 3 4\n1\nE 2 1\n5 4 3\n",
"4\n3\n4 2 2 3 E 5 6\n13 12 11 10 9 8 7\n1\n4 1 2\n5 E 3\n2\n4 2 3 1 5\n6 9 8 7 E\n1\n4 5 1\n2 E 3\n",
"4\n2\n7 9 3 2 4\n8 6 5 2 E\n3\n7 13 6 2 E 1 3\n9 12 4 11 10 5 8\n2\n8 1 E 3 4\n2 6 5 7 9\n2\n8 9 3 4 E\n5 1 7 6 2\n",
"4\n2\nE 1 2 9 4\n3 8 7 6 5\n5\nE 1 15 3 4 5 6 7 8 9 10\n21 20 19 18 17 16 2 14 13 12 11\n1\nE 2 1\n5 3 4\n1\nE 2 2\n5 4 3\n",
"4\n3\n4 2 2 3 E 5 6\n13 12 11 10 9 8 7\n1\n4 1 2\n5 E 3\n2\n4 2 3 2 5\n6 9 8 7 E\n1\n4 5 1\n2 E 3\n",
"4\n5\n15 12 5 13 20 14 18 21 E 19 9\n16 10 8 7 2 11 17 6 3 2 4\n7\n16 13 2 E 9 19 3 18 22 27 17 7 20 11 8\n26 24 28 6 29 5 14 10 23 21 15 1 25 12 4\n8\n3 22 16 33 28 11 1 4 23 17 E 7 15 14 24 9 32\n31 26 13 5 29 10 25 18 20 27 21 2 30 19 12 8 6\n7\n15 13 5 29 28 19 12 9 6 22 14 23 3 1 26\n27 4 11 10 17 8 16 21 E 18 25 20 2 7 24\n",
"4\n2\n9 8 7 6 5\nE 1 2 3 4\n4\n11 6 7 13 12 15 16 1 5\n8 9 E 2 17 3 10 4 14\n3\n13 2 E 3 4 5 8\n2 12 11 10 9 6 7\n3\n13 4 6 5 1 11 E\n3 9 2 7 8 10 12\n",
"4\n3\n1 E 2 3 4 5 6\n13 12 11 10 9 8 7\n1\n1 E 2\n4 5 3\n1\n2 E 2\n5 4 3\n2\n1 E 3 4 5\n9 8 7 6 2\n",
"4\n3\n1 2 E 3 4 12 6\n13 5 11 10 9 8 7\n1\n1 2 E\n5 4 3\n1\n1 2 3\nE 4 5\n1\n2 2 3\nE 5 4\n",
"4\n1\n2 2 3\n5 E 4\n1\n1 2 3\n5 4 E\n2\n1 2 3 8 E\n9 4 7 6 5\n2\n1 2 3 9 5\n4 8 E 7 6\n",
"4\n3\n1 2 E 3 4 12 6\n13 5 11 10 9 8 7\n1\n1 2 E\n5 4 3\n1\n2 2 3\nE 4 5\n1\n1 2 3\nE 5 4\n",
"4\n4\n2 10 14 3 16 17 9 7 8\n1 5 12 E 6 15 13 11 4\n3\n2 12 E 13 11 4 9\n10 8 7 6 2 3 5\n6\n2 20 9 12 19 25 23 8 3 18 6 13 21\n4 E 7 10 11 16 22 5 15 17 1 24 14\n1\n3 E 2\n5 4 1\n",
"4\n3\n1 2 3 4 7 6 5\n13 12 E 11 10 9 8\n3\n2 2 3 4 7 6 5\n13 12 11 10 E 9 8\n15\n1 2 3 4 16 6 54 8 9 10 11 12 13 E 14 15 5 17 18 19 20 21 22 23 24 25 26 27 28 29 30\n61 60 59 58 57 56 55 7 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31\n15\n1 2 3 4 51 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31\n61 60 59 58 57 56 55 54 53 52 5 50 49 48 47 46 45 44 43 42 41 40 E 39 38 37 36 35 34 33 32\n",
"4\n3\n4 1 2 3 E 5 6\n13 12 11 10 9 8 7\n1\n4 1 2\n5 E 3\n2\n4 2 3 1 5\n6 9 8 7 E\n1\n4 5 2\n2 E 3\n",
"4\n3\n2 E 2 3 4 5 6\n13 12 11 10 9 8 7\n1\n1 E 2\n4 5 3\n1\n2 E 1\n5 4 3\n2\n1 E 3 4 5\n9 8 7 6 2\n",
"4\n3\nE 2 2 3 4 5 6\n8 9 10 11 12 13 7\n3\nE 1 2 3 4 5 6\n13 12 11 10 9 8 7\n3\nE 1 2 3 4 5 6\n13 12 11 10 9 8 7\n14\nE 1 2 3 4 5 6 47 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28\n57 56 55 54 53 52 51 50 49 48 7 46 45 44 43 42 40 41 39 38 37 36 35 34 33 32 31 30 29\n",
"4\n3\n1 2 3 10 5 13 6\nE 12 11 9 4 8 7\n3\n1 2 3 11 5 6 7\n13 12 4 8 10 9 E\n15\n1 2 3 15 5 6 7 8 9 10 11 12 13 14 4 16 17 18 19 20 21 22 23 24 25 26 27 56 29 50 31\nE 61 60 59 58 57 28 55 54 53 52 51 30 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32\n11\n2 2 3 18 5 6 7 8 9 25 11 12 13 14 26 16 17 4 19 20 21 22 23\n45 44 43 42 41 40 E 39 38 37 36 35 34 33 32 31 30 29 28 27 15 10 24\n",
"4\n5\n18 19 17 7 3 21 5 10 1 15 4\nE 6 16 2 11 14 12 8 9 13 20\n8\n21 18 27 2 32 4 17 25 29 19 14 E 23 1 24 7 26\n15 28 22 31 16 12 33 13 8 20 10 9 5 11 6 30 3\n15\n21 33 59 58 57 56 55 54 53 52 51 50 49 48 47 E 46 45 44 43 42 41 40 39 38 37 36 35 34 60 32\n2 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 61 22 23 24 30 26 27 28 29 25 31\n13\n23 34 21 22 20 42 13 11 16 44 2 45 E 10 3 43 37 49 50 30 24 1 53 25 4 18 51\n12 15 29 38 27 19 8 41 14 47 40 35 26 33 28 6 39 31 36 17 7 48 5 32 46 52 9\n",
"4\n10\n5 39 27 32 10 34 3 35 20 23 2 24 22 7 E 29 12 13 19 26 17\n9 21 16 31 30 6 40 11 18 14 33 25 41 2 28 36 15 37 38 4 8\n3\n6 1 13 3 4 8 E\n2 12 11 10 9 5 7\n3\n6 2 3 4 8 1 7\n13 12 11 10 E 9 5\n2\n6 7 8 9 5\nE 1 2 3 4\n",
"4\n2\n9 8 7 6 5\nE 1 2 3 4\n4\n11 6 7 13 12 15 16 1 5\n8 9 E 2 17 3 10 4 14\n3\n13 4 E 3 4 5 8\n2 12 11 10 9 6 7\n3\n13 4 6 5 1 11 E\n3 9 2 7 8 10 12\n",
"4\n3\n2 E 2 3 4 5 6\n13 12 11 10 9 8 7\n1\n1 E 2\n4 5 3\n1\n2 E 2\n5 4 3\n2\n1 E 3 4 5\n9 8 7 6 2\n",
"4\n3\n1 2 E 3 4 12 6\n13 5 11 10 9 8 7\n1\n2 2 E\n5 4 3\n1\n1 2 3\nE 4 5\n1\n2 2 3\nE 5 4\n",
"4\n3\n1 E 2 3 4 5 6\n13 12 11 10 9 8 7\n1\n1 E 2\n4 5 3\n1\n3 E 2\n5 4 3\n2\n1 E 3 4 5\n9 8 7 6 2\n",
"4\n3\n1 2 E 3 4 12 6\n13 5 11 10 9 8 7\n1\n1 2 E\n5 4 3\n1\n3 2 3\nE 4 5\n1\n1 2 3\nE 5 4\n",
"4\n3\n1 2 E 3 4 12 6\n13 5 11 10 9 8 7\n1\n1 2 E\n5 4 3\n1\n1 2 3\nE 4 5\n1\n2 4 3\nE 5 4\n",
"4\n3\n2 E 2 3 4 5 6\n13 12 11 10 9 8 7\n1\n2 E 2\n4 5 3\n1\n2 E 2\n5 4 3\n2\n1 E 3 4 5\n9 8 7 6 2\n"
],
"output": [
"\nSURGERY COMPLETE\nIR\nR SrS\nS rr\nI lldll\nDONE\nSURGERY FAILED\n",
"SURGERY COMPLETE\nrdGLLLLLLLGRGRGRGRGRGGLGGLGGLGGLGGLGGLGLLGLL\nL llllllurrrrrrd\nR ulllllldrrrrrr\nC lllurrrd\nD CCRRRRRRRCCRRRRRRRR\nF RRDDRRRRRRRDLLLLLLDDLLL\nG FF\nDONE\nSURGERY FAILED\n",
"SURGERY COMPLETE\nrrrrrrLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGGLLGRGGLLGRGGLGGLLLGRGRGGLGLGGLLLLGRGRGGLGLGGLL\nL llllllurrrrrrd\nR ulllllldrrrrrr\nC lllurrrd\nD CCRRRRRRRCCRRRRRRRR\nF RRDDRRRRRRRDLLLLLLDDLLL\nG FF\nDONE\nSURGERY FAILED\nSURGERY FAILED\nSURGERY FAILED\n",
"SURGERY COMPLETE\nrrrrdGGLLLLLLLLLLGRGRGRGRGRGRGRGRGRGGLLLGRGRGGLLLLLLLLGRGRGRGRGRGRGRGGLGGLLLLGRGRGGLLLGGLGGLL\nL llllllurrrrrrd\nR ulllllldrrrrrr\nC lllurrrd\nD CCRRRRRRRCCRRRRRRRR\nF RRDDRRRRRRRDLLLLLLDDLLL\nG FF\nDONE\nSURGERY FAILED\nSURGERY COMPLETE\nrrrrrrdGLLLLLGRGRGRGRGGLLLLLLGRGRGRGRGRGGLLLLLLGRGRGRGRGRGGLLLLLLGRGRGRGRGRGGLGGLLLGRGRGGLGGLLLGRGRGGLLGRGGLGLL\nL llllllurrrrrrd\nR ulllllldrrrrrr\nC lllurrrd\nD CCRRRRRRRCCRRRRRRRR\nF RRDDRRRRRRRDLLLLLLDDLLL\nG FF\nDONE\nSURGERY COMPLETE\nrrrdGLLLLGRGR...",
"SURGERY FAILED\nSURGERY FAILED\nSURGERY FAILED\nSURGERY COMPLETE\nrrrrrGLLGLLGLLGRGGLLLLLGRGRGRGRGGLGLLLGRGRGGLGLLL\nL llllllurrrrrrd\nR ulllllldrrrrrr\nC lllurrrd\nD CCRRRRRRRCCRRRRRRRR\nF RRDDRRRRRRRDLLLLLLDDLLL\nG FF\nDONE\n",
"SURGERY COMPLETE\nrrrrdLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLGLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLGRGRGRGRGGLLLLGRGRGGLLGRGGLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLL...",
"SURGERY COMPLETE\nrrrrrrrrrrdLLLLLLGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRG...",
"SURGERY COMPLETE\nrrrrrrrrrrrrrrrrrrrrrdLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRG...",
"SURGERY FAILED\nSURGERY FAILED\nSURGERY FAILED\nSURGERY FAILED\n",
"SURGERY COMPLETE\nrrrrGLLGLLGLLGLL\nL llllurrrrd\nR ulllldrrrr\nC llurrd\nD CCRRRRRCCRRRRRR\nF RDDRRRRRDLLLLDDLL\nG FF\nDONE\nSURGERY COMPLETE\nrrrrrrrrrrrrrrrrrrrrrrrrrdGLLGLLGLLGLLGLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLGRGRGRGGLLLLGRGRGRGGLLLLGRGRGRGGLGLGLLLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLGL...",
"SURGERY FAILED\nSURGERY COMPLETE\nrrdGLLGLL\nL llurrd\nR ulldrr\nC lurd\nD CCRRRCCRRRR\nF DDRRRDLLDDL\nG FF\nDONE\nSURGERY FAILED\nSURGERY FAILED\n",
"SURGERY COMPLETE\nLGRGGLLGRGGLGGLL\nL llurrd\nR ulldrr\nC lurd\nD CCRRRCCRRRR\nF DDRRRDLLDDL\nG FF\nDONE\nSURGERY FAILED\nSURGERY COMPLETE\nrrLGLGGLL\nL llurrd\nR ulldrr\nC lurd\nD CCRRRCCRRRR\nF DDRRRDLLDDL\nG FF\nDONE\nSURGERY FAILED\n",
"SURGERY COMPLETE\nrrrrdLLLLLGRGRGRGRGRGGLGLLLLGRGRGRGGLGLLGRGGLGLLL\nL llllurrrrd\nR ulllldrrrr\nC llurrd\nD CCRRRRRCCRRRRRR\nF RDDRRRRRDLLLLDDLL\nG FF\nDONE\nSURGERY FAILED\nSURGERY COMPLETE\nrrrrrrdLLLLLLLLLGRGRGRGRGRGRGRGRGRGGLGLLLLLLLLGRGRGRGRGRGRGRGGLGLLLLLLGRGRGRGRGRGGLGLLLLGRGRGRGGLGLLGRGGLGLLL\nL llllllurrrrrrd\nR ulllllldrrrrrr\nC lllurrrd\nD CCRRRRRRRCCRRRRRRRR\nF RRDDRRRRRRRDLLLLLLDDLLL\nG FF\nDONE\nSURGERY COMPLETE\nrrrrdLLLLLGRGRGRGRGRGGLGLLLLGRGRGRGGLGLLLLL\nL llllurrrrd\nR ulllldrrrr\nC llur...",
"SURGERY COMPLETE\nrrrrrrGLLLLLLLGRGRGRGRGRGGLLGRGGLLLGRGRGGLLLGRGRGGLGGLLLLGRGRGRGGLGLGGLGGLL\nL llllllurrrrrrd\nR ulllllldrrrrrr\nC lllurrrd\nD CCRRRRRRRCCRRRRRRRR\nF RRDDRRRRRRRDLLLLLLDDLLL\nG FF\nDONE\nSURGERY COMPLETE\nGLLLLLLLLGRGRGRGRGRGRGGLLGRGGLLGRGGLLGRGGLLLLLGRGRGRGRGGLGLLLGRGGLGLL\nL llllllurrrrrrd\nR ulllllldrrrrrr\nC lllurrrd\nD CCRRRRRRRCCRRRRRRRR\nF RRDDRRRRRRRDLLLLLLDDLLL\nG FF\nDONE\nSURGERY COMPLETE\nrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrGLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGGLLGRGGLLGRGGLLGRGGLLGRGG...",
"SURGERY COMPLETE\nrrrrrLGGLLLLLLGRGRGRGRGRGGLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLGRGRGRGRGRGRGRGRGRGGLLLLLLLGRGRGRGRGRGRGGLLLGRGRGGLGGLLLLGRGRGRGGLGLGGLGGLLGRGGLLLL\nL llllllllurrrrrrrrd\nR ulllllllldrrrrrrrr\nC llllurrrrd\nD CCRRRRRRRRRCCRRRRRRRRRR\nF RRRDDRRRRRRRRRDLLLLLLLLDDLLLL\nG FF\nDONE\nSURGERY COMPLETE\nrrrrdLLLLLGRGRGRGRGGLLLGRGRGGLGGLLLLGRGRGRGGLLLLGRGRGRGGLLLGRGRGGLLLLGRGGLLL\nL llllllurrrrrrd\nR ulllllldrrrrrr\nC lllurrrd\nD CCRRRRRRRCCRRRRRRRR\nF RRDDRRRRRRRDLLLLLLDDLLL\nG FF\nDONE\nSUR...",
"SURGERY FAILED\nSURGERY COMPLETE\nrrrrrrrrrrdLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLLLLLLLLGRGRGRGRGRGRGRGRGGLGLLLLLLLGRGRGRGRGRGRGGLGLLLLLGRGRGRGRGGLGLLGLGGLL\nL llllllllllurrrrrrrrrrd\nR ulllllllllldrrrrrrrrrr\nC lllllurrrrrd\nD CCRRRRRRRRRRRCCRRRRRRRRRRRR\nF RRRRDDRRRRRRRRRRRDLLLLLLLLLLDDLLLLL\nG FF\nDONE\nSURGERY FAILED\nSURGERY COMPLETE\nrrdLGLGGLL\nL llurrd\nR ulldrr\nC lurd\nD CCRRRCCRRRR\nF DDRRRDLLDDL\nG FF\nDONE\n",
"SURGERY FAILED\nSURGERY COMPLETE\nrrrrrrrdLLLGRGRGRGGLLLLLGRGRGRGRGGLLLGRGRGGLLLLLLLLLGRGRGRGRGRGRGRGGLGLLLLGRGRGRGGLLGGLLLGRGRGGLLGGLGLLGRGGLGGLL\nL llllllllurrrrrrrrd\nR ulllllllldrrrrrrrr\nC llllurrrrd\nD CCRRRRRRRRRCCRRRRRRRRRR\nF RRRDDRRRRRRRRRDLLLLLLLLDDLLLL\nG FF\nDONE\n",
"SURGERY COMPLETE\nrrdLLLGRGRGRGGLGLLGRGGLGLLLGRGRGGLLGGLL\nL llllurrrrd\nR ulllldrrrr\nC llurrd\nD CCRRRRRCCRRRRRR\nF RDDRRRRRDLLLLDDLL\nG FF\nDONE\nSURGERY COMPLETE\nrrrrLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLGRGRGRGRGRGRGRGGLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLGRGRGRGRGRGRGRGRGGLGLLLLLLLGRGRGRGRGRGRGGLLLLLLLLGRGRGRGRGRGRGRGGLLLGRGRGGLLLLLGRGRGRGGLLLGRGRGGLLLGRGRGGLGGLGLLL\nL llllllllurrrrrrrrd\nR ulllllllldrrrrrrrr\nC llllurrrrd\nD CCRRRRRRRRRCCRRRRRRRRRR\nF RRRDDRRRRRRRRRDLLLLLLLLDDLLLL\n...",
"SURGERY FAILED\nSURGERY COMPLETE\nrrrrdGLLGLLGLLGLL\nL llllurrrrd\nR ulllldrrrr\nC llurrd\nD CCRRRRRCCRRRRRR\nF RDDRRRRRDLLLLDDLL\nG FF\nDONE\nSURGERY COMPLETE\nrrrrdGLLGLLLLGRGRGGLGLGGLL\nL llllurrrrd\nR ulllldrrrr\nC llurrd\nD CCRRRRRCCRRRRRR\nF RDDRRRRRDLLLLDDLL\nG FF\nDONE\nSURGERY COMPLETE\nrrrrdGLLGLLLLGRGRGGLGLGGLL\nL llllurrrrd\nR ulllldrrrr\nC llurrd\nD CCRRRRRCCRRRRRR\nF RDDRRRRRDLLLLDDLL\nG FF\nDONE\n",
"SURGERY FAILED\nSURGERY FAILED\nSURGERY COMPLETE\nrrrrrrrrrrrrrrrrdGLLLLLLLLLLGRGRGRGRGRGRGRGRGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLGLGLLGLLGLLGLLGLLGLLGLLGLLGLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLGLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLGLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLGLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLGLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGR...",
"SURGERY COMPLETE\nrrrrGLLGLLLLGRGRGGLGLGGLL\nL llllurrrrd\nR ulllldrrrr\nC llurrd\nD CCRRRRRCCRRRRRR\nF RDDRRRRRDLLLLDDLL\nG FF\nDONE\nSURGERY COMPLETE\nrrrrrrGLLGLLGLLGLLGLLGLL\nL llllllurrrrrrd\nR ulllllldrrrrrr\nC lllurrrd\nD CCRRRRRRRCCRRRRRRRR\nF RRDDRRRRRRRDLLLLLLDDLLL\nG FF\nDONE\nSURGERY COMPLETE\nrrrrrrGLLGLLGLLLGRGGLGLLGLGGLL\nL llllllurrrrrrd\nR ulllllldrrrrrr\nC lllurrrd\nD CCRRRRRRRCCRRRRRRRR\nF RRDDRRRRRRRDLLLLLLDDLLL\nG FF\nDONE\nSURGERY FAILED\n",
"SURGERY FAILED\nSURGERY COMPLETE\nrrrrrrLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLGRGRGRGRGRGRGRGRGRGGLLLLLLLGRGRGRGRGRGRGGLLLLLLGRGRGRGRGGLLLGRGRGGLGLGGLGLGGLGGLL\nL llllllurrrrrrd\nR ulllllldrrrrrr\nC lllurrrd\nD CCRRRRRRRCCRRRRRRRR\nF RRDDRRRRRRRDLLLLLLDDLLL\nG FF\nDONE\nSURGERY FAILED\nSURGERY FAILED\n",
"SURGERY FAILED\nSURGERY COMPLETE\nrrGLGLGGLGGLLLGRGRGGLGLGLL\nL llllurrrrd\nR ulllldrrrr\nC llurrd\nD CCRRRRRCCRRRRRR\nF RDDRRRRRDLLLLDDLL\nG FF\nDONE\nSURGERY COMPLETE\nrrLGRGGLLGLL\nL llurrd\nR ulldrr\nC lurd\nD CCRRRCCRRRR\nF DDRRRDLLDDL\nG FF\nDONE\nSURGERY COMPLETE\nrrrrrrrrrrrrrrrrrLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGR...",
"SURGERY COMPLETE\nrrrrdLLGRGRGGLLLGRGRGGLLLLLLLGRGRGRGRGRGRGGLLLLGRGRGRGGLLGRGGLLLLGRGRGGLLGLGGLGGLL\nL llllllurrrrrrd\nR ulllllldrrrrrr\nC lllurrrd\nD CCRRRRRRRCCRRRRRRRR\nF RRDDRRRRRRRDLLLLLLDDLLL\nG FF\nDONE\nSURGERY FAILED\nSURGERY FAILED\nSURGERY FAILED\n",
"SURGERY FAILED\nSURGERY COMPLETE\nrrdLLGRGGLLL\nL llurrd\nR ulldrr\nC lurd\nD CCRRRCCRRRR\nF DDRRRDLLDDL\nG FF\nDONE\nSURGERY FAILED\nSURGERY FAILED\n",
"SURGERY COMPLETE\nrrrrLLLLLGRGRGRGRGRGGLGLLLLGRGRGRGGLGLLLLL\nL llllurrrrd\nR ulllldrrrr\nC llurrd\nD CCRRRRRCCRRRRRR\nF RDDRRRRRDLLLLDDLL\nG FF\nDONE\nSURGERY FAILED\nSURGERY FAILED\nSURGERY COMPLETE\ndLLLLLLLLGRGRGRGRGRGRGRGRGGLLLLLLLLLLGRGRGRGRGRGRGRGRGRGGLLGRGGLLLGRGRGGLGLLLLGRGGLGLGGLGLL\nL llllllurrrrrrd\nR ulllllldrrrrrr\nC lllurrrd\nD CCRRRRRRRCCRRRRRRRR\nF RRDDRRRRRRRDLLLLLLDDLLL\nG FF\nDONE\n",
"SURGERY FAILED\n",
"SURGERY FAILED\nSURGERY FAILED\nSURGERY FAILED\nSURGERY FAILED\n",
"SURGERY COMPLETE\nrrrrGLLGLLGRGGLGLGLLLLLGRGRGRGRGGLGLLLGRGRGGLGLGGLL\nL llllllurrrrrrd\nR ulllllldrrrrrr\nC lllurrrd\nD CCRRRRRRRCCRRRRRRRR\nF RRDDRRRRRRRDLLLLLLDDLLL\nG FF\nDONE\nSURGERY COMPLETE\nrrGLLGLLGRGGLGLGLLLLLGRGRGRGRGGLGLLLGRGRGGLGLGGLL\nL llllllurrrrrrd\nR ulllllldrrrrrr\nC lllurrrd\nD CCRRRRRRRCCRRRRRRRR\nF RRDDRRRRRRRDLLLLLLDDLLL\nG FF\nDONE\nSURGERY FAILED\nSURGERY COMPLETE\nrrrrrrrrGLLGLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRG...",
"SURGERY FAILED\nSURGERY COMPLETE\nrLLLGRGRGRGGLLLLLLLLGRGRGRGRGRGRGRGGLGLLLLLLGRGRGRGRGRGGLGLLLLGRGRGRGGLLGGLGGLLLL\nL llllllurrrrrrd\nR ulllllldrrrrrr\nC lllurrrd\nD CCRRRRRRRCCRRRRRRRR\nF RRDDRRRRRRRDLLLLLLDDLLL\nG FF\nDONE\nSURGERY FAILED\nSURGERY FAILED\n",
"SURGERY COMPLETE\nrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLGLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLGLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGR...",
"SURGERY COMPLETE\nrrrrrrrrrrdGLLGLLGLLGLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLGLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLGLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLGLLLLLLLLL...",
"SURGERY COMPLETE\nrrrrrrrrrrLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLGRGRGRGGLLLLLLLLLGRGRGRGRGRGRGRGRGGLLLLLLGRGRGRGRGRGGLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLGRGRGGLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGGLGLLLLLLGRGRGRGRGRGGLLLLGRGRGRGGLGLLLLLGRGRGRGRGGLLLLGRGRGRGGLLLGRGRGGLLGLGLLGRGGLLL\nL llllllllllurrrrrrrrrrd\nR ulllllllllldrrrrrrrrrr\nC lllllurrrrrd\nD CCRRRRRRRRRRRCCRRRRRRRRRRRR\nF RRRRDDRRRRRRRRRRRDLLLLLLLLLLDDLLLLL\nG FF\nDONE\nSURGERY FAILED\nSURGERY COMPLETE\nrrrrrrrrrrrrrrrdLLL...",
"SURGERY COMPLETE\nrrrrrrrrrrrrrrrrLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRG...",
"SURGERY COMPLETE\nrrdLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGGLLLLGRGRGRGGLLLLLLLLLLGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGGLLLLGRGRGRGGLLLLLLLLLLGRGRGRGRGRGRGRGRGRGGLLLLLLGRGRGRGRGRGGLLLGRGRGGLLLLLLGRGRGRGRGRGGLLLLLGRGRGRGRGGLLLLGRGRGRGGLGGLLLLGRGRGRGGLLLGLL\nL llllllllllurrrrrrrrrrd\nR ulllllllllldrrrrrrrrrr\nC lllllurrrrrd\nD CCRRRRRRRRRRRCCRRRRRRRRRRRR\nF RRRRDDRRRRRRRRRRRDLLLLLLLLLLDDL...",
"SURGERY COMPLETE\nrdGLGGLGLL\nL llurrd\nR ulldrr\nC lurd\nD CCRRRCCRRRR\nF DDRRRDLLDDL\nG FF\nDONE\nSURGERY COMPLETE\nrrGGLLLLLLGRGRGRGRGRGGLLLGRGGLLGRGGLLGRGGLLL\nL llllurrrrd\nR ulllldrrrr\nC llurrd\nD CCRRRRRCCRRRRRR\nF RDDRRRRRDLLLLDDLL\nG FF\nDONE\nSURGERY FAILED\nSURGERY COMPLETE\nrrrrLGRGGLLLLLLGRGRGRGRGRGGLLLLGRGRGRGGLGGLLGRGGLGLGGLL\nL llllurrrrd\nR ulllldrrrr\nC llurrd\nD CCRRRRRCCRRRRRR\nF RDDRRRRRDLLLLDDLL\nG FF\nDONE\n",
"SURGERY COMPLETE\nrrrrrrLLLLLLGRGRGRGRGRGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLLLLGRGRGRGRGGLGLLLGRGRGGLGLGLL\nL llllllurrrrrrd\nR ulllllldrrrrrr\nC lllurrrd\nD CCRRRRRRRCCRRRRRRRR\nF RRDDRRRRRRRDLLLLLLDDLLL\nG FF\nDONE\nSURGERY COMPLETE\nrrrrLLLLGRGRGRGRGGLLLGRGRGGLLLGRGRGGLLGRGGLGGLLGRGGLGLL\nL llllurrrrd\nR ulllldrrrr\nC llurrd\nD CCRRRRRCCRRRRRR\nF RDDRRRRRDLLLLDDLL\nG FF\nDONE\nSURGERY COMPLETE\nrrrrrrrrrrrrrLLLLLLLLLGRGRGRGRGRGRGRGRGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLLLLLLLLGRGRGRGRGRGRGRGRGGLLLLGRGRGRG...",
"SURGERY FAILED\nSURGERY COMPLETE\nrdGLLGLL\nL llurrd\nR ulldrr\nC lurd\nD CCRRRCCRRRR\nF DDRRRDLLDDL\nG FF\nDONE\nSURGERY FAILED\nSURGERY FAILED\n",
"SURGERY FAILED\nSURGERY FAILED\nSURGERY COMPLETE\nrdLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGGLLLLGRGRGRGGLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLLLL...",
"SURGERY FAILED\nSURGERY FAILED\nSURGERY COMPLETE\nrrdLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLGRGGLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGGLGLLLLLLLLLLGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLGRGRGRGGLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLGRGRGRGRGRGRGRGRGRGGLLLLLLLL...",
"SURGERY COMPLETE\nrrrrrrLLLLLLLLLGRGRGRGRGRGRGRGRGRGGLGLLLLLLLLGRGRGRGRGRGRGRGGLGLLLLLLGRGRGRGRGRGGLGLLLLGRGRGRGGLGLLGRGGLGLLL\nL llllllurrrrrrd\nR ulllllldrrrrrr\nC lllurrrd\nD CCRRRRRRRCCRRRRRRRR\nF RRDDRRRRRRRDLLLLLLDDLLL\nG FF\nDONE\nSURGERY FAILED\nSURGERY COMPLETE\nrrrrrrrrrrrrrrrrrrLLLGRGRGRGGLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGR...",
"SURGERY FAILED\nSURGERY FAILED\nSURGERY COMPLETE\nrrrrrrrrrrrrrrrrrrrrrrrrrrdGLLGLLGLLGLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLGRGRGRGGLLLLGRGRGRGGLLLLGRGRGRGGLLLLGRGRGRGGLLLLGRGRGRGGLLLLGRGRGRGGLLLLGRGRGRGGLLLLGRGRGRGGLLLLGRGRGRGGLLLLGRGRGRGGLLLLGRGRGRGGLLLLGRGRGRGGLLLLGRGRG...",
"SURGERY COMPLETE\nrrdGGLGGLLGLLGLLLLLGRGRGRGRGGLGLLLGRGRGGLGLGGLL\nL llllllurrrrrrd\nR ulllllldrrrrrr\nC lllurrrd\nD CCRRRRRRRCCRRRRRRRR\nF RRDDRRRRRRRDLLLLLLDDLLL\nG FF\nDONE\nSURGERY COMPLETE\nrGGLGGLGGLL\nL llurrd\nR ulldrr\nC lurd\nD CCRRRCCRRRR\nF DDRRRDLLDDL\nG FF\nDONE\nSURGERY COMPLETE\nGLLLGLLGRGGLGLGLL\nL llllurrrrd\nR ulllldrrrr\nC llurrd\nD CCRRRRRCCRRRRRR\nF RDDRRRRRDLLLLDDLL\nG FF\nDONE\nSURGERY COMPLETE\nrLLGRGRGGLGLLL\nL llurrd\nR ulldrr\nC lurd\nD CCRRRCCRRRR\nF DDRRRDLLDDL\nG FF\nDONE\n",
"SURGERY COMPLETE\nrrrrrrdLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLL...",
"SURGERY FAILED\nSURGERY FAILED\nSURGERY FAILED\nSURGERY FAILED\n",
"SURGERY COMPLETE\nrrLGRGGLGLLL\nL llurrd\nR ulldrr\nC lurd\nD CCRRRCCRRRR\nF DDRRRDLLDDL\nG FF\nDONE\nSURGERY FAILED\nSURGERY COMPLETE\nGLLGLGLLLGRGRGGLLGRGGLGLL\nL llllurrrrd\nR ulllldrrrr\nC llurrd\nD CCRRRRRCCRRRRRR\nF RDDRRRRRDLLLLDDLL\nG FF\nDONE\nSURGERY FAILED\n",
"SURGERY COMPLETE\nrrrrdGLLGLLLLLLLGRGRGRGRGRGRGGLLGRGGLLGRGGLLLLLGRGRGRGRGGLLGLGLGGLL\nL llllllurrrrrrd\nR ulllllldrrrrrr\nC lllurrrd\nD CCRRRRRRRCCRRRRRRRR\nF RRDDRRRRRRRDLLLLLLDDLLL\nG FF\nDONE\nSURGERY FAILED\nSURGERY COMPLETE\nrrGLLGLL\nL llurrd\nR ulldrr\nC lurd\nD CCRRRCCRRRR\nF DDRRRDLLDDL\nG FF\nDONE\nSURGERY FAILED\n",
"SURGERY COMPLETE\nrrrrrdLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLGRGRGRGGLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRG...",
"SURGERY COMPLETE\nrrrrrrrrrrrrLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLGRGGLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLGRGRGGLLLLLLLLLLGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLGRGRGRGRGRGRGRGRGRGGLGLGLLLLLLLLLLLLGRG...",
"SURGERY FAILED\nSURGERY FAILED\nSURGERY COMPLETE\nrrrrrrrrrrrrrrrrrrrrrrdLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLGLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLGLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLGLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRG...",
"SURGERY COMPLETE\nrrrrrrdGLLGLLGLLGLLGLLGLL\nL llllllurrrrrrd\nR ulllllldrrrrrr\nC lllurrrd\nD CCRRRRRRRCCRRRRRRRR\nF RRDDRRRRRRRDLLLLLLDDLLL\nG FF\nDONE\nSURGERY FAILED\nSURGERY FAILED\nSURGERY COMPLETE\nrrrrrrrrrrrrrrrrrrrrrrrrrrrrdGLLGLLGLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLLLLLLLLLLLLLLLLL...",
"SURGERY COMPLETE\nrrrrrGLLLGRGRGGLLLLLLLLLGRGRGRGRGRGRGRGGLLGRGGLLGRGGLLLLLGRGRGGLGLGGLL\nL llllllurrrrrrd\nR ulllllldrrrrrr\nC lllurrrd\nD CCRRRRRRRCCRRRRRRRR\nF RRDDRRRRRRRDLLLLLLDDLLL\nG FF\nDONE\nSURGERY FAILED\nSURGERY COMPLETE\ndGLLLGRGRGGLLGRGGLLLGRGRGGLLLGRGRGGLGLLL\nL llllurrrrd\nR ulllldrrrr\nC llurrd\nD CCRRRRRCCRRRRRR\nF RDDRRRRRDLLLLDDLL\nG FF\nDONE\nSURGERY FAILED\n",
"SURGERY COMPLETE\nrrdLGRGGLGLLL\nL llurrd\nR ulldrr\nC lurd\nD CCRRRCCRRRR\nF DDRRRDLLDDL\nG FF\nDONE\nSURGERY COMPLETE\nrrdGLLLL\nL llurrd\nR ulldrr\nC lurd\nD CCRRRCCRRRR\nF DDRRRDLLDDL\nG FF\nDONE\nSURGERY FAILED\nSURGERY FAILED\n",
"SURGERY COMPLETE\nrrGLLGLLLLGRGRGGLGLGGLL\nL llllurrrrd\nR ulllldrrrr\nC llurrd\nD CCRRRRRCCRRRRRR\nF RDDRRRRRDLLLLDDLL\nG FF\nDONE\nSURGERY COMPLETE\nrGLLGLLLLGRGRGGLGLGGLL\nL llllurrrrd\nR ulllldrrrr\nC llurrd\nD CCRRRRRCCRRRRRR\nF RDDRRRRRDLLLLDDLL\nG FF\nDONE\nSURGERY COMPLETE\nGLLGLLLLGRGRGGLGLGGLL\nL llllurrrrd\nR ulllldrrrr\nC llurrd\nD CCRRRRRCCRRRRRR\nF RDDRRRRRDLLLLDDLL\nG FF\nDONE\nSURGERY COMPLETE\ndGLLGLGGLLLGRGRGGLLLLLLGRGRGRGRGGLGLLLGRGRGGLGLGGLL\nL llllllurrrrrrd\nR ulllllldrrrrrr\nC lllurr...",
"SURGERY FAILED\nSURGERY FAILED\nSURGERY COMPLETE\ndLGGLGGLL\nL llurrd\nR ulldrr\nC lurd\nD CCRRRCCRRRR\nF DDRRRDLLDDL\nG FF\nDONE\nSURGERY FAILED\n",
"SURGERY COMPLETE\nrrrrrrrrrrrrrrrrrrrrrrrrrrrrGLLGLLGLLGLLGLLGLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLGLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLGLLLLLLLGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLGLLLLLLLLLLLLLLLL...",
"SURGERY COMPLETE\nLLLGRGRGRGGLLGRGGLGGLLGRGGLGGLLGRGGLLL\nL llllurrrrd\nR ulllldrrrr\nC llurrd\nD CCRRRRRCCRRRRRR\nF RDDRRRRRDLLLLDDLL\nG FF\nDONE\nSURGERY COMPLETE\nrrdLGRGGLLLGRGRGGLLLLLLLGRGRGRGRGRGRGGLLLLLGRGRGRGRGGLLLGRGRGGLLLGRGGLLLGRGRGGLGGLGLGGLL\nL llllllurrrrrrd\nR ulllllldrrrrrr\nC lllurrrd\nD CCRRRRRRRCCRRRRRRRR\nF RRDDRRRRRRRDLLLLLLDDLLL\nG FF\nDONE\nSURGERY COMPLETE\nrrdLLLLLLGRGRGRGRGRGRGGLLGRGGLLGRGGLLLLGRGRGRGGLLLGRGRGGLLGLL\nL llllurrrrd\nR ulllldrrrr\nC llurrd\nD CCRRRRRCCRRRRRR\nF RDDRR...",
"SURGERY FAILED\nSURGERY COMPLETE\nrrdGLLGLL\nL llurrd\nR ulldrr\nC lurd\nD CCRRRCCRRRR\nF DDRRRDLLDDL\nG FF\nDONE\nSURGERY FAILED\nSURGERY FAILED\n",
"SURGERY FAILED\nSURGERY FAILED\nSURGERY FAILED\nSURGERY COMPLETE\nrrdLGLGGLL\nL llurrd\nR ulldrr\nC lurd\nD CCRRRCCRRRR\nF DDRRRDLLDDL\nG FF\nDONE\n",
"SURGERY FAILED\nSURGERY COMPLETE\nrGGLGGLGGLL\nL llurrd\nR ulldrr\nC lurd\nD CCRRRCCRRRR\nF DDRRRDLLDDL\nG FF\nDONE\nSURGERY COMPLETE\nGLLLGLLGRGGLGLGLL\nL llllurrrrd\nR ulllldrrrr\nC llurrd\nD CCRRRRRCCRRRRRR\nF RDDRRRRRDLLLLDDLL\nG FF\nDONE\nSURGERY COMPLETE\nrLLGRGRGGLGLLL\nL llurrd\nR ulldrr\nC lurd\nD CCRRRCCRRRR\nF DDRRRDLLDDL\nG FF\nDONE\n",
"SURGERY FAILED\nSURGERY COMPLETE\nrrdLGRGGLLLGRGRGGLLLLLLLGRGRGRGRGRGRGGLLLLLGRGRGRGRGGLLLGRGRGGLLLGRGGLLLGRGRGGLGGLGLGGLL\nL llllllurrrrrrd\nR ulllllldrrrrrr\nC lllurrrd\nD CCRRRRRRRCCRRRRRRRR\nF RRDDRRRRRRRDLLLLLLDDLLL\nG FF\nDONE\nSURGERY COMPLETE\nrrdLLLLLLGRGRGRGRGRGRGGLLGRGGLLGRGGLLLLGRGRGRGGLLLGRGRGGLLGLL\nL llllurrrrd\nR ulllldrrrr\nC llurrd\nD CCRRRRRCCRRRRRR\nF RDDRRRRRDLLLLDDLL\nG FF\nDONE\nSURGERY FAILED\n",
"SURGERY FAILED\nSURGERY COMPLETE\nrrrrrrrrrrdLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLLLLLLLLGRGRGRGRGRGRGRGRGGLGLLLLLLLGRGRGRGRGRGRGGLGLLLLLGRGRGRGRGGLGLLGLGGLL\nL llllllllllurrrrrrrrrrd\nR ulllllllllldrrrrrrrrrr\nC lllllurrrrrd\nD CCRRRRRRRRRRRCCRRRRRRRRRRRR\nF RRRRDDRRRRRRRRRRRDLLLLLLLLLLDDLLLLL\nG FF\nDONE\nSURGERY FAILED\nSURGERY FAILED\n",
"SURGERY FAILED\nSURGERY COMPLETE\nrGGLGGLGGLL\nL llurrd\nR ulldrr\nC lurd\nD CCRRRCCRRRR\nF DDRRRDLLDDL\nG FF\nDONE\nSURGERY FAILED\nSURGERY COMPLETE\nrLLGRGRGGLGLLL\nL llurrd\nR ulldrr\nC lurd\nD CCRRRCCRRRR\nF DDRRRDLLDDL\nG FF\nDONE\n",
"SURGERY FAILED\nSURGERY COMPLETE\nrrrrrrrrrrrdGGLLLGRGRGGLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLGRGRGRGRGRGRGRGRGRGGLLLGRGRGGLLLLLGRGRGRGRGGLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLGRGRGRGRGRGRGRGRGRGGLLLGRGRGGLLLGRGRGGLLLLLLLLLLGRGRGRGRGRGRGRGRGRGGLLLLLGRGRGRGRGGLLLLLLLLLLGRGRGRGRGRGRGRGRGRGGLLLLLGRGRGRGRGGLLLLLLLLLLGRGRGRGRGRGRGRGRGRGGLLLLLLLLLGRGRGRGRGRGRGRGRGGLGGLGGLGLLLGRGGLLGRGGLLGRGGLGGLL\nL llllllllllllllurrrrrrrrrrrrrrd\nR ulllllllllllllldrrrrrrrrrrrrrr\nC lllllllurrrrrrrd\nD CCRRRRRRRRRRRRRRRCCRRRRRRRRRRRRRRRR\nF RRRRRRDDRRRRRRRRRRRRRRRDLLLLLLLLLLLLLLDDLLLLLLL\nG FF\nDONE\nSURGERY COMPLETE\nrrrrrrdLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGGLGLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGGLGLLLLLLLLLGRGRGRGRGRGRGRGRGGLGGLLLLLLLLGRGRGRGRGRGRGRGGLLLLLLGRGRGRGRGRGGLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGGLGGLLLLLLGRGRGRGRGRGGLLLLLGRGRGRGRGGLLLLLLLLGRGRGRGRGRGRGRGGLLLGRGRGGLGLGGLLLGRGRGGLGLGLLGRGGLGLL\nL llllllllllllllllurrrrrrrrrrrrrrrrd\nR ulllllllllllllllldrrrrrrrrrrrrrrrr\nC llllllllurrrrrrrrd\nD CCRRRRRRRRRRRRRRRRRCCRRRRRRRRRRRRRRRRRR\nF RRRRRRRDDRRRRRRRRRRRRRRRRRDLLLLLLLLLLLLLLLLDDLLLLLLLL\nG FF\nDONE\nSURGERY COMPLETE\nrrrrrrLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLGRGRGRGGLLLLLLLLLGRGRGRGRGRGRGRGRGGLLLLGRGRGRGGLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLGRGGLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLGRGRGRGGLLLLLLLGRGRGRGRGRGRGGLGGLLLLLLLGRGRGRGRGRGRGGLLLLLGRGRGRGGLLLLGRGRGRGGLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGGLLLLLLGRGRGRGRGRGGLLLLLLLLGRGRGRGRGRGRGRGGLLLLLLLGRGRGRGRGRGRGGLLLLGRGRGRGGLLLGLLGRGGLLGRGGLGLL\nL llllllllllllllurrrrrrrrrrrrrrd\nR ulllllllllllllldrrrrrrrrrrrrrr\nC lllllllurrrrrrrd\nD CCRRRRRRRRRRRRRRRCCRRRRRRRRRRRRRRRR\nF RRRRRRDDRRRRRRRRRRRRRRRDLLLLLLLLLLLLLLDDLLLLLLL\nG FF\nDONE\n",
"SURGERY COMPLETE\nrrrrLLLLLGRGRGRGRGRGGLGLLLLGRGRGRGGLGLLLLL\nL llllurrrrd\nR ulllldrrrr\nC llurrd\nD CCRRRRRCCRRRRRR\nF RDDRRRRRDLLLLDDLL\nG FF\nDONE\nSURGERY FAILED\nSURGERY FAILED\nSURGERY COMPLETE\ndLLLLLLLLGRGRGRGRGRGRGRGRGGLLLLLLLLLLGRGRGRGRGRGRGRGRGRGGLLGRGGLLLGRGRGGLGLLLLGRGGLGLGGLGLL\nL llllllurrrrrrd\nR ulllllldrrrrrr\nC lllurrrd\nD CCRRRRRRRCCRRRRRRRR\nF RRDDRRRRRRRDLLLLLLDDLLL\nG FF\nDONE\n",
"SURGERY FAILED\nSURGERY COMPLETE\nrdGLLGLL\nL llurrd\nR ulldrr\nC lurd\nD CCRRRCCRRRR\nF DDRRRDLLDDL\nG FF\nDONE\nSURGERY FAILED\nSURGERY FAILED\n",
"SURGERY COMPLETE\nrrrrdGLLGLLLLLLLGRGRGRGRGRGRGGLLGRGGLLGRGGLLLLLGRGRGRGRGGLLGLGLGGLL\nL llllllurrrrrrd\nR ulllllldrrrrrr\nC lllurrrd\nD CCRRRRRRRCCRRRRRRRR\nF RRDDRRRRRRRDLLLLLLDDLLL\nG FF\nDONE\nSURGERY FAILED\nSURGERY COMPLETE\nrrGLLGLL\nL llurrd\nR ulldrr\nC lurd\nD CCRRRCCRRRR\nF DDRRRDLLDDL\nG FF\nDONE\nSURGERY FAILED\n",
"SURGERY FAILED\nSURGERY FAILED\nSURGERY FAILED\nSURGERY FAILED\n",
"SURGERY COMPLETE\nrrrrdGLLGLLLLLLLGRGRGRGRGRGRGGLLGRGGLLGRGGLLLLLGRGRGRGRGGLLGLGLGGLL\nL llllllurrrrrrd\nR ulllllldrrrrrr\nC lllurrrd\nD CCRRRRRRRCCRRRRRRRR\nF RRDDRRRRRRRDLLLLLLDDLLL\nG FF\nDONE\nSURGERY FAILED\nSURGERY FAILED\nSURGERY FAILED\n",
"SURGERY COMPLETE\nrrrrrLGGLLLLLLGRGRGRGRGRGGLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLGRGRGRGRGRGRGRGRGRGGLLLLLLLGRGRGRGRGRGRGGLLLGRGRGGLGGLLLLGRGRGRGGLGLGGLGGLLGRGGLLLL\nL llllllllurrrrrrrrd\nR ulllllllldrrrrrrrr\nC llllurrrrd\nD CCRRRRRRRRRCCRRRRRRRRRR\nF RRRDDRRRRRRRRRDLLLLLLLLDDLLLL\nG FF\nDONE\nSURGERY FAILED\nSURGERY COMPLETE\nrrrrrrrrrrrLLLLLLGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLGRGRGRGRGRGRGRGRGGLLGRGGLLGRGGLLGRGGLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLGLLGRGGLLLLLGRGRGRGRGGLLLLGRGRGRGGLLLLLLGRGRGRGRGRGGLLGRGGLLLLLLLGRGRGRGRGRGRGGLLLLLGRGRGRGRGGLGLGGLLGRGGLLLGRGGLGGLL\nL llllllllllllurrrrrrrrrrrrd\nR ulllllllllllldrrrrrrrrrrrr\nC llllllurrrrrrd\nD CCRRRRRRRRRRRRRCCRRRRRRRRRRRRRR\nF RRRRRDDRRRRRRRRRRRRRDLLLLLLLLLLLLDDLLLLLL\nG FF\nDONE\nSURGERY COMPLETE\nrdGLGLGGLL\nL llurrd\nR ulldrr\nC lurd\nD CCRRRCCRRRR\nF DDRRRDLLDDL\nG FF\nDONE\n",
"SURGERY COMPLETE\nrrrrGLLGLLGRGGLGLGLLLLLGRGRGRGRGGLGLLLGRGRGGLGLGGLL\nL llllllurrrrrrd\nR ulllllldrrrrrr\nC lllurrrd\nD CCRRRRRRRCCRRRRRRRR\nF RRDDRRRRRRRDLLLLLLDDLLL\nG FF\nDONE\nSURGERY FAILED\nSURGERY FAILED\nSURGERY COMPLETE\nrrrrrrrrGLLGLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLGLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLGLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLGLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLGLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLGLGLGLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLGLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLGLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGGLGLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGGLGLLLLLLLLLGRGRGRGRGRGRGRGRGGLGLLLLLLLGRGRGRGRGRGRGGLGLLLLLGRGRGRGRGGLGLLLGRGRGGLGLGGLL\nL llllllllllllllllllllllllllllllurrrrrrrrrrrrrrrrrrrrrrrrrrrrrrd\nR ulllllllllllllllllllllllllllllldrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr\nC lllllllllllllllurrrrrrrrrrrrrrrd\nD CCRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRCCRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR\nF RRRRRRRRRRRRRRDDRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRDLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLDDLLLLLLLLLLLLLLL\nG FF\nDONE\n",
"SURGERY COMPLETE\nrrdGGLGGLLGLLGLLLLLGRGRGRGRGGLGLLLGRGRGGLGLGGLL\nL llllllurrrrrrd\nR ulllllldrrrrrr\nC lllurrrd\nD CCRRRRRRRCCRRRRRRRR\nF RRDDRRRRRRRDLLLLLLDDLLL\nG FF\nDONE\nSURGERY COMPLETE\nrGGLGGLGGLL\nL llurrd\nR ulldrr\nC lurd\nD CCRRRCCRRRR\nF DDRRRDLLDDL\nG FF\nDONE\nSURGERY COMPLETE\nGLLLGLLGRGGLGLGLL\nL llllurrrrd\nR ulllldrrrr\nC llurrd\nD CCRRRRRCCRRRRRR\nF RDDRRRRRDLLLLDDLL\nG FF\nDONE\nSURGERY FAILED\n",
"SURGERY FAILED\nSURGERY COMPLETE\nrdGLLGLL\nL llurrd\nR ulldrr\nC lurd\nD CCRRRCCRRRR\nF DDRRRDLLDDL\nG FF\nDONE\nSURGERY COMPLETE\nrdLGLGGLL\nL llurrd\nR ulldrr\nC lurd\nD CCRRRCCRRRR\nF DDRRRDLLDDL\nG FF\nDONE\nSURGERY FAILED\n",
"SURGERY FAILED\nSURGERY FAILED\nSURGERY FAILED\nSURGERY COMPLETE\nrrrrrrrrrrrrrrrrrrrrrrrrrrrrdGLLGLLGLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLGLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLGLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLGLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLGLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLGLGLGLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLGLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGGLGLLLLLLLLLLGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLGRGRGRGRGRGRGRGRGRGGLGGLGLLLLLLLGRGRGRGRGRGRGGLGLLLLLGRGRGRGRGGLGLLLGRGRGGLGLGGLL\nL llllllllllllllllllllllllllllurrrrrrrrrrrrrrrrrrrrrrrrrrrrd\nR ulllllllllllllllllllllllllllldrrrrrrrrrrrrrrrrrrrrrrrrrrrr\nC llllllllllllllurrrrrrrrrrrrrrd\nD CCRRRRRRRRRRRRRRRRRRRRRRRRRRRRRCCRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR\nF RRRRRRRRRRRRRDDRRRRRRRRRRRRRRRRRRRRRRRRRRRRRDLLLLLLLLLLLLLLLLLLLLLLLLLLLLDDLLLLLLLLLLLLLL\nG FF\nDONE\n",
"SURGERY COMPLETE\nrrrrrrGLLLLLLLGRGRGRGRGRGGLLGRGGLLLGRGRGGLLLGRGRGGLGGLLLLGRGRGRGGLGLGGLGGLL\nL llllllurrrrrrd\nR ulllllldrrrrrr\nC lllurrrd\nD CCRRRRRRRCCRRRRRRRR\nF RRDDRRRRRRRDLLLLLLDDLLL\nG FF\nDONE\nSURGERY COMPLETE\nGLLLLLLLLGRGRGRGRGRGRGGLLGRGGLLGRGGLLGRGGLLLLLGRGRGRGRGGLGLLLGRGGLGLL\nL llllllurrrrrrd\nR ulllllldrrrrrr\nC lllurrrd\nD CCRRRRRRRCCRRRRRRRR\nF RRDDRRRRRRRDLLLLLLDDLLL\nG FF\nDONE\nSURGERY COMPLETE\nrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrGLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLLGRGGLGGLGLLGLLGLLGLLGLLGLLGLLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLGRGGLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLGRGRGRGGLLLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLGLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLGLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLGRGRGGLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLGLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLGGLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLGLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGGLGLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGGLGLLLLLLLLLGRGRGRGRGRGRGRGRGGLGLLLLLLLGRGRGRGRGRGRGGLGLLLLLGRGRGRGRGGLGLLLGRGRGGLGLGGLL\nL llllllllllllllllllllllllllllllurrrrrrrrrrrrrrrrrrrrrrrrrrrrrrd\nR ulllllllllllllllllllllllllllllldrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr\nC lllllllllllllllurrrrrrrrrrrrrrrd\nD CCRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRCCRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR\nF RRRRRRRRRRRRRRDDRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRDLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLDDLLLLLLLLLLLLLLL\nG FF\nDONE\nSURGERY FAILED\n",
"SURGERY COMPLETE\nrrrrrrrrrrLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLGRGRGRGGLLLLLLLLLGRGRGRGRGRGRGRGRGGLLLLLLGRGRGRGRGRGGLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLGRGRGGLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGGLGLLLLLLGRGRGRGRGRGGLLLLGRGRGRGGLGLLLLLGRGRGRGRGGLLLLGRGRGRGGLLLGRGRGGLLGLGLLGRGGLLL\nL llllllllllurrrrrrrrrrd\nR ulllllllllldrrrrrrrrrr\nC lllllurrrrrd\nD CCRRRRRRRRRRRCCRRRRRRRRRRRR\nF RRRRDDRRRRRRRRRRRDLLLLLLLLLLDDLLLLL\nG FF\nDONE\nSURGERY FAILED\nSURGERY FAILED\nSURGERY COMPLETE\nrrrrrrrrrrrrrrdLLLLLLLLGRGRGRGRGRGRGRGRGGLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLGRGRGRGRGRGGLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLGGLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLGGLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGGLGGLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLGRGRGRGRGGLLLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLLLLLLLLGRGRGRGRGRGRGRGGLLLLLLLLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGRGGLGLLLLLLLLLGRGRGRGRGRGRGRGRGGLLLLLLGRGRGRGRGRGGLLLLLLLGRGRGRGRGRGRGGLLLLLLLLLLGRGRGRGRGRGRGRGRGRGGLGLLLLLLLLLGRGRGRGRGRGRGRGRGGLGGLLGRGGLLLLGRGRGRGGLLLLLGRGRGRGRGGLLLLLLLLLGRGRGRGRGRGRGRGRGGLLLLLLGRGRGRGRGRGGLLLLLLGRGRGRGRGRGGLLLGRGRGGLLGRGGLLLGRGRGGLGGLLGRGGLLGGLL\nL llllllllllllllllllllllllllurrrrrrrrrrrrrrrrrrrrrrrrrrd\nR ulllllllllllllllllllllllllldrrrrrrrrrrrrrrrrrrrrrrrrrr\nC lllllllllllllurrrrrrrrrrrrrd\nD CCRRRRRRRRRRRRRRRRRRRRRRRRRRRCCRRRRRRRRRRRRRRRRRRRRRRRRRRRR\nF RRRRRRRRRRRRDDRRRRRRRRRRRRRRRRRRRRRRRRRRRDLLLLLLLLLLLLLLLLLLLLLLLLLLDDLLLLLLLLLLLLL\nG FF\nDONE\n",
"SURGERY FAILED\nSURGERY COMPLETE\ndLLLLLLLLLLGRGRGRGRGRGRGRGRGRGRGGLLLGRGRGGLLLGRGRGGLLLLLGRGRGRGRGGLLLGLLLLGRGRGGLGLGGLL\nL llllllurrrrrrd\nR ulllllldrrrrrr\nC lllurrrd\nD CCRRRRRRRCCRRRRRRRR\nF RRDDRRRRRRRDLLLLLLDDLLL\nG FF\nDONE\nSURGERY FAILED\nSURGERY COMPLETE\nrrrrLLLLLGRGRGRGRGRGGLGLLLLGRGRGRGGLGLLGRGGLGLLL\nL llllurrrrd\nR ulllldrrrr\nC llurrd\nD CCRRRRRCCRRRRRR\nF RDDRRRRRDLLLLDDLL\nG FF\nDONE\n",
"SURGERY COMPLETE\nrrrrLLLLLGRGRGRGRGRGGLGLLLLGRGRGRGGLGLLLLL\nL llllurrrrd\nR ulllldrrrr\nC llurrd\nD CCRRRRRCCRRRRRR\nF RDDRRRRRDLLLLDDLL\nG FF\nDONE\nSURGERY FAILED\nSURGERY FAILED\nSURGERY COMPLETE\ndLLLLLLLLGRGRGRGRGRGRGRGRGGLLLLLLLLLLGRGRGRGRGRGRGRGRGRGGLLGRGGLLLGRGRGGLGLLLLGRGGLGLGGLGLL\nL llllllurrrrrrd\nR ulllllldrrrrrr\nC lllurrrd\nD CCRRRRRRRCCRRRRRRRR\nF RRDDRRRRRRRDLLLLLLDDLLL\nG FF\nDONE\n",
"SURGERY FAILED\nSURGERY COMPLETE\nrdGLLGLL\nL llurrd\nR ulldrr\nC lurd\nD CCRRRCCRRRR\nF DDRRRDLLDDL\nG FF\nDONE\nSURGERY FAILED\nSURGERY FAILED\n",
"SURGERY COMPLETE\nrrrrdGLLGLLLLLLLGRGRGRGRGRGRGGLLGRGGLLGRGGLLLLLGRGRGRGRGGLLGLGLGGLL\nL llllllurrrrrrd\nR ulllllldrrrrrr\nC lllurrrd\nD CCRRRRRRRCCRRRRRRRR\nF RRDDRRRRRRRDLLLLLLDDLLL\nG FF\nDONE\nSURGERY FAILED\nSURGERY COMPLETE\nrrGLLGLL\nL llurrd\nR ulldrr\nC lurd\nD CCRRRCCRRRR\nF DDRRRDLLDDL\nG FF\nDONE\nSURGERY FAILED\n",
"SURGERY FAILED\nSURGERY COMPLETE\nrdGLLGLL\nL llurrd\nR ulldrr\nC lurd\nD CCRRRCCRRRR\nF DDRRRDLLDDL\nG FF\nDONE\nSURGERY FAILED\nSURGERY FAILED\n",
"SURGERY COMPLETE\nrrrrdGLLGLLLLLLLGRGRGRGRGRGRGGLLGRGGLLGRGGLLLLLGRGRGRGRGGLLGLGLGGLL\nL llllllurrrrrrd\nR ulllllldrrrrrr\nC lllurrrd\nD CCRRRRRRRCCRRRRRRRR\nF RRDDRRRRRRRDLLLLLLDDLLL\nG FF\nDONE\nSURGERY FAILED\nSURGERY FAILED\nSURGERY FAILED\n",
"SURGERY COMPLETE\nrrrrdGLLGLLLLLLLGRGRGRGRGRGRGGLLGRGGLLGRGGLLLLLGRGRGRGRGGLLGLGLGGLL\nL llllllurrrrrrd\nR ulllllldrrrrrr\nC lllurrrd\nD CCRRRRRRRCCRRRRRRRR\nF RRDDRRRRRRRDLLLLLLDDLLL\nG FF\nDONE\nSURGERY FAILED\nSURGERY COMPLETE\nrrGLLGLL\nL llurrd\nR ulldrr\nC lurd\nD CCRRRCCRRRR\nF DDRRRDLLDDL\nG FF\nDONE\nSURGERY FAILED\n",
"SURGERY FAILED\nSURGERY FAILED\nSURGERY FAILED\nSURGERY FAILED\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You are an intergalactic surgeon and you have an alien patient. For the purposes of this problem, we can and we will model this patient's body using a 2 × (2k + 1) rectangular grid. The alien has 4k + 1 distinct organs, numbered 1 to 4k + 1.
In healthy such aliens, the organs are arranged in a particular way. For example, here is how the organs of a healthy such alien would be positioned, when viewed from the top, for k = 4:
<image>
Here, the E represents empty space.
In general, the first row contains organs 1 to 2k + 1 (in that order from left to right), and the second row contains organs 2k + 2 to 4k + 1 (in that order from left to right) and then empty space right after.
Your patient's organs are complete, and inside their body, but they somehow got shuffled around! Your job, as an intergalactic surgeon, is to put everything back in its correct position. All organs of the alien must be in its body during the entire procedure. This means that at any point during the procedure, there is exactly one cell (in the grid) that is empty. In addition, you can only move organs around by doing one of the following things:
* You can switch the positions of the empty space E with any organ to its immediate left or to its immediate right (if they exist). In reality, you do this by sliding the organ in question to the empty space;
* You can switch the positions of the empty space E with any organ to its immediate top or its immediate bottom (if they exist) only if the empty space is on the leftmost column, rightmost column or in the centermost column. Again, you do this by sliding the organ in question to the empty space.
Your job is to figure out a sequence of moves you must do during the surgical procedure in order to place back all 4k + 1 internal organs of your patient in the correct cells. If it is impossible to do so, you must say so.
Input
The first line of input contains a single integer t (1 ≤ t ≤ 4) denoting the number of test cases. The next lines contain descriptions of the test cases.
Each test case consists of three lines. The first line contains a single integer k (1 ≤ k ≤ 15) which determines the size of the grid. Then two lines follow. Each of them contains 2k + 1 space-separated integers or the letter E. They describe the first and second rows of organs, respectively. It is guaranteed that all 4k + 1 organs are present and there is exactly one E.
Output
For each test case, first, print a single line containing either:
* SURGERY COMPLETE if it is possible to place back all internal organs in the correct locations;
* SURGERY FAILED if it is impossible.
If it is impossible, then this is the only line of output for the test case. However, if it is possible, output a few more lines describing the sequence of moves to place the organs in the correct locations.
The sequence of moves will be a (possibly empty) string of letters u, d, l or r, representing sliding the organ that's directly above, below, to the left or to the right of the empty space, respectively, into the empty space. Print the sequence of moves in the following line, as such a string.
For convenience, you may use shortcuts to reduce the size of your output. You may use uppercase letters as shortcuts for sequences of moves. For example, you could choose T to represent the string lddrr. These shortcuts may also include other shortcuts on their own! For example, you could choose E to represent TruT, etc.
You may use any number of uppercase letters (including none) as shortcuts. The only requirements are the following:
* The total length of all strings in your output for a single case is at most 10^4;
* There must be no cycles involving the shortcuts that are reachable from the main sequence;
* The resulting sequence of moves is finite, after expanding all shortcuts. Note that the final sequence of moves (after expanding) may be much longer than 10^4; the only requirement is that it's finite.
As an example, if T = lddrr, E = TruT and R = rrr, then TurTlER expands to:
* TurTlER
* lddrrurTlER
* lddrrurlddrrlER
* lddrrurlddrrlTruTR
* lddrrurlddrrllddrrruTR
* lddrrurlddrrllddrrrulddrrR
* lddrrurlddrrllddrrrulddrrrrr
To use shortcuts, print each one of them in a single line as the uppercase letter, then space, and then the string that this shortcut represents. They may be printed in any order. At the end of all of those, print a single line containing DONE.
Note: You still need to print DONE even if you don't plan on using shortcuts.
Your sequence does not need to be the shortest. Any valid sequence of moves (satisfying the requirements above) will be accepted.
Example
Input
2
3
1 2 3 5 6 E 7
8 9 10 4 11 12 13
11
34 45 6 22 16 43 38 44 5 4 41 14 7 29 28 19 9 18 42 8 17 33 1
E 15 40 36 31 24 10 2 21 11 32 23 30 27 35 25 13 12 39 37 26 20 3
Output
SURGERY COMPLETE
IR
R SrS
S rr
I lldll
DONE
SURGERY FAILED
Note
There are three shortcuts defined in the first sample output:
* R = SrS
* S = rr
* I = lldll
The sequence of moves is IR and it expands to:
* IR
* lldllR
* lldllSrS
* lldllrrrS
* lldllrrrrr
### Input:
2
3
1 2 3 5 6 E 7
8 9 10 4 11 12 13
11
34 45 6 22 16 43 38 44 5 4 41 14 7 29 28 19 9 18 42 8 17 33 1
E 15 40 36 31 24 10 2 21 11 32 23 30 27 35 25 13 12 39 37 26 20 3
### Output:
SURGERY COMPLETE
IR
R SrS
S rr
I lldll
DONE
SURGERY FAILED
### Input:
2
3
1 2 3 5 6 E 7
8 9 10 4 11 12 13
11
34 45 6 22 16 43 38 44 5 4 41 14 7 29 28 19 9 18 42 8 17 33 1
E 15 40 36 31 24 10 2 21 11 32 23 30 27 35 25 13 12 39 37 26 20 3
### Output:
SURGERY COMPLETE
rdGLLLLLLLGRGRGRGRGRGGLGGLGGLGGLGGLGGLGLLGLL
L llllllurrrrrrd
R ulllllldrrrrrr
C lllurrrd
D CCRRRRRRRCCRRRRRRRR
F RRDDRRRRRRRDLLLLLLDDLLL
G FF
DONE
SURGERY FAILED
### Code:
def solve(k, grid):
seek = *range(2*k + 2), *range(4*k + 1, 2*k + 1, -1)
flat = [seek[v] for v in grid[0] + grid[1][::-1] if v]
m = {
'L': 'l'*2*k + 'u' + 'r'*2*k + 'd',
'R': 'u' + 'l'*2*k + 'd' + 'r'*2*k,
'C': 'l'*k + 'u' + 'r'*k + 'd',
'D': 'CC' + 'R'*(2*k + 1) + 'CC' + 'R'*(2*k + 2),
'F': 'R'*(k - 1) + 'DD' + 'R'*(2*k + 1) + 'D' + 'L'*2*k + 'DD' + 'L'*k,
'G': 'FF',
}
[(i, j)] = [(i, j) for i in range(2) for j in range(2*k + 1) if grid[i][j] == 0]
st = 'r'*(2*k - j) + 'd'*(1 - i)
for v in range(2, 4*k + 2):
ct = flat.index(v)
if ct >= 2:
st += 'L'*(ct - 2) + 'GR'*(ct - 2) + 'G'
flat = flat[ct - 1: ct + 1] + flat[:ct - 1] + flat[ct + 1:]
if ct >= 1:
st += 'G'
flat = flat[1:3] + flat[:1] + flat[3:]
st += 'L'
flat = flat[1:] + flat[:1]
if flat[0] == 1: return st, m
def main():
def get_line():
return [0 if x == 'E' else int(x) for x in input().split()]
for cas in range(int(input())):
res = solve(int(input()), [get_line() for i in range(2)])
if res is None:
print('SURGERY FAILED')
else:
print('SURGERY COMPLETE')
st, m = res
print(st)
for shortcut in m.items(): print(*shortcut)
print('DONE')
main()
|
1300_E. Water Balance_10503
|
There are n water tanks in a row, i-th of them contains a_i liters of water. The tanks are numbered from 1 to n from left to right.
You can perform the following operation: choose some subsegment [l, r] (1≤ l ≤ r ≤ n), and redistribute water in tanks l, l+1, ..., r evenly. In other words, replace each of a_l, a_{l+1}, ..., a_r by \frac{a_l + a_{l+1} + ... + a_r}{r-l+1}. For example, if for volumes [1, 3, 6, 7] you choose l = 2, r = 3, new volumes of water will be [1, 4.5, 4.5, 7]. You can perform this operation any number of times.
What is the lexicographically smallest sequence of volumes of water that you can achieve?
As a reminder:
A sequence a is lexicographically smaller than a sequence b of the same length if and only if the following holds: in the first (leftmost) position where a and b differ, the sequence a has a smaller element than the corresponding element in b.
Input
The first line contains an integer n (1 ≤ n ≤ 10^6) — the number of water tanks.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^6) — initial volumes of water in the water tanks, in liters.
Because of large input, reading input as doubles is not recommended.
Output
Print the lexicographically smallest sequence you can get. In the i-th line print the final volume of water in the i-th tank.
Your answer is considered correct if the absolute or relative error of each a_i does not exceed 10^{-9}.
Formally, let your answer be a_1, a_2, ..., a_n, and the jury's answer be b_1, b_2, ..., b_n. Your answer is accepted if and only if \frac{|a_i - b_i|}{max{(1, |b_i|)}} ≤ 10^{-9} for each i.
Examples
Input
4
7 5 5 7
Output
5.666666667
5.666666667
5.666666667
7.000000000
Input
5
7 8 8 10 12
Output
7.000000000
8.000000000
8.000000000
10.000000000
12.000000000
Input
10
3 9 5 5 1 7 5 3 8 7
Output
3.000000000
5.000000000
5.000000000
5.000000000
5.000000000
5.000000000
5.000000000
5.000000000
7.500000000
7.500000000
Note
In the first sample, you can get the sequence by applying the operation for subsegment [1, 3].
In the second sample, you can't get any lexicographically smaller sequence.
|
def main():
from sys import stdin,stdout
ans = []
stdin.readline()
for ai in map(int, map(int, stdin.readline().split())):
cnt=1
while ans and ai*ans[-1][0]<=ans[-1][1]*cnt:
c, r = ans.pop()
ai+=r
cnt+=c
ans.append((cnt, ai))
for i, res in ans:
m = str(res/i)
stdout.write((m+"\n")*i)
main()
|
{
"input": [
"5\n7 8 8 10 12\n",
"10\n3 9 5 5 1 7 5 3 8 7\n",
"4\n7 5 5 7\n",
"3\n20 90 100\n",
"13\n987069 989619 960831 976342 972924 961800 954209 956033 998067 984513 977987 963504 985482\n",
"3\n20 100 50\n",
"2\n100 20\n",
"5\n742710 834126 850058 703320 972844\n",
"7\n765898 894083 551320 290139 300748 299067 592728\n",
"12\n8 10 4 6 6 4 1 2 2 6 9 5\n",
"1\n12345\n",
"3\n100 20 50\n",
"65\n1000000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64\n",
"3\n29 90 100\n",
"13\n987069 989619 960831 976342 972924 961800 954209 956033 998067 1311542 977987 963504 985482\n",
"3\n20 100 0\n",
"2\n101 20\n",
"5\n1206297 834126 850058 703320 972844\n",
"7\n765898 894083 551320 290139 300748 299067 1031363\n",
"12\n8 9 4 6 6 4 1 2 2 6 9 5\n",
"1\n897\n",
"3\n101 20 50\n",
"65\n1000000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 35 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64\n",
"5\n7 8 8 10 23\n",
"10\n3 9 5 5 0 7 5 3 8 7\n",
"4\n7 5 5 13\n",
"3\n29 90 101\n",
"13\n987069 989619 960831 976342 972924 961800 937670 956033 998067 1311542 977987 963504 985482\n",
"3\n20 100 1\n",
"2\n101 19\n",
"5\n1206297 834126 243876 703320 972844\n",
"7\n835378 894083 551320 290139 300748 299067 1031363\n",
"12\n8 9 4 4 6 4 1 2 2 6 9 5\n",
"1\n479\n",
"3\n111 20 50\n",
"65\n1000000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 44 25 26 35 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64\n",
"5\n7 8 13 10 23\n",
"10\n3 9 5 5 0 7 5 3 0 7\n",
"4\n7 1 5 13\n",
"3\n29 24 101\n",
"13\n987069 989619 960831 976342 972924 961800 937670 956033 998067 1311542 450665 963504 985482\n",
"3\n20 000 1\n",
"2\n101 26\n",
"5\n1206297 834126 243876 703320 1773609\n",
"7\n835378 894083 551320 453873 300748 299067 1031363\n",
"12\n8 9 4 4 0 4 1 2 2 6 9 5\n",
"1\n894\n",
"3\n011 20 50\n",
"65\n1000000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 16 19 20 21 22 23 44 25 26 35 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64\n",
"5\n7 8 23 10 23\n",
"10\n3 9 5 5 0 7 4 3 0 7\n",
"4\n5 1 5 13\n",
"3\n23 24 101\n",
"13\n987069 989619 960831 976342 972924 961800 937670 956033 998067 1311542 450665 963504 1716586\n",
"3\n20 010 1\n",
"2\n100 19\n",
"5\n1206297 834126 243876 612353 1773609\n",
"7\n835378 894083 551320 453873 300748 394191 1031363\n",
"12\n8 9 4 2 0 4 1 2 2 6 9 5\n",
"1\n1005\n",
"3\n011 20 92\n",
"65\n1000000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 16 19 20 21 22 23 44 25 26 35 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 104 59 60 61 62 63 64\n",
"5\n7 8 23 10 0\n",
"10\n3 9 5 5 0 14 5 3 0 7\n",
"4\n5 1 5 7\n",
"3\n22 24 101\n"
],
"output": [
"7.000000000\n8.000000000\n8.000000000\n10.000000000\n12.000000000\n",
"3.000000000\n5.000000000\n5.000000000\n5.000000000\n5.000000000\n5.000000000\n5.000000000\n5.000000000\n7.500000000\n7.500000000\n",
"5.666666667\n5.666666667\n5.666666667\n7.000000000\n",
"20.000000000\n90.000000000\n100.000000000\n",
"969853.375000000\n969853.375000000\n969853.375000000\n969853.375000000\n969853.375000000\n969853.375000000\n969853.375000000\n969853.375000000\n981017.750000000\n981017.750000000\n981017.750000000\n981017.750000000\n985482.000000000\n",
"20.000000000\n75.000000000\n75.000000000\n",
"60.000000000\n60.000000000\n",
"742710.000000000\n795834.666666667\n795834.666666667\n795834.666666667\n972844.000000000\n",
"516875.833333333\n516875.833333333\n516875.833333333\n516875.833333333\n516875.833333333\n516875.833333333\n592728.000000000\n",
"4.777777778\n4.777777778\n4.777777778\n4.777777778\n4.777777778\n4.777777778\n4.777777778\n4.777777778\n4.777777778\n6.000000000\n7.000000000\n7.000000000\n",
"12345.000000000\n",
"56.666666667\n56.666666667\n56.666666667\n",
"15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n15416.615384615\n",
"29.0\n90.0\n100.0\n",
"969853.375\n969853.375\n969853.375\n969853.375\n969853.375\n969853.375\n969853.375\n969853.375\n998067.0\n1059628.75\n1059628.75\n1059628.75\n1059628.75\n",
"20.0\n50.0\n50.0\n",
"60.5\n60.5\n",
"898450.25\n898450.25\n898450.25\n898450.25\n972844.0\n",
"516875.8333333333\n516875.8333333333\n516875.8333333333\n516875.8333333333\n516875.8333333333\n516875.8333333333\n1031363.0\n",
"4.666666666666667\n4.666666666666667\n4.666666666666667\n4.666666666666667\n4.666666666666667\n4.666666666666667\n4.666666666666667\n4.666666666666667\n4.666666666666667\n6.0\n7.0\n7.0\n",
"897.0\n",
"57.0\n57.0\n57.0\n",
"15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n15416.738461538462\n",
"7.0\n8.0\n8.0\n10.0\n23.0\n",
"3.0\n4.75\n4.75\n4.75\n4.75\n5.0\n5.0\n5.0\n7.5\n7.5\n",
"5.666666666666667\n5.666666666666667\n5.666666666666667\n13.0\n",
"29.0\n90.0\n101.0\n",
"967786.0\n967786.0\n967786.0\n967786.0\n967786.0\n967786.0\n967786.0\n967786.0\n998067.0\n1059628.75\n1059628.75\n1059628.75\n1059628.75\n",
"20.0\n50.5\n50.5\n",
"60.0\n60.0\n",
"746904.75\n746904.75\n746904.75\n746904.75\n972844.0\n",
"528455.8333333334\n528455.8333333334\n528455.8333333334\n528455.8333333334\n528455.8333333334\n528455.8333333334\n1031363.0\n",
"4.444444444444445\n4.444444444444445\n4.444444444444445\n4.444444444444445\n4.444444444444445\n4.444444444444445\n4.444444444444445\n4.444444444444445\n4.444444444444445\n6.0\n7.0\n7.0\n",
"479.0\n",
"60.333333333333336\n60.333333333333336\n60.333333333333336\n",
"15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n15417.046153846153\n",
"7.0\n8.0\n11.5\n11.5\n23.0\n",
"3.0\n4.25\n4.25\n4.25\n4.25\n4.25\n4.25\n4.25\n4.25\n7.0\n",
"4.0\n4.0\n5.0\n13.0\n",
"26.5\n26.5\n101.0\n",
"954778.3636363636\n954778.3636363636\n954778.3636363636\n954778.3636363636\n954778.3636363636\n954778.3636363636\n954778.3636363636\n954778.3636363636\n954778.3636363636\n954778.3636363636\n954778.3636363636\n963504.0\n985482.0\n",
"7.0\n7.0\n7.0\n",
"63.5\n63.5\n",
"746904.75\n746904.75\n746904.75\n746904.75\n1773609.0\n",
"555744.8333333334\n555744.8333333334\n555744.8333333334\n555744.8333333334\n555744.8333333334\n555744.8333333334\n1031363.0\n",
"3.7777777777777777\n3.7777777777777777\n3.7777777777777777\n3.7777777777777777\n3.7777777777777777\n3.7777777777777777\n3.7777777777777777\n3.7777777777777777\n3.7777777777777777\n6.0\n7.0\n7.0\n",
"894.0\n",
"11.0\n20.0\n50.0\n",
"15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n15417.015384615384\n",
"7.0\n8.0\n16.5\n16.5\n23.0\n",
"3.0\n4.125\n4.125\n4.125\n4.125\n4.125\n4.125\n4.125\n4.125\n7.0\n",
"3.0\n3.0\n5.0\n13.0\n",
"23.0\n24.0\n101.0\n",
"954778.3636363636\n954778.3636363636\n954778.3636363636\n954778.3636363636\n954778.3636363636\n954778.3636363636\n954778.3636363636\n954778.3636363636\n954778.3636363636\n954778.3636363636\n954778.3636363636\n963504.0\n1716586.0\n",
"10.333333333333334\n10.333333333333334\n10.333333333333334\n",
"59.5\n59.5\n",
"724163.0\n724163.0\n724163.0\n724163.0\n1773609.0\n",
"571598.8333333334\n571598.8333333334\n571598.8333333334\n571598.8333333334\n571598.8333333334\n571598.8333333334\n1031363.0\n",
"3.5555555555555554\n3.5555555555555554\n3.5555555555555554\n3.5555555555555554\n3.5555555555555554\n3.5555555555555554\n3.5555555555555554\n3.5555555555555554\n3.5555555555555554\n6.0\n7.0\n7.0\n",
"1005.0\n",
"11.0\n20.0\n92.0\n",
"15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n15417.723076923077\n",
"7.0\n8.0\n11.0\n11.0\n11.0\n",
"3.0\n4.75\n4.75\n4.75\n4.75\n5.5\n5.5\n5.5\n5.5\n7.0\n",
"3.0\n3.0\n5.0\n7.0\n",
"22.0\n24.0\n101.0\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
There are n water tanks in a row, i-th of them contains a_i liters of water. The tanks are numbered from 1 to n from left to right.
You can perform the following operation: choose some subsegment [l, r] (1≤ l ≤ r ≤ n), and redistribute water in tanks l, l+1, ..., r evenly. In other words, replace each of a_l, a_{l+1}, ..., a_r by \frac{a_l + a_{l+1} + ... + a_r}{r-l+1}. For example, if for volumes [1, 3, 6, 7] you choose l = 2, r = 3, new volumes of water will be [1, 4.5, 4.5, 7]. You can perform this operation any number of times.
What is the lexicographically smallest sequence of volumes of water that you can achieve?
As a reminder:
A sequence a is lexicographically smaller than a sequence b of the same length if and only if the following holds: in the first (leftmost) position where a and b differ, the sequence a has a smaller element than the corresponding element in b.
Input
The first line contains an integer n (1 ≤ n ≤ 10^6) — the number of water tanks.
The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^6) — initial volumes of water in the water tanks, in liters.
Because of large input, reading input as doubles is not recommended.
Output
Print the lexicographically smallest sequence you can get. In the i-th line print the final volume of water in the i-th tank.
Your answer is considered correct if the absolute or relative error of each a_i does not exceed 10^{-9}.
Formally, let your answer be a_1, a_2, ..., a_n, and the jury's answer be b_1, b_2, ..., b_n. Your answer is accepted if and only if \frac{|a_i - b_i|}{max{(1, |b_i|)}} ≤ 10^{-9} for each i.
Examples
Input
4
7 5 5 7
Output
5.666666667
5.666666667
5.666666667
7.000000000
Input
5
7 8 8 10 12
Output
7.000000000
8.000000000
8.000000000
10.000000000
12.000000000
Input
10
3 9 5 5 1 7 5 3 8 7
Output
3.000000000
5.000000000
5.000000000
5.000000000
5.000000000
5.000000000
5.000000000
5.000000000
7.500000000
7.500000000
Note
In the first sample, you can get the sequence by applying the operation for subsegment [1, 3].
In the second sample, you can't get any lexicographically smaller sequence.
### Input:
5
7 8 8 10 12
### Output:
7.000000000
8.000000000
8.000000000
10.000000000
12.000000000
### Input:
10
3 9 5 5 1 7 5 3 8 7
### Output:
3.000000000
5.000000000
5.000000000
5.000000000
5.000000000
5.000000000
5.000000000
5.000000000
7.500000000
7.500000000
### Code:
def main():
from sys import stdin,stdout
ans = []
stdin.readline()
for ai in map(int, map(int, stdin.readline().split())):
cnt=1
while ans and ai*ans[-1][0]<=ans[-1][1]*cnt:
c, r = ans.pop()
ai+=r
cnt+=c
ans.append((cnt, ai))
for i, res in ans:
m = str(res/i)
stdout.write((m+"\n")*i)
main()
|
1324_F. Maximum White Subtree_10507
|
You are given a tree consisting of n vertices. A tree is a connected undirected graph with n-1 edges. Each vertex v of this tree has a color assigned to it (a_v = 1 if the vertex v is white and 0 if the vertex v is black).
You have to solve the following problem for each vertex v: what is the maximum difference between the number of white and the number of black vertices you can obtain if you choose some subtree of the given tree that contains the vertex v? The subtree of the tree is the connected subgraph of the given tree. More formally, if you choose the subtree that contains cnt_w white vertices and cnt_b black vertices, you have to maximize cnt_w - cnt_b.
Input
The first line of the input contains one integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the number of vertices in the tree.
The second line of the input contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 1), where a_i is the color of the i-th vertex.
Each of the next n-1 lines describes an edge of the tree. Edge i is denoted by two integers u_i and v_i, the labels of vertices it connects (1 ≤ u_i, v_i ≤ n, u_i ≠ v_i).
It is guaranteed that the given edges form a tree.
Output
Print n integers res_1, res_2, ..., res_n, where res_i is the maximum possible difference between the number of white and black vertices in some subtree that contains the vertex i.
Examples
Input
9
0 1 1 1 0 0 0 0 1
1 2
1 3
3 4
3 5
2 6
4 7
6 8
5 9
Output
2 2 2 2 2 1 1 0 2
Input
4
0 0 1 0
1 2
1 3
1 4
Output
0 -1 1 -1
Note
The first example is shown below:
<image>
The black vertices have bold borders.
In the second example, the best subtree for vertices 2, 3 and 4 are vertices 2, 3 and 4 correspondingly. And the best subtree for the vertex 1 is the subtree consisting of vertices 1 and 3.
|
import os
import sys
from io import BytesIO, IOBase
from types import GeneratorType
from collections import defaultdict
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
sys.setrecursionlimit(2 * 10 ** 5)
ans=0
def bootstrap(f, stack=[]):
def wrappedfunc(*args, **kwargs):
if stack:
return f(*args, **kwargs)
else:
to = f(*args, **kwargs)
while True:
if type(to) is GeneratorType:
stack.append(to)
to = next(to)
else:
stack.pop()
if not stack:
break
to = stack[-1].send(to)
return to
return wrappedfunc
@bootstrap
def dfs(now, lay, fa):
SUM[now] = 0
NUM[now] = C[now]
for to in A[now]:
if to != fa:
yield dfs(to, lay + 1, now)
SUM[now] += SUM[to]
SUM[now] += NUM[to]
NUM[now] += NUM[to]
yield
@bootstrap
def change(now, fa):
global ans
ans = max(ans, SUM[now])
for to in A[now]:
if to != fa:
SUM[now] -= SUM[to]
SUM[now] -= NUM[to]
NUM[now] -= NUM[to]
NUM[to] += NUM[now]
SUM[to] += SUM[now]
SUM[to] += NUM[now]
yield change(to, now)
SUM[to] -= SUM[now]
SUM[to] -= NUM[now]
NUM[to] -= NUM[now]
NUM[now] += NUM[to]
SUM[now] += SUM[to]
SUM[now] += NUM[to]
yield
n = int(input())
A = [[] for i in range(n + 1)]
C = [0] + (list(map(int, input().split())))
NUM = [0] * (n + 1)
SUM = [0] * (n + 1)
for i in range(n - 1):
x, y = map(int, input().split())
A[x].append(y)
A[y].append(x)
dfs(1, 0, 0)
change(1, 0)
print(ans)
# print(NUM)
# print(SUM)
|
{
"input": [
"9\n0 1 1 1 0 0 0 0 1\n1 2\n1 3\n3 4\n3 5\n2 6\n4 7\n6 8\n5 9\n",
"4\n0 0 1 0\n1 2\n1 3\n1 4\n",
"8\n9 4 1 7 10 1 6 5\n1 2\n2 3\n1 4\n1 5\n5 6\n5 7\n5 8\n",
"1\n1337\n",
"2\n12345 65432\n2 1\n",
"8\n9 4 1 7 10 1 6 5\n1 2\n2 3\n1 4\n1 5\n2 6\n5 7\n5 8\n",
"1\n1197\n",
"9\n0 1 0 1 0 0 0 0 1\n1 2\n1 3\n3 4\n3 5\n2 6\n4 7\n6 8\n5 9\n",
"4\n0 -1 1 0\n1 2\n1 3\n1 4\n",
"4\n0 -1 0 0\n1 2\n1 3\n1 4\n",
"9\n1 2 0 1 0 0 0 0 1\n1 2\n1 3\n3 4\n3 5\n2 6\n4 7\n6 8\n5 9\n",
"1\n0\n",
"1\n1797\n",
"9\n0 2 0 1 0 0 0 0 1\n1 2\n1 3\n3 4\n3 5\n2 6\n4 7\n6 8\n5 9\n",
"1\n232\n",
"1\n358\n",
"1\n244\n",
"1\n441\n",
"1\n769\n",
"1\n240\n",
"1\n133\n",
"1\n13\n",
"1\n22\n",
"1\n31\n",
"1\n5\n",
"1\n2\n",
"1\n1\n",
"1\n-1\n",
"1\n-2\n",
"1\n-3\n",
"1\n-6\n",
"1\n3\n",
"1\n6\n",
"1\n4\n",
"1\n8\n",
"1\n12\n",
"1\n-4\n",
"1\n-5\n",
"1\n7\n",
"1\n-7\n",
"1\n-8\n",
"1\n-16\n",
"1\n-18\n",
"1\n-12\n",
"1\n-13\n",
"1\n-19\n",
"1\n-21\n",
"1\n11\n",
"1\n18\n",
"1\n30\n",
"1\n36\n",
"1\n16\n",
"1\n-10\n",
"1\n10\n",
"1\n9\n",
"1\n-15\n",
"1\n-32\n",
"1\n-54\n",
"1\n-76\n",
"1\n-133\n",
"1\n-244\n",
"1\n-418\n",
"1\n-164\n",
"1\n-120\n",
"1\n-49\n",
"1\n-46\n",
"1\n-87\n",
"1\n-80\n",
"1\n-66\n",
"1\n-14\n",
"1\n-11\n",
"1\n-36\n",
"1\n-23\n",
"1\n15\n",
"1\n14\n",
"1\n-9\n",
"1\n-25\n",
"1\n-20\n",
"1\n-31\n",
"1\n-43\n",
"1\n-52\n",
"1\n24\n",
"1\n-37\n",
"1\n-34\n",
"1\n-64\n",
"1\n-73\n",
"1\n-85\n",
"1\n-134\n",
"1\n-211\n",
"1\n-27\n",
"1\n-35\n",
"1\n-24\n"
],
"output": [
"2 2 2 2 2 1 1 0 2 ",
"0 -1 1 -1 ",
"121\n",
"0\n",
"65432\n",
"8 8 8 8 8 8 8 8\n",
"1\n",
"0 1 0 1 0 0 0 -1 1\n",
"1 1 1 0\n",
"0 1 -1 -1\n",
"2 2 2 2 2 1 1 0 2\n",
"-1\n",
"1\n",
"0 1 0 1 0 0 0 -1 1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You are given a tree consisting of n vertices. A tree is a connected undirected graph with n-1 edges. Each vertex v of this tree has a color assigned to it (a_v = 1 if the vertex v is white and 0 if the vertex v is black).
You have to solve the following problem for each vertex v: what is the maximum difference between the number of white and the number of black vertices you can obtain if you choose some subtree of the given tree that contains the vertex v? The subtree of the tree is the connected subgraph of the given tree. More formally, if you choose the subtree that contains cnt_w white vertices and cnt_b black vertices, you have to maximize cnt_w - cnt_b.
Input
The first line of the input contains one integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the number of vertices in the tree.
The second line of the input contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 1), where a_i is the color of the i-th vertex.
Each of the next n-1 lines describes an edge of the tree. Edge i is denoted by two integers u_i and v_i, the labels of vertices it connects (1 ≤ u_i, v_i ≤ n, u_i ≠ v_i).
It is guaranteed that the given edges form a tree.
Output
Print n integers res_1, res_2, ..., res_n, where res_i is the maximum possible difference between the number of white and black vertices in some subtree that contains the vertex i.
Examples
Input
9
0 1 1 1 0 0 0 0 1
1 2
1 3
3 4
3 5
2 6
4 7
6 8
5 9
Output
2 2 2 2 2 1 1 0 2
Input
4
0 0 1 0
1 2
1 3
1 4
Output
0 -1 1 -1
Note
The first example is shown below:
<image>
The black vertices have bold borders.
In the second example, the best subtree for vertices 2, 3 and 4 are vertices 2, 3 and 4 correspondingly. And the best subtree for the vertex 1 is the subtree consisting of vertices 1 and 3.
### Input:
9
0 1 1 1 0 0 0 0 1
1 2
1 3
3 4
3 5
2 6
4 7
6 8
5 9
### Output:
2 2 2 2 2 1 1 0 2
### Input:
4
0 0 1 0
1 2
1 3
1 4
### Output:
0 -1 1 -1
### Code:
import os
import sys
from io import BytesIO, IOBase
from types import GeneratorType
from collections import defaultdict
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
sys.setrecursionlimit(2 * 10 ** 5)
ans=0
def bootstrap(f, stack=[]):
def wrappedfunc(*args, **kwargs):
if stack:
return f(*args, **kwargs)
else:
to = f(*args, **kwargs)
while True:
if type(to) is GeneratorType:
stack.append(to)
to = next(to)
else:
stack.pop()
if not stack:
break
to = stack[-1].send(to)
return to
return wrappedfunc
@bootstrap
def dfs(now, lay, fa):
SUM[now] = 0
NUM[now] = C[now]
for to in A[now]:
if to != fa:
yield dfs(to, lay + 1, now)
SUM[now] += SUM[to]
SUM[now] += NUM[to]
NUM[now] += NUM[to]
yield
@bootstrap
def change(now, fa):
global ans
ans = max(ans, SUM[now])
for to in A[now]:
if to != fa:
SUM[now] -= SUM[to]
SUM[now] -= NUM[to]
NUM[now] -= NUM[to]
NUM[to] += NUM[now]
SUM[to] += SUM[now]
SUM[to] += NUM[now]
yield change(to, now)
SUM[to] -= SUM[now]
SUM[to] -= NUM[now]
NUM[to] -= NUM[now]
NUM[now] += NUM[to]
SUM[now] += SUM[to]
SUM[now] += NUM[to]
yield
n = int(input())
A = [[] for i in range(n + 1)]
C = [0] + (list(map(int, input().split())))
NUM = [0] * (n + 1)
SUM = [0] * (n + 1)
for i in range(n - 1):
x, y = map(int, input().split())
A[x].append(y)
A[y].append(x)
dfs(1, 0, 0)
change(1, 0)
print(ans)
# print(NUM)
# print(SUM)
|
1343_E. Weights Distributing_10511
|
You are given an undirected unweighted graph consisting of n vertices and m edges (which represents the map of Bertown) and the array of prices p of length m. It is guaranteed that there is a path between each pair of vertices (districts).
Mike has planned a trip from the vertex (district) a to the vertex (district) b and then from the vertex (district) b to the vertex (district) c. He can visit the same district twice or more. But there is one issue: authorities of the city want to set a price for using the road so if someone goes along the road then he should pay the price corresponding to this road (he pays each time he goes along the road). The list of prices that will be used p is ready and they just want to distribute it between all roads in the town in such a way that each price from the array corresponds to exactly one road.
You are a good friend of Mike (and suddenly a mayor of Bertown) and want to help him to make his trip as cheap as possible. So, your task is to distribute prices between roads in such a way that if Mike chooses the optimal path then the price of the trip is the minimum possible. Note that you cannot rearrange prices after the start of the trip.
You have to answer t independent test cases.
Input
The first line of the input contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases. Then t test cases follow.
The first line of the test case contains five integers n, m, a, b and c (2 ≤ n ≤ 2 ⋅ 10^5, n-1 ≤ m ≤ min((n(n-1))/(2), 2 ⋅ 10^5), 1 ≤ a, b, c ≤ n) — the number of vertices, the number of edges and districts in Mike's trip.
The second line of the test case contains m integers p_1, p_2, ..., p_m (1 ≤ p_i ≤ 10^9), where p_i is the i-th price from the array.
The following m lines of the test case denote edges: edge i is represented by a pair of integers v_i, u_i (1 ≤ v_i, u_i ≤ n, u_i ≠ v_i), which are the indices of vertices connected by the edge. There are no loops or multiple edges in the given graph, i. e. for each pair (v_i, u_i) there are no other pairs (v_i, u_i) or (u_i, v_i) in the array of edges, and for each pair (v_i, u_i) the condition v_i ≠ u_i is satisfied. It is guaranteed that the given graph is connected.
It is guaranteed that the sum of n (as well as the sum of m) does not exceed 2 ⋅ 10^5 (∑ n ≤ 2 ⋅ 10^5, ∑ m ≤ 2 ⋅ 10^5).
Output
For each test case, print the answer — the minimum possible price of Mike's trip if you distribute prices between edges optimally.
Example
Input
2
4 3 2 3 4
1 2 3
1 2
1 3
1 4
7 9 1 5 7
2 10 4 8 5 6 7 3 3
1 2
1 3
1 4
3 2
3 5
4 2
5 6
1 7
6 7
Output
7
12
Note
One of the possible solution to the first test case of the example:
<image>
One of the possible solution to the second test case of the example:
<image>
|
import collections
tests = int(input())
def bfs(start, edges):
q = collections.deque([start])
dist = [-1]*(n+1)
dist[start] = 0
while(len(q) > 0):
curr_node = q.popleft()
for idx, neighbour in enumerate(edges[curr_node]):
if dist[neighbour] == -1:
q.append(neighbour)
dist[neighbour] = dist[curr_node] + 1
return dist
for t in range(tests):
(n,m,a,b,c) = map(int, input().split(" "))
costs = map(int, input().split(" "))
costs = sorted(costs)
edges = [[] for i in range(n+1)]
partial_sums = [0]
for nod, cost in enumerate(costs):
costs[nod] = cost
partial_sums.append(partial_sums[nod] + cost)
for edge in range(m):
(u,v) = map(int, input().split(" "))
edges[u].append(v)
edges[v].append(u)
dist = [[],[],[]]
dist[0] = bfs(a,edges)
dist[1] = bfs(b,edges)
dist[2] = bfs(c,edges)
min_sum = 1<<62
for i in range(1,n+1,1):
if dist[0][i]+dist[1][i]+dist[2][i] > m: continue
min_sum = min(min_sum, partial_sums[dist[1][i]] + partial_sums[dist[0][i]+dist[1][i]+dist[2][i]])
print(min_sum)
|
{
"input": [
"2\n4 3 2 3 4\n1 2 3\n1 2\n1 3\n1 4\n7 9 1 5 7\n2 10 4 8 5 6 7 3 3\n1 2\n1 3\n1 4\n3 2\n3 5\n4 2\n5 6\n1 7\n6 7\n",
"2\n4 3 2 3 4\n1 2 3\n1 2\n1 3\n1 4\n7 9 1 5 7\n2 10 4 8 5 6 7 3 3\n1 2\n1 3\n1 4\n3 2\n3 5\n4 2\n5 6\n1 4\n6 7\n",
"2\n4 3 2 3 4\n2 2 3\n1 2\n1 3\n1 4\n7 9 1 5 7\n2 10 4 8 5 6 7 3 3\n1 2\n1 3\n1 4\n3 2\n3 5\n4 2\n5 6\n1 4\n6 7\n",
"2\n4 3 2 3 4\n1 2 3\n1 2\n1 3\n1 4\n7 9 1 3 7\n2 10 4 8 5 6 7 3 3\n1 2\n1 3\n1 4\n3 2\n3 5\n4 2\n5 7\n1 4\n6 7\n",
"2\n4 3 3 3 4\n1 2 3\n1 2\n1 3\n1 4\n7 9 1 5 7\n2 10 4 8 5 6 7 3 3\n1 2\n1 3\n1 4\n3 2\n3 5\n4 2\n5 6\n1 7\n6 7\n",
"2\n4 3 2 3 4\n2 4 3\n1 2\n1 3\n1 4\n7 9 1 5 7\n2 10 4 8 5 6 7 3 3\n1 2\n1 3\n1 4\n3 2\n3 5\n4 2\n5 6\n1 4\n6 7\n",
"2\n4 3 2 3 4\n1 2 3\n1 2\n1 3\n1 4\n7 9 1 3 7\n2 10 4 8 5 6 7 4 3\n1 2\n1 3\n1 4\n3 2\n3 5\n4 2\n5 6\n1 4\n6 7\n",
"2\n4 3 2 3 4\n0 2 3\n1 2\n1 3\n1 4\n7 9 1 3 7\n2 10 4 8 5 6 7 3 3\n1 2\n1 3\n1 4\n3 2\n3 5\n4 2\n5 7\n1 4\n6 7\n",
"2\n4 3 1 3 4\n1 2 3\n1 2\n1 3\n1 4\n7 9 2 5 7\n2 10 4 8 5 6 7 3 3\n1 2\n2 3\n1 4\n3 2\n3 5\n4 3\n5 6\n1 4\n6 7\n",
"2\n4 3 1 3 4\n1 4 3\n1 2\n1 3\n1 4\n7 9 2 5 7\n2 10 4 8 5 6 7 3 3\n1 2\n2 3\n1 4\n3 2\n3 5\n4 3\n5 6\n1 4\n6 7\n",
"2\n4 3 3 3 4\n1 2 3\n1 2\n1 3\n1 4\n7 9 1 5 7\n2 10 4 8 5 6 3 3 3\n1 2\n1 3\n1 4\n3 2\n3 5\n4 2\n5 6\n1 7\n6 7\n",
"2\n4 3 2 3 4\n1 2 3\n1 2\n1 3\n1 4\n7 9 2 5 7\n2 10 4 8 5 6 7 3 3\n1 2\n1 3\n1 4\n3 4\n3 5\n4 2\n5 6\n1 4\n6 7\n",
"2\n4 3 1 3 4\n1 4 3\n1 2\n1 3\n1 4\n7 9 2 5 7\n2 10 4 8 5 8 7 3 6\n1 2\n2 3\n1 4\n3 2\n3 5\n4 3\n5 6\n1 4\n6 7\n",
"2\n4 3 1 3 4\n1 4 3\n1 2\n1 3\n1 4\n7 9 2 5 7\n3 10 4 8 5 8 7 3 3\n2 2\n2 3\n1 4\n3 2\n3 5\n4 3\n5 6\n1 4\n6 7\n",
"2\n4 3 2 3 4\n1 2 3\n1 2\n1 3\n1 4\n7 9 1 5 7\n2 10 4 8 5 6 3 3 3\n1 2\n1 3\n1 4\n3 2\n3 5\n4 2\n5 6\n1 7\n6 7\n",
"2\n4 3 2 3 4\n0 4 3\n1 2\n1 3\n1 4\n7 9 1 3 7\n2 10 4 8 5 6 7 3 4\n1 2\n1 3\n1 4\n3 2\n3 5\n4 2\n5 7\n1 4\n6 7\n",
"2\n4 3 2 3 4\n1 2 3\n1 2\n1 3\n1 4\n7 9 2 5 7\n2 3 4 8 5 6 7 3 3\n1 2\n1 3\n1 4\n3 2\n4 5\n4 3\n5 6\n1 4\n6 7\n",
"2\n4 3 1 3 4\n1 4 3\n1 2\n1 3\n1 4\n7 9 2 5 7\n2 10 1 8 5 8 7 3 6\n1 2\n2 3\n1 4\n3 2\n3 5\n4 3\n5 6\n1 4\n6 7\n",
"2\n4 3 2 3 3\n1 2 3\n1 2\n1 3\n1 4\n7 9 1 5 7\n2 10 4 8 5 6 7 3 3\n1 2\n1 3\n1 4\n3 2\n3 3\n4 2\n5 6\n2 7\n6 7\n",
"2\n4 3 1 3 4\n1 2 3\n1 2\n2 3\n1 4\n7 9 2 5 7\n2 10 4 8 4 6 7 3 3\n1 2\n2 3\n1 4\n3 2\n3 6\n4 3\n5 6\n1 4\n6 7\n",
"2\n4 3 1 3 4\n1 4 3\n1 2\n1 3\n1 4\n7 9 2 5 7\n2 10 1 8 5 8 7 3 6\n1 2\n2 3\n1 4\n3 2\n3 5\n4 3\n5 6\n1 4\n5 7\n",
"2\n4 3 2 3 3\n1 2 3\n1 2\n1 3\n1 4\n7 9 1 5 7\n2 10 4 8 5 6 7 3 3\n1 2\n1 3\n1 4\n3 2\n3 3\n5 2\n5 6\n2 7\n6 7\n",
"2\n4 3 2 3 4\n0 4 3\n1 2\n1 3\n1 4\n7 9 1 3 7\n2 10 0 8 5 6 7 3 4\n1 2\n1 3\n1 4\n4 2\n3 5\n4 2\n5 7\n1 4\n6 7\n",
"2\n4 3 1 3 4\n1 2 3\n1 2\n2 3\n1 4\n7 9 2 5 7\n2 10 4 8 7 6 7 3 3\n1 2\n2 3\n1 4\n3 2\n3 6\n4 3\n5 6\n1 4\n4 7\n",
"2\n4 3 1 3 4\n1 2 3\n1 2\n2 3\n1 4\n7 9 2 5 7\n2 10 2 8 7 6 7 3 3\n1 2\n1 3\n1 4\n3 2\n3 6\n4 3\n5 6\n1 4\n4 7\n",
"2\n4 3 2 3 4\n2 4 3\n1 2\n1 3\n1 4\n7 9 1 5 7\n2 10 4 8 5 6 7 3 0\n1 2\n1 3\n1 4\n3 2\n3 5\n4 2\n5 6\n1 4\n6 7\n",
"2\n4 3 1 3 4\n1 2 3\n1 2\n1 3\n1 4\n7 9 2 5 7\n2 10 4 8 2 6 7 3 3\n1 2\n2 3\n1 4\n3 2\n3 5\n4 3\n5 6\n1 4\n6 7\n",
"2\n4 3 2 3 4\n1 2 3\n1 2\n1 3\n2 4\n7 9 1 3 7\n2 10 4 8 5 6 7 3 3\n2 2\n1 4\n1 4\n3 2\n3 5\n4 2\n5 7\n1 4\n6 7\n",
"2\n4 3 2 3 4\n1 5 3\n1 2\n1 3\n1 4\n7 9 2 5 7\n3 10 4 8 5 8 7 3 3\n2 2\n2 3\n1 4\n3 2\n3 5\n4 3\n5 6\n1 4\n6 7\n",
"2\n4 3 2 3 3\n1 2 3\n1 2\n1 3\n1 4\n7 9 1 5 7\n2 10 4 8 5 6 7 3 1\n1 2\n1 3\n1 4\n3 2\n3 3\n4 2\n5 6\n2 7\n6 7\n",
"2\n4 3 1 3 4\n1 2 3\n1 2\n2 3\n1 4\n7 9 2 5 7\n2 10 4 8 4 6 7 3 6\n1 2\n2 3\n1 4\n3 2\n3 6\n4 3\n5 6\n1 4\n6 7\n",
"2\n4 3 1 3 4\n1 4 3\n1 2\n1 3\n1 4\n7 9 2 5 7\n3 10 1 8 5 8 7 3 6\n1 2\n2 3\n1 4\n3 2\n3 5\n4 3\n5 6\n1 4\n5 7\n",
"2\n4 3 1 3 4\n1 2 3\n1 2\n2 3\n1 4\n7 9 2 5 7\n2 10 4 8 7 6 7 3 3\n1 2\n2 3\n1 4\n3 2\n3 6\n3 3\n5 6\n1 4\n4 7\n",
"2\n4 3 2 3 4\n1 2 3\n1 2\n1 3\n1 4\n7 9 1 3 7\n2 10 4 8 5 6 7 3 3\n1 2\n1 3\n1 4\n3 2\n3 5\n4 2\n5 6\n1 4\n6 7\n",
"2\n4 3 2 3 4\n1 2 3\n1 2\n1 3\n1 4\n7 9 2 5 7\n2 10 4 8 5 6 7 3 3\n1 2\n1 3\n1 4\n3 2\n3 5\n4 2\n5 6\n1 4\n6 7\n",
"2\n4 3 2 3 4\n1 2 3\n1 2\n1 3\n1 4\n7 9 2 5 7\n2 10 4 8 5 6 7 3 3\n1 2\n1 3\n1 4\n3 2\n3 5\n4 3\n5 6\n1 4\n6 7\n",
"2\n4 3 2 3 4\n1 2 3\n1 2\n1 3\n1 4\n7 9 1 3 7\n2 10 4 8 5 6 7 4 3\n1 2\n1 3\n1 4\n3 2\n3 5\n4 4\n5 6\n1 4\n6 7\n",
"2\n4 3 2 3 4\n1 2 3\n1 2\n1 3\n1 4\n7 9 2 5 7\n2 10 4 8 5 6 7 3 3\n1 2\n2 3\n1 4\n3 2\n3 5\n4 3\n5 6\n1 4\n6 7\n",
"2\n4 3 1 3 4\n1 4 3\n1 2\n1 3\n1 4\n7 9 2 5 7\n2 10 4 8 5 8 7 3 3\n1 2\n2 3\n1 4\n3 2\n3 5\n4 3\n5 6\n1 4\n6 7\n",
"2\n4 3 1 3 4\n1 4 3\n1 2\n1 3\n1 4\n7 9 2 5 7\n2 10 4 8 5 8 7 3 3\n2 2\n2 3\n1 4\n3 2\n3 5\n4 3\n5 6\n1 4\n6 7\n",
"2\n4 3 2 3 4\n1 2 3\n1 2\n1 3\n1 4\n7 9 1 5 7\n2 10 4 8 5 6 7 3 3\n1 2\n1 3\n1 4\n3 2\n3 3\n4 2\n5 6\n1 7\n6 7\n",
"2\n4 3 2 3 4\n1 2 3\n1 2\n1 3\n1 4\n7 9 2 3 7\n2 10 4 8 5 6 7 3 3\n1 2\n1 3\n1 4\n3 2\n3 5\n4 2\n5 6\n1 4\n6 7\n",
"2\n4 3 2 3 4\n1 2 3\n1 2\n1 3\n1 4\n7 9 1 3 7\n2 10 4 8 5 6 7 3 3\n2 2\n1 3\n1 4\n3 2\n3 5\n4 2\n5 7\n1 4\n6 7\n",
"2\n4 3 2 3 4\n2 4 3\n1 2\n1 3\n1 4\n7 9 1 5 7\n2 10 4 8 5 6 7 3 3\n1 2\n1 3\n1 1\n3 2\n3 5\n4 2\n5 6\n1 4\n6 7\n",
"2\n4 3 2 3 4\n0 4 3\n1 2\n1 3\n1 4\n7 9 1 3 7\n2 10 4 8 5 6 7 3 3\n1 2\n1 3\n1 4\n3 2\n3 5\n4 2\n5 7\n1 4\n6 7\n",
"2\n4 3 2 3 4\n1 2 3\n1 2\n1 3\n1 4\n7 9 2 5 7\n2 10 4 8 5 6 7 3 3\n1 2\n1 3\n1 4\n3 2\n4 5\n4 3\n5 6\n1 4\n6 7\n",
"2\n4 3 2 3 4\n1 2 3\n1 2\n1 3\n1 4\n7 9 1 3 7\n2 10 4 8 5 6 7 4 3\n1 2\n1 3\n1 4\n3 2\n3 5\n4 4\n5 6\n2 4\n6 7\n",
"2\n4 3 2 3 4\n1 2 3\n1 2\n1 3\n1 4\n7 9 2 5 7\n2 10 4 8 5 6 7 3 3\n1 2\n2 3\n2 4\n3 2\n3 5\n4 3\n5 6\n1 4\n6 7\n",
"2\n4 3 1 3 4\n1 2 3\n1 2\n1 3\n1 4\n7 9 2 5 7\n2 10 4 8 4 6 7 3 3\n1 2\n2 3\n1 4\n3 2\n3 5\n4 3\n5 6\n1 4\n6 7\n",
"2\n4 3 2 3 4\n1 2 3\n1 2\n1 3\n1 4\n7 9 1 5 7\n2 10 4 8 5 6 7 3 3\n1 2\n1 3\n1 4\n3 2\n3 3\n4 2\n5 6\n2 7\n6 7\n",
"2\n4 3 2 3 4\n1 2 3\n1 2\n1 3\n1 4\n7 9 1 3 7\n2 10 4 8 5 6 7 3 3\n2 2\n1 4\n1 4\n3 2\n3 5\n4 2\n5 7\n1 4\n6 7\n",
"2\n4 3 1 3 4\n1 2 3\n1 2\n2 3\n1 4\n7 9 2 5 7\n2 10 4 8 4 6 7 3 3\n1 2\n2 3\n1 4\n3 2\n3 5\n4 3\n5 6\n1 4\n6 7\n",
"2\n4 3 1 3 4\n1 5 3\n1 2\n1 3\n1 4\n7 9 2 5 7\n3 10 4 8 5 8 7 3 3\n2 2\n2 3\n1 4\n3 2\n3 5\n4 3\n5 6\n1 4\n6 7\n",
"2\n4 3 2 3 4\n0 4 3\n1 2\n1 3\n1 4\n7 9 1 3 7\n2 10 4 8 5 6 7 3 4\n1 2\n1 3\n1 4\n4 2\n3 5\n4 2\n5 7\n1 4\n6 7\n",
"2\n4 3 1 3 4\n1 2 3\n1 2\n2 3\n1 4\n7 9 2 5 7\n2 10 4 8 7 6 7 3 3\n1 2\n2 3\n1 4\n3 2\n3 6\n4 3\n5 6\n1 4\n6 7\n",
"2\n4 3 1 3 4\n1 2 3\n1 2\n2 3\n1 4\n7 9 2 5 7\n2 10 4 8 7 6 7 3 3\n1 2\n1 3\n1 4\n3 2\n3 6\n4 3\n5 6\n1 4\n4 7\n",
"2\n4 3 2 3 4\n1 2 3\n1 2\n1 3\n1 4\n7 9 1 5 7\n2 10 4 8 5 6 7 3 3\n1 2\n1 3\n1 4\n3 2\n3 5\n4 2\n1 6\n1 7\n6 7\n",
"2\n4 3 2 3 4\n1 2 3\n1 2\n1 3\n1 4\n7 9 1 5 7\n2 10 4 8 5 6 7 3 3\n1 2\n1 4\n1 4\n3 2\n3 5\n4 2\n5 6\n1 4\n6 7\n",
"2\n4 3 2 3 4\n1 2 3\n1 2\n1 3\n1 4\n7 9 1 3 7\n2 10 4 8 5 6 7 3 3\n1 2\n1 3\n1 3\n3 2\n3 5\n4 2\n5 6\n1 4\n6 7\n",
"2\n4 3 2 1 4\n1 2 3\n1 2\n1 3\n1 4\n7 9 2 5 7\n2 10 4 8 5 6 7 3 3\n1 2\n1 3\n1 4\n3 2\n3 5\n4 2\n5 6\n1 4\n6 7\n",
"2\n4 3 2 3 4\n1 2 3\n1 2\n1 3\n1 4\n7 9 1 3 7\n2 10 4 15 5 6 7 4 3\n1 2\n1 3\n1 4\n3 2\n3 5\n4 2\n5 6\n1 4\n6 7\n",
"2\n4 3 2 3 4\n0 2 3\n1 2\n1 3\n1 4\n7 9 1 3 7\n2 10 4 8 5 6 7 3 3\n1 2\n1 3\n1 4\n3 2\n3 5\n4 2\n2 7\n1 4\n6 7\n",
"2\n4 3 2 3 4\n1 2 3\n1 2\n1 3\n1 4\n7 9 1 3 7\n2 10 4 8 5 6 7 4 3\n1 2\n1 3\n1 4\n3 2\n3 5\n4 1\n5 6\n1 4\n6 7\n",
"2\n4 3 2 3 4\n1 0 3\n1 2\n1 3\n1 4\n7 9 2 5 7\n2 10 4 8 5 6 7 3 3\n1 2\n2 3\n1 4\n3 2\n3 5\n4 3\n5 6\n1 4\n6 7\n",
"2\n4 3 2 3 4\n1 2 3\n1 2\n1 3\n1 4\n7 9 1 5 7\n2 10 2 8 5 6 7 3 3\n1 2\n1 3\n1 4\n3 2\n3 3\n4 2\n5 6\n1 7\n6 7\n",
"2\n4 3 2 3 4\n1 4 3\n1 2\n1 3\n1 4\n7 9 2 3 7\n2 10 4 8 5 6 7 3 3\n1 2\n1 3\n1 4\n3 2\n3 5\n4 2\n5 6\n1 4\n6 7\n",
"2\n4 3 2 3 4\n1 2 3\n1 2\n1 3\n1 4\n7 9 1 3 7\n2 10 7 8 5 6 7 3 3\n2 2\n1 3\n1 4\n3 2\n3 5\n4 2\n5 7\n1 4\n6 7\n",
"2\n4 3 3 3 4\n1 2 3\n1 2\n1 3\n1 4\n7 9 1 5 7\n2 10 4 8 5 6 3 3 3\n1 2\n1 3\n1 4\n5 2\n3 5\n4 2\n5 6\n1 7\n6 7\n",
"2\n4 3 2 3 4\n1 2 3\n1 2\n1 3\n1 4\n7 9 2 4 7\n2 10 4 8 5 6 7 3 3\n1 2\n2 3\n2 4\n3 2\n3 5\n4 3\n5 6\n1 4\n6 7\n",
"2\n4 3 1 3 4\n1 2 3\n1 2\n1 3\n1 4\n7 9 2 5 7\n2 10 4 8 4 6 7 3 3\n1 1\n2 3\n1 4\n3 2\n3 5\n4 3\n5 6\n1 4\n6 7\n",
"2\n4 3 1 3 4\n1 4 3\n1 2\n1 3\n1 4\n7 9 2 2 7\n3 10 4 8 5 8 7 3 3\n2 2\n2 3\n1 4\n3 2\n3 5\n4 3\n5 6\n1 4\n6 7\n",
"2\n4 3 2 3 4\n1 2 3\n1 2\n1 3\n1 4\n7 9 1 5 7\n2 10 4 8 5 10 7 3 3\n1 2\n1 3\n1 4\n3 2\n3 3\n4 2\n5 6\n2 7\n6 7\n",
"2\n4 3 2 3 4\n1 2 3\n1 2\n1 3\n1 4\n7 9 1 5 7\n2 10 4 8 5 6 4 3 3\n1 2\n1 3\n1 4\n3 2\n3 5\n4 2\n5 6\n1 7\n6 7\n",
"2\n4 3 2 3 4\n1 2 3\n1 2\n1 3\n1 4\n7 9 2 5 7\n2 3 4 8 5 6 7 3 3\n1 2\n1 3\n1 2\n3 2\n4 5\n4 3\n5 6\n1 4\n6 7\n",
"2\n4 3 1 3 4\n1 2 3\n1 2\n2 3\n2 4\n7 9 2 5 7\n2 10 4 8 4 6 7 3 3\n1 2\n2 3\n1 4\n3 2\n3 5\n4 3\n5 6\n1 4\n6 7\n",
"2\n4 3 2 3 3\n1 2 3\n1 2\n1 3\n1 4\n7 9 1 5 7\n2 10 4 4 5 6 7 3 3\n1 2\n1 3\n1 4\n3 2\n3 3\n5 2\n5 6\n2 7\n6 7\n",
"2\n4 3 1 3 4\n1 2 3\n1 2\n2 3\n1 4\n7 9 2 5 7\n2 10 4 8 7 6 7 3 3\n1 2\n2 3\n1 4\n3 1\n3 6\n4 3\n5 6\n1 4\n6 7\n",
"2\n4 3 2 3 4\n1 2 3\n1 2\n1 3\n1 4\n7 9 1 5 7\n0 10 4 8 5 6 7 3 3\n1 2\n1 4\n1 4\n3 2\n3 5\n4 2\n5 6\n1 4\n6 7\n",
"2\n4 3 2 3 4\n1 2 3\n1 2\n1 3\n1 4\n7 9 1 3 7\n2 10 6 8 5 6 7 3 3\n1 2\n1 3\n1 3\n3 2\n3 5\n4 2\n5 6\n1 4\n6 7\n",
"2\n4 3 2 1 4\n1 2 3\n1 2\n2 3\n1 4\n7 9 2 5 7\n2 10 4 8 5 6 7 3 3\n1 2\n1 3\n1 4\n3 2\n3 5\n4 2\n5 6\n1 4\n6 7\n",
"2\n4 3 2 3 4\n1 2 3\n1 2\n1 3\n1 4\n7 9 1 3 7\n2 10 4 8 5 6 7 4 3\n1 2\n1 3\n1 4\n2 2\n3 5\n4 1\n5 6\n1 4\n6 7\n",
"2\n4 3 2 3 4\n1 2 3\n1 2\n1 3\n1 4\n7 9 1 5 7\n2 10 2 8 4 6 7 3 3\n1 2\n1 3\n1 4\n3 2\n3 3\n4 2\n5 6\n1 7\n6 7\n"
],
"output": [
"7\n12\n",
"7\n12\n",
"9\n12\n",
"7\n8\n",
"3\n12\n",
"11\n12\n",
"7\n13\n",
"5\n8\n",
"4\n12\n",
"5\n12\n",
"3\n11\n",
"7\n17\n",
"5\n14\n",
"5\n13\n",
"7\n11\n",
"7\n9\n",
"7\n15\n",
"5\n11\n",
"3\n17\n",
"9\n14\n",
"5\n6\n",
"3\n10\n",
"7\n5\n",
"9\n23\n",
"9\n20\n",
"11\n9\n",
"4\n10\n",
"9\n17\n",
"10\n13\n",
"3\n13\n",
"9\n15\n",
"5\n7\n",
"9\n33\n",
"7\n12\n",
"7\n12\n",
"7\n12\n",
"7\n13\n",
"7\n12\n",
"5\n12\n",
"5\n12\n",
"7\n13\n",
"7\n12\n",
"7\n8\n",
"11\n12\n",
"7\n8\n",
"7\n17\n",
"7\n13\n",
"7\n12\n",
"4\n12\n",
"7\n17\n",
"7\n17\n",
"9\n12\n",
"5\n13\n",
"7\n9\n",
"9\n14\n",
"9\n23\n",
"7\n13\n",
"7\n17\n",
"7\n12\n",
"3\n12\n",
"7\n13\n",
"5\n8\n",
"7\n13\n",
"4\n12\n",
"7\n11\n",
"9\n12\n",
"7\n8\n",
"3\n11\n",
"7\n17\n",
"4\n12\n",
"5\n13\n",
"7\n17\n",
"7\n12\n",
"7\n15\n",
"7\n12\n",
"3\n10\n",
"9\n14\n",
"7\n15\n",
"7\n13\n",
"3\n12\n",
"7\n13\n",
"7\n11\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You are given an undirected unweighted graph consisting of n vertices and m edges (which represents the map of Bertown) and the array of prices p of length m. It is guaranteed that there is a path between each pair of vertices (districts).
Mike has planned a trip from the vertex (district) a to the vertex (district) b and then from the vertex (district) b to the vertex (district) c. He can visit the same district twice or more. But there is one issue: authorities of the city want to set a price for using the road so if someone goes along the road then he should pay the price corresponding to this road (he pays each time he goes along the road). The list of prices that will be used p is ready and they just want to distribute it between all roads in the town in such a way that each price from the array corresponds to exactly one road.
You are a good friend of Mike (and suddenly a mayor of Bertown) and want to help him to make his trip as cheap as possible. So, your task is to distribute prices between roads in such a way that if Mike chooses the optimal path then the price of the trip is the minimum possible. Note that you cannot rearrange prices after the start of the trip.
You have to answer t independent test cases.
Input
The first line of the input contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases. Then t test cases follow.
The first line of the test case contains five integers n, m, a, b and c (2 ≤ n ≤ 2 ⋅ 10^5, n-1 ≤ m ≤ min((n(n-1))/(2), 2 ⋅ 10^5), 1 ≤ a, b, c ≤ n) — the number of vertices, the number of edges and districts in Mike's trip.
The second line of the test case contains m integers p_1, p_2, ..., p_m (1 ≤ p_i ≤ 10^9), where p_i is the i-th price from the array.
The following m lines of the test case denote edges: edge i is represented by a pair of integers v_i, u_i (1 ≤ v_i, u_i ≤ n, u_i ≠ v_i), which are the indices of vertices connected by the edge. There are no loops or multiple edges in the given graph, i. e. for each pair (v_i, u_i) there are no other pairs (v_i, u_i) or (u_i, v_i) in the array of edges, and for each pair (v_i, u_i) the condition v_i ≠ u_i is satisfied. It is guaranteed that the given graph is connected.
It is guaranteed that the sum of n (as well as the sum of m) does not exceed 2 ⋅ 10^5 (∑ n ≤ 2 ⋅ 10^5, ∑ m ≤ 2 ⋅ 10^5).
Output
For each test case, print the answer — the minimum possible price of Mike's trip if you distribute prices between edges optimally.
Example
Input
2
4 3 2 3 4
1 2 3
1 2
1 3
1 4
7 9 1 5 7
2 10 4 8 5 6 7 3 3
1 2
1 3
1 4
3 2
3 5
4 2
5 6
1 7
6 7
Output
7
12
Note
One of the possible solution to the first test case of the example:
<image>
One of the possible solution to the second test case of the example:
<image>
### Input:
2
4 3 2 3 4
1 2 3
1 2
1 3
1 4
7 9 1 5 7
2 10 4 8 5 6 7 3 3
1 2
1 3
1 4
3 2
3 5
4 2
5 6
1 7
6 7
### Output:
7
12
### Input:
2
4 3 2 3 4
1 2 3
1 2
1 3
1 4
7 9 1 5 7
2 10 4 8 5 6 7 3 3
1 2
1 3
1 4
3 2
3 5
4 2
5 6
1 4
6 7
### Output:
7
12
### Code:
import collections
tests = int(input())
def bfs(start, edges):
q = collections.deque([start])
dist = [-1]*(n+1)
dist[start] = 0
while(len(q) > 0):
curr_node = q.popleft()
for idx, neighbour in enumerate(edges[curr_node]):
if dist[neighbour] == -1:
q.append(neighbour)
dist[neighbour] = dist[curr_node] + 1
return dist
for t in range(tests):
(n,m,a,b,c) = map(int, input().split(" "))
costs = map(int, input().split(" "))
costs = sorted(costs)
edges = [[] for i in range(n+1)]
partial_sums = [0]
for nod, cost in enumerate(costs):
costs[nod] = cost
partial_sums.append(partial_sums[nod] + cost)
for edge in range(m):
(u,v) = map(int, input().split(" "))
edges[u].append(v)
edges[v].append(u)
dist = [[],[],[]]
dist[0] = bfs(a,edges)
dist[1] = bfs(b,edges)
dist[2] = bfs(c,edges)
min_sum = 1<<62
for i in range(1,n+1,1):
if dist[0][i]+dist[1][i]+dist[2][i] > m: continue
min_sum = min(min_sum, partial_sums[dist[1][i]] + partial_sums[dist[0][i]+dist[1][i]+dist[2][i]])
print(min_sum)
|
1365_F. Swaps Again_10515
|
Ayush, Ashish and Vivek are busy preparing a new problem for the next Codeforces round and need help checking if their test cases are valid.
Each test case consists of an integer n and two arrays a and b, of size n. If after some (possibly zero) operations described below, array a can be transformed into array b, the input is said to be valid. Otherwise, it is invalid.
An operation on array a is:
* select an integer k (1 ≤ k ≤ ⌊n/2⌋)
* swap the prefix of length k with the suffix of length k
For example, if array a initially is \{1, 2, 3, 4, 5, 6\}, after performing an operation with k = 2, it is transformed into \{5, 6, 3, 4, 1, 2\}.
Given the set of test cases, help them determine if each one is valid or invalid.
Input
The first line contains one integer t (1 ≤ t ≤ 500) — the number of test cases. The description of each test case is as follows.
The first line of each test case contains a single integer n (1 ≤ n ≤ 500) — the size of the arrays.
The second line of each test case contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — elements of array a.
The third line of each test case contains n integers b_1, b_2, ..., b_n (1 ≤ b_i ≤ 10^9) — elements of array b.
Output
For each test case, print "Yes" if the given input is valid. Otherwise print "No".
You may print the answer in any case.
Example
Input
5
2
1 2
2 1
3
1 2 3
1 2 3
3
1 2 4
1 3 4
4
1 2 3 2
3 1 2 2
3
1 2 3
1 3 2
Output
yes
yes
No
yes
No
Note
For the first test case, we can swap prefix a[1:1] with suffix a[2:2] to get a=[2, 1].
For the second test case, a is already equal to b.
For the third test case, it is impossible since we cannot obtain 3 in a.
For the fourth test case, we can first swap prefix a[1:1] with suffix a[4:4] to obtain a=[2, 2, 3, 1]. Now we can swap prefix a[1:2] with suffix a[3:4] to obtain a=[3, 1, 2, 2].
For the fifth test case, it is impossible to convert a to b.
|
t = int(input())
for _ in range(t):
n = int(input())
a = list(map(int, input().split()))
b = list(map(int, input().split()))
pair = dict()
possible = 1
if n % 2 == 1:
if a[n//2] != b[n//2]:
possible = 0
for i in range(n//2):
M, m = max(a[i], a[n- i - 1]), min(a[i], a[n - i - 1])
try:
pair[str(m) + " " + str(M)] += 1
except:
pair[str(m) + " " + str(M)] = 1
for i in range(n//2):
M, m = max(b[i], b[n - i - 1]), min(b[i], b[n - i - 1])
x = str(m) + " " + str(M)
if x not in pair:
#print(x, "...1")
possible = 0
break
else:
if pair[x] >= 1:
pair[x] -= 1
#print(x, "....2")
else:
#print(x, "......3")
possible = 0
break
if possible:
print("yes")
else:
print("No")
|
{
"input": [
"5\n2\n1 2\n2 1\n3\n1 2 3\n1 2 3\n3\n1 2 4\n1 3 4\n4\n1 2 3 2\n3 1 2 2\n3\n1 2 3\n1 3 2\n",
"24\n4\n1 2 3 4\n1 2 3 4\n4\n1 2 3 4\n1 2 4 3\n4\n1 2 3 4\n1 3 2 4\n4\n1 2 3 4\n1 3 4 2\n4\n1 2 3 4\n1 4 2 3\n4\n1 2 3 4\n1 4 3 2\n4\n1 2 3 4\n2 1 3 4\n4\n1 2 3 4\n2 1 4 3\n4\n1 2 3 4\n2 3 1 4\n4\n1 2 3 4\n2 3 4 1\n4\n1 2 3 4\n2 4 1 3\n4\n1 2 3 4\n2 4 3 1\n4\n1 2 3 4\n3 1 2 4\n4\n1 2 3 4\n3 1 4 2\n4\n1 2 3 4\n3 2 1 4\n4\n1 2 3 4\n3 2 4 1\n4\n1 2 3 4\n3 4 1 2\n4\n1 2 3 4\n3 4 2 1\n4\n1 2 3 4\n4 1 2 3\n4\n1 2 3 4\n4 1 3 2\n4\n1 2 3 4\n4 2 1 3\n4\n1 2 3 4\n4 2 3 1\n4\n1 2 3 4\n4 3 1 2\n4\n1 2 3 4\n4 3 2 1\n",
"1\n3\n1 2 1\n2 1 2\n",
"1\n3\n8 9 8\n9 8 9\n",
"6\n3\n3 2 1\n1 2 3\n3\n3 2 1\n1 3 2\n3\n3 2 1\n2 1 3\n3\n3 2 1\n2 3 1\n3\n3 2 1\n3 1 2\n3\n3 2 1\n3 2 1\n",
"1\n1\n1\n1\n",
"2\n2\n2 1\n1 2\n2\n2 1\n2 1\n",
"1\n3\n114514 1919810 114514\n1919810 114514 1919810\n",
"1\n3\n4 5 4\n5 4 5\n",
"1\n3\n3 7 3\n7 3 7\n",
"24\n4\n1 2 3 4\n1 2 3 4\n4\n1 2 3 4\n1 2 4 3\n4\n1 2 3 4\n1 3 2 4\n4\n1 2 3 4\n1 3 4 2\n4\n1 2 3 4\n1 4 2 3\n4\n1 2 3 4\n1 4 3 2\n4\n1 2 3 4\n2 1 3 4\n4\n1 2 3 4\n2 1 4 3\n4\n1 2 3 4\n2 3 1 4\n4\n1 2 3 4\n2 3 4 1\n4\n1 2 3 4\n2 4 1 3\n4\n1 2 3 4\n2 4 3 1\n4\n1 2 3 4\n3 1 2 4\n4\n1 2 3 4\n3 1 4 2\n4\n1 2 3 4\n3 2 1 4\n4\n1 2 0 4\n3 2 4 1\n4\n1 2 3 4\n3 4 1 2\n4\n1 2 3 4\n3 4 2 1\n4\n1 2 3 4\n4 1 2 3\n4\n1 2 3 4\n4 1 3 2\n4\n1 2 3 4\n4 2 1 3\n4\n1 2 3 4\n4 2 3 1\n4\n1 2 3 4\n4 3 1 2\n4\n1 2 3 4\n4 3 2 1\n",
"1\n3\n1 2 1\n1 1 2\n",
"6\n3\n3 2 2\n1 2 3\n3\n3 2 1\n1 3 2\n3\n3 2 1\n2 1 3\n3\n3 2 1\n2 3 1\n3\n3 2 1\n3 1 2\n3\n3 2 1\n3 2 1\n",
"2\n2\n2 1\n0 2\n2\n2 1\n2 1\n",
"24\n4\n1 2 3 4\n1 2 3 4\n4\n1 2 3 4\n1 2 4 3\n4\n1 2 3 4\n1 3 2 4\n4\n1 2 3 4\n1 3 4 2\n4\n1 2 3 4\n1 4 2 3\n4\n1 2 3 4\n1 4 3 2\n4\n1 2 3 4\n2 1 3 4\n4\n1 2 3 4\n2 1 4 3\n4\n1 2 3 4\n2 3 1 4\n4\n1 2 3 4\n2 3 4 1\n4\n1 2 3 4\n2 2 1 3\n4\n1 2 3 4\n2 4 3 1\n4\n1 2 3 4\n3 1 2 4\n4\n1 2 3 4\n3 1 4 2\n4\n1 2 3 4\n3 2 1 4\n4\n1 2 0 4\n3 2 4 1\n4\n1 2 3 4\n3 4 1 2\n4\n1 2 3 4\n3 4 2 1\n4\n1 2 3 4\n4 1 2 3\n4\n1 2 3 4\n4 1 3 2\n4\n1 2 3 4\n4 2 1 3\n4\n1 2 3 4\n4 2 3 1\n4\n1 2 3 4\n4 3 1 2\n4\n1 2 3 4\n4 3 2 1\n",
"2\n2\n2 1\n0 2\n2\n2 2\n2 1\n",
"24\n4\n1 2 3 4\n1 2 3 4\n4\n1 2 3 4\n1 2 4 3\n4\n1 2 3 4\n1 3 2 4\n4\n1 2 3 4\n1 3 4 2\n4\n1 2 3 4\n1 4 2 3\n4\n1 2 3 4\n1 4 3 2\n4\n1 2 3 4\n2 1 3 4\n4\n1 2 4 4\n2 1 4 3\n4\n1 2 3 4\n2 3 1 4\n4\n1 2 3 4\n2 3 4 1\n4\n1 2 3 4\n2 2 1 3\n4\n1 2 3 4\n2 4 3 1\n4\n1 2 3 4\n3 1 2 4\n4\n1 2 3 4\n3 1 4 2\n4\n1 2 3 4\n3 2 1 4\n4\n1 2 0 4\n3 2 4 1\n4\n1 2 3 4\n3 4 1 2\n4\n1 2 3 4\n3 4 2 1\n4\n1 2 3 4\n4 1 2 3\n4\n1 2 3 4\n4 1 3 2\n4\n1 2 3 4\n4 2 1 3\n4\n1 2 3 4\n4 2 3 1\n4\n1 2 3 4\n4 3 1 2\n4\n1 2 3 4\n4 3 2 1\n",
"6\n3\n3 2 2\n1 0 3\n3\n6 2 1\n1 3 6\n3\n3 1 1\n2 1 3\n3\n3 2 0\n2 3 1\n3\n3 2 1\n3 1 2\n3\n3 0 1\n3 2 1\n",
"6\n3\n3 2 1\n1 2 3\n3\n3 2 1\n1 3 2\n3\n3 2 1\n2 1 3\n3\n3 2 1\n2 3 1\n3\n3 2 1\n3 1 2\n3\n3 2 1\n1 2 1\n",
"2\n2\n2 1\n1 2\n2\n2 0\n2 1\n",
"5\n2\n1 2\n1 1\n3\n1 2 3\n1 2 3\n3\n1 2 4\n1 3 4\n4\n1 2 3 2\n3 1 2 2\n3\n1 2 3\n1 3 2\n",
"24\n4\n1 2 3 4\n1 2 3 4\n4\n1 2 3 4\n1 2 4 3\n4\n1 2 3 7\n1 3 2 4\n4\n1 2 3 4\n1 3 4 2\n4\n1 2 3 4\n1 4 2 3\n4\n1 2 3 4\n1 4 3 2\n4\n1 2 3 4\n2 1 3 4\n4\n1 2 3 4\n2 1 4 3\n4\n1 2 3 4\n2 3 1 4\n4\n1 2 3 4\n2 3 4 1\n4\n1 2 3 4\n2 4 1 3\n4\n1 2 3 4\n2 4 3 1\n4\n1 2 3 4\n3 1 2 4\n4\n1 2 3 4\n3 1 4 2\n4\n1 2 3 4\n3 2 1 4\n4\n1 2 0 4\n3 2 4 1\n4\n1 2 3 4\n3 4 1 2\n4\n1 2 3 4\n3 4 2 1\n4\n1 2 3 4\n4 1 2 3\n4\n1 2 3 4\n4 1 3 2\n4\n1 2 3 4\n4 2 1 3\n4\n1 2 3 4\n4 2 3 1\n4\n1 2 3 4\n4 3 1 2\n4\n1 2 3 4\n4 3 2 1\n",
"24\n4\n1 2 3 4\n1 2 3 4\n4\n1 2 3 4\n1 2 4 3\n4\n1 2 3 4\n1 3 2 4\n4\n1 2 3 4\n1 3 4 2\n4\n1 2 3 4\n1 4 2 3\n4\n1 2 3 4\n1 4 3 2\n4\n1 2 3 4\n2 1 3 4\n4\n1 2 3 4\n2 1 4 3\n4\n1 2 3 4\n2 3 1 4\n4\n1 2 3 4\n2 3 4 1\n4\n1 2 3 4\n2 2 1 3\n4\n1 2 3 4\n2 4 3 1\n4\n1 2 3 4\n3 1 2 4\n4\n1 2 3 4\n3 1 4 0\n4\n1 2 3 4\n3 2 1 4\n4\n1 2 0 4\n3 2 4 1\n4\n1 2 3 4\n3 4 1 2\n4\n1 2 3 4\n3 4 2 1\n4\n1 2 3 4\n4 1 2 3\n4\n1 2 3 4\n4 1 3 2\n4\n1 2 3 4\n4 2 1 3\n4\n1 2 3 4\n4 2 3 1\n4\n1 2 3 4\n4 3 1 2\n4\n1 2 3 4\n4 3 2 1\n",
"1\n3\n8 9 8\n0 8 9\n",
"1\n3\n114514 1919810 114514\n3274865 114514 1919810\n",
"1\n3\n4 5 2\n5 4 5\n",
"1\n3\n3 7 3\n7 1 7\n",
"1\n3\n1 2 0\n1 1 2\n",
"6\n3\n3 2 2\n1 0 3\n3\n3 2 1\n1 3 2\n3\n3 2 1\n2 1 3\n3\n3 2 1\n2 3 1\n3\n3 2 1\n3 1 2\n3\n3 2 1\n3 2 1\n",
"1\n3\n114514 1919810 114514\n3274865 174015 1919810\n",
"1\n3\n3 5 3\n7 1 7\n",
"1\n3\n1 2 0\n1 1 1\n",
"6\n3\n3 2 2\n1 0 3\n3\n3 2 1\n1 3 2\n3\n3 0 1\n2 1 3\n3\n3 2 1\n2 3 1\n3\n3 2 1\n3 1 2\n3\n3 2 1\n3 2 1\n",
"2\n2\n4 1\n0 2\n2\n2 2\n2 1\n",
"1\n3\n114514 1919810 114514\n3274865 310807 1919810\n",
"1\n3\n1 2 0\n2 1 1\n",
"6\n3\n3 2 2\n1 0 3\n3\n3 2 1\n1 3 1\n3\n3 0 1\n2 1 3\n3\n3 2 1\n2 3 1\n3\n3 2 1\n3 1 2\n3\n3 2 1\n3 2 1\n",
"1\n3\n151782 1919810 114514\n3274865 310807 1919810\n",
"6\n3\n3 2 2\n1 0 3\n3\n3 2 1\n1 3 3\n3\n3 0 1\n2 1 3\n3\n3 2 1\n2 3 1\n3\n3 2 1\n3 1 2\n3\n3 2 1\n3 2 1\n",
"1\n3\n151782 2674654 114514\n3274865 310807 1919810\n",
"6\n3\n3 2 2\n1 0 3\n3\n6 2 1\n1 3 3\n3\n3 0 1\n2 1 3\n3\n3 2 1\n2 3 1\n3\n3 2 1\n3 1 2\n3\n3 2 1\n3 2 1\n",
"1\n3\n151782 2674654 14769\n3274865 310807 1919810\n",
"6\n3\n3 2 2\n1 0 3\n3\n6 2 1\n1 3 3\n3\n3 0 1\n2 1 3\n3\n6 2 1\n2 3 1\n3\n3 2 1\n3 1 2\n3\n3 2 1\n3 2 1\n",
"1\n3\n151782 2674654 14769\n3099651 310807 1919810\n",
"6\n3\n3 2 2\n1 0 3\n3\n6 2 1\n1 3 3\n3\n3 1 1\n2 1 3\n3\n6 2 1\n2 3 1\n3\n3 2 1\n3 1 2\n3\n3 2 1\n3 2 1\n",
"1\n3\n298244 2674654 14769\n3099651 310807 1919810\n",
"6\n3\n3 2 2\n1 0 3\n3\n6 2 1\n1 3 3\n3\n3 1 1\n2 1 3\n3\n3 2 1\n2 3 1\n3\n3 2 1\n3 1 2\n3\n3 2 1\n3 2 1\n",
"1\n3\n298244 2674654 14769\n3099651 310807 3706091\n",
"6\n3\n3 2 2\n1 0 3\n3\n6 2 1\n1 3 6\n3\n3 1 1\n2 1 3\n3\n3 2 1\n2 3 1\n3\n3 2 1\n3 1 2\n3\n3 2 1\n3 2 1\n",
"1\n3\n298244 3971348 14769\n3099651 310807 3706091\n",
"6\n3\n3 2 2\n1 0 3\n3\n6 2 1\n1 3 6\n3\n3 1 1\n2 1 3\n3\n3 2 0\n2 3 1\n3\n3 2 1\n3 1 2\n3\n3 2 1\n3 2 1\n",
"1\n3\n298244 3971348 14769\n3099651 310807 248503\n",
"1\n3\n298244 3971348 14769\n3099651 148986 248503\n",
"6\n3\n3 2 2\n1 0 3\n3\n6 2 1\n1 3 6\n3\n3 1 1\n2 1 3\n3\n3 2 0\n2 3 0\n3\n3 2 1\n3 1 2\n3\n3 0 1\n3 2 1\n",
"1\n3\n298244 3971348 14769\n40164 148986 248503\n",
"6\n3\n3 2 2\n1 0 3\n3\n6 2 1\n1 3 6\n3\n3 1 1\n2 1 3\n3\n3 2 0\n2 3 0\n3\n3 2 1\n3 0 2\n3\n3 0 1\n3 2 1\n",
"1\n3\n298244 400668 14769\n40164 148986 248503\n",
"1\n3\n298244 552974 14769\n40164 148986 248503\n",
"1\n3\n298244 552974 14769\n66381 148986 248503\n",
"1\n3\n298244 552974 14769\n79918 148986 248503\n",
"1\n3\n103599 552974 14769\n79918 148986 248503\n",
"1\n3\n203544 552974 14769\n79918 148986 248503\n",
"24\n4\n1 2 3 4\n1 2 3 4\n4\n1 2 3 4\n1 2 4 3\n4\n1 2 3 4\n1 3 2 4\n4\n1 2 3 4\n1 3 4 2\n4\n1 2 3 4\n1 4 2 3\n4\n1 2 3 4\n1 4 3 2\n4\n1 2 3 4\n2 1 3 4\n4\n1 2 3 4\n2 1 4 3\n4\n1 2 3 4\n2 3 1 4\n4\n1 2 3 4\n2 3 3 1\n4\n1 2 3 4\n2 4 1 3\n4\n1 2 3 4\n2 4 3 1\n4\n1 2 3 4\n3 1 2 4\n4\n1 2 3 4\n3 1 4 2\n4\n1 2 3 4\n3 2 1 4\n4\n1 2 3 4\n3 2 4 1\n4\n1 2 3 4\n3 4 1 2\n4\n1 2 3 4\n3 4 2 1\n4\n1 2 3 4\n4 1 2 3\n4\n1 2 3 4\n4 1 3 2\n4\n1 2 3 4\n4 2 1 3\n4\n1 2 3 4\n4 2 3 1\n4\n1 2 3 4\n4 3 1 2\n4\n1 2 3 4\n4 3 2 1\n",
"1\n3\n11 9 8\n9 8 9\n",
"1\n1\n0\n1\n",
"1\n3\n4 5 4\n5 4 9\n",
"1\n3\n3 7 3\n1 3 7\n",
"1\n3\n1 2 1\n1 1 1\n",
"1\n3\n8 9 8\n-1 8 9\n",
"6\n3\n3 2 2\n1 2 3\n3\n3 2 1\n1 3 2\n3\n3 2 1\n2 1 3\n3\n3 2 1\n2 3 1\n3\n3 2 2\n3 1 2\n3\n3 2 1\n3 2 1\n",
"2\n2\n2 1\n0 2\n2\n2 1\n2 0\n",
"1\n3\n114514 1383211 114514\n3274865 114514 1919810\n",
"1\n3\n4 5 2\n5 0 5\n",
"1\n3\n3 7 3\n6 1 7\n",
"6\n3\n3 2 2\n1 0 3\n3\n3 2 1\n1 3 2\n3\n3 2 1\n2 1 3\n3\n3 2 1\n2 3 1\n3\n3 2 1\n3 1 2\n3\n3 2 1\n3 3 1\n",
"1\n3\n114514 1919810 55787\n3274865 174015 1919810\n",
"1\n3\n3 5 3\n7 1 12\n",
"1\n3\n1 2 0\n0 1 1\n",
"6\n3\n3 2 2\n1 0 3\n3\n3 2 1\n1 3 2\n3\n3 0 0\n2 1 3\n3\n3 2 1\n2 3 1\n3\n3 2 1\n3 1 2\n3\n3 2 1\n3 2 1\n",
"2\n2\n4 1\n0 2\n2\n2 1\n2 1\n",
"1\n3\n114514 112362 114514\n3274865 310807 1919810\n",
"1\n3\n61710 1919810 114514\n3274865 310807 1919810\n",
"6\n3\n3 2 2\n1 0 3\n3\n3 2 1\n1 3 3\n3\n3 0 1\n2 1 3\n3\n3 2 1\n2 2 1\n3\n3 2 1\n3 1 2\n3\n3 2 1\n3 2 1\n",
"1\n3\n151782 2674654 205476\n3274865 310807 1919810\n",
"6\n3\n3 2 2\n1 0 3\n3\n6 2 1\n1 3 3\n3\n3 0 1\n2 1 3\n3\n3 2 1\n2 3 1\n3\n3 2 1\n3 1 2\n3\n3 2 1\n3 2 0\n",
"1\n3\n151782 2688111 14769\n3274865 310807 1919810\n",
"6\n3\n3 2 2\n1 0 3\n3\n6 2 1\n1 3 3\n3\n3 0 1\n2 1 3\n3\n6 2 1\n2 3 1\n3\n3 1 1\n3 1 2\n3\n3 2 1\n3 2 1\n",
"1\n3\n151782 2674654 28271\n3099651 310807 1919810\n",
"6\n3\n3 2 2\n1 0 3\n3\n6 2 1\n1 3 3\n3\n3 1 1\n2 1 3\n3\n6 2 1\n2 3 1\n3\n3 2 1\n3 1 2\n3\n3 2 0\n3 2 1\n",
"1\n3\n298244 4036930 14769\n3099651 310807 1919810\n",
"6\n3\n3 2 4\n1 0 3\n3\n6 2 1\n1 3 3\n3\n3 1 1\n2 1 3\n3\n3 2 1\n2 3 1\n3\n3 2 1\n3 1 2\n3\n3 2 1\n3 2 1\n",
"1\n3\n298244 2674654 14769\n3099651 153808 3706091\n",
"1\n3\n298244 3971348 14769\n983129 310807 3706091\n",
"6\n3\n3 2 2\n1 0 3\n3\n6 4 1\n1 3 6\n3\n3 1 1\n2 1 3\n3\n3 2 0\n2 3 1\n3\n3 2 1\n3 1 2\n3\n3 2 1\n3 2 1\n",
"1\n3\n298244 3971348 14769\n3099651 545178 248503\n",
"6\n3\n3 2 2\n1 0 3\n3\n6 2 1\n1 3 6\n3\n3 1 1\n2 1 3\n3\n3 2 0\n2 3 1\n3\n3 2 1\n3 1 2\n3\n3 -1 1\n3 2 1\n",
"1\n3\n298244 3971348 19379\n3099651 148986 248503\n",
"6\n3\n3 2 2\n2 0 3\n3\n6 2 1\n1 3 6\n3\n3 1 1\n2 1 3\n3\n3 2 0\n2 3 0\n3\n3 2 1\n3 1 2\n3\n3 0 1\n3 2 1\n"
],
"output": [
"Yes\nYes\nNo\nYes\nNo\n",
"Yes\nNo\nYes\nNo\nNo\nNo\nNo\nYes\nNo\nNo\nYes\nNo\nNo\nYes\nNo\nNo\nYes\nNo\nNo\nNo\nNo\nYes\nNo\nYes\n",
"No\n",
"No\n",
"Yes\nNo\nNo\nNo\nNo\nYes\n",
"Yes\n",
"Yes\nYes\n",
"No\n",
"No\n",
"No\n",
"Yes\nNo\nYes\nNo\nNo\nNo\nNo\nYes\nNo\nNo\nYes\nNo\nNo\nYes\nNo\nNo\nYes\nNo\nNo\nNo\nNo\nYes\nNo\nYes\n",
"No\n",
"No\nNo\nNo\nNo\nNo\nYes\n",
"No\nYes\n",
"Yes\nNo\nYes\nNo\nNo\nNo\nNo\nYes\nNo\nNo\nNo\nNo\nNo\nYes\nNo\nNo\nYes\nNo\nNo\nNo\nNo\nYes\nNo\nYes\n",
"No\nNo\n",
"Yes\nNo\nYes\nNo\nNo\nNo\nNo\nNo\nNo\nNo\nNo\nNo\nNo\nYes\nNo\nNo\nYes\nNo\nNo\nNo\nNo\nYes\nNo\nYes\n",
"No\nNo\nNo\nNo\nNo\nNo\n",
"Yes\nNo\nNo\nNo\nNo\nNo\n",
"Yes\nNo\n",
"No\nYes\nNo\nYes\nNo\n",
"Yes\nNo\nNo\nNo\nNo\nNo\nNo\nYes\nNo\nNo\nYes\nNo\nNo\nYes\nNo\nNo\nYes\nNo\nNo\nNo\nNo\nYes\nNo\nYes\n",
"Yes\nNo\nYes\nNo\nNo\nNo\nNo\nYes\nNo\nNo\nNo\nNo\nNo\nNo\nNo\nNo\nYes\nNo\nNo\nNo\nNo\nYes\nNo\nYes\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\nNo\nNo\nNo\nNo\nYes\n",
"No\n",
"No\n",
"No\n",
"No\nNo\nNo\nNo\nNo\nYes\n",
"No\nNo\n",
"No\n",
"No\n",
"No\nNo\nNo\nNo\nNo\nYes\n",
"No\n",
"No\nNo\nNo\nNo\nNo\nYes\n",
"No\n",
"No\nNo\nNo\nNo\nNo\nYes\n",
"No\n",
"No\nNo\nNo\nNo\nNo\nYes\n",
"No\n",
"No\nNo\nNo\nNo\nNo\nYes\n",
"No\n",
"No\nNo\nNo\nNo\nNo\nYes\n",
"No\n",
"No\nNo\nNo\nNo\nNo\nYes\n",
"No\n",
"No\nNo\nNo\nNo\nNo\nYes\n",
"No\n",
"No\n",
"No\nNo\nNo\nNo\nNo\nNo\n",
"No\n",
"No\nNo\nNo\nNo\nNo\nNo\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"Yes\nNo\nYes\nNo\nNo\nNo\nNo\nYes\nNo\nNo\nYes\nNo\nNo\nYes\nNo\nNo\nYes\nNo\nNo\nNo\nNo\nYes\nNo\nYes\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\nNo\nNo\nNo\nNo\nYes\n",
"No\nNo\n",
"No\n",
"No\n",
"No\n",
"No\nNo\nNo\nNo\nNo\nNo\n",
"No\n",
"No\n",
"No\n",
"No\nNo\nNo\nNo\nNo\nYes\n",
"No\nYes\n",
"No\n",
"No\n",
"No\nNo\nNo\nNo\nNo\nYes\n",
"No\n",
"No\nNo\nNo\nNo\nNo\nNo\n",
"No\n",
"No\nNo\nNo\nNo\nNo\nYes\n",
"No\n",
"No\nNo\nNo\nNo\nNo\nNo\n",
"No\n",
"No\nNo\nNo\nNo\nNo\nYes\n",
"No\n",
"No\n",
"No\nNo\nNo\nNo\nNo\nYes\n",
"No\n",
"No\nNo\nNo\nNo\nNo\nNo\n",
"No\n",
"No\nNo\nNo\nNo\nNo\nNo\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Ayush, Ashish and Vivek are busy preparing a new problem for the next Codeforces round and need help checking if their test cases are valid.
Each test case consists of an integer n and two arrays a and b, of size n. If after some (possibly zero) operations described below, array a can be transformed into array b, the input is said to be valid. Otherwise, it is invalid.
An operation on array a is:
* select an integer k (1 ≤ k ≤ ⌊n/2⌋)
* swap the prefix of length k with the suffix of length k
For example, if array a initially is \{1, 2, 3, 4, 5, 6\}, after performing an operation with k = 2, it is transformed into \{5, 6, 3, 4, 1, 2\}.
Given the set of test cases, help them determine if each one is valid or invalid.
Input
The first line contains one integer t (1 ≤ t ≤ 500) — the number of test cases. The description of each test case is as follows.
The first line of each test case contains a single integer n (1 ≤ n ≤ 500) — the size of the arrays.
The second line of each test case contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — elements of array a.
The third line of each test case contains n integers b_1, b_2, ..., b_n (1 ≤ b_i ≤ 10^9) — elements of array b.
Output
For each test case, print "Yes" if the given input is valid. Otherwise print "No".
You may print the answer in any case.
Example
Input
5
2
1 2
2 1
3
1 2 3
1 2 3
3
1 2 4
1 3 4
4
1 2 3 2
3 1 2 2
3
1 2 3
1 3 2
Output
yes
yes
No
yes
No
Note
For the first test case, we can swap prefix a[1:1] with suffix a[2:2] to get a=[2, 1].
For the second test case, a is already equal to b.
For the third test case, it is impossible since we cannot obtain 3 in a.
For the fourth test case, we can first swap prefix a[1:1] with suffix a[4:4] to obtain a=[2, 2, 3, 1]. Now we can swap prefix a[1:2] with suffix a[3:4] to obtain a=[3, 1, 2, 2].
For the fifth test case, it is impossible to convert a to b.
### Input:
5
2
1 2
2 1
3
1 2 3
1 2 3
3
1 2 4
1 3 4
4
1 2 3 2
3 1 2 2
3
1 2 3
1 3 2
### Output:
Yes
Yes
No
Yes
No
### Input:
24
4
1 2 3 4
1 2 3 4
4
1 2 3 4
1 2 4 3
4
1 2 3 4
1 3 2 4
4
1 2 3 4
1 3 4 2
4
1 2 3 4
1 4 2 3
4
1 2 3 4
1 4 3 2
4
1 2 3 4
2 1 3 4
4
1 2 3 4
2 1 4 3
4
1 2 3 4
2 3 1 4
4
1 2 3 4
2 3 4 1
4
1 2 3 4
2 4 1 3
4
1 2 3 4
2 4 3 1
4
1 2 3 4
3 1 2 4
4
1 2 3 4
3 1 4 2
4
1 2 3 4
3 2 1 4
4
1 2 3 4
3 2 4 1
4
1 2 3 4
3 4 1 2
4
1 2 3 4
3 4 2 1
4
1 2 3 4
4 1 2 3
4
1 2 3 4
4 1 3 2
4
1 2 3 4
4 2 1 3
4
1 2 3 4
4 2 3 1
4
1 2 3 4
4 3 1 2
4
1 2 3 4
4 3 2 1
### Output:
Yes
No
Yes
No
No
No
No
Yes
No
No
Yes
No
No
Yes
No
No
Yes
No
No
No
No
Yes
No
Yes
### Code:
t = int(input())
for _ in range(t):
n = int(input())
a = list(map(int, input().split()))
b = list(map(int, input().split()))
pair = dict()
possible = 1
if n % 2 == 1:
if a[n//2] != b[n//2]:
possible = 0
for i in range(n//2):
M, m = max(a[i], a[n- i - 1]), min(a[i], a[n - i - 1])
try:
pair[str(m) + " " + str(M)] += 1
except:
pair[str(m) + " " + str(M)] = 1
for i in range(n//2):
M, m = max(b[i], b[n - i - 1]), min(b[i], b[n - i - 1])
x = str(m) + " " + str(M)
if x not in pair:
#print(x, "...1")
possible = 0
break
else:
if pair[x] >= 1:
pair[x] -= 1
#print(x, "....2")
else:
#print(x, "......3")
possible = 0
break
if possible:
print("yes")
else:
print("No")
|
1385_F. Removing Leaves_10519
|
You are given a tree (connected graph without cycles) consisting of n vertices. The tree is unrooted — it is just a connected undirected graph without cycles.
In one move, you can choose exactly k leaves (leaf is such a vertex that is connected to only one another vertex) connected to the same vertex and remove them with edges incident to them. I.e. you choose such leaves u_1, u_2, ..., u_k that there are edges (u_1, v), (u_2, v), ..., (u_k, v) and remove these leaves and these edges.
Your task is to find the maximum number of moves you can perform if you remove leaves optimally.
You have to answer t independent test cases.
Input
The first line of the input contains one integer t (1 ≤ t ≤ 2 ⋅ 10^4) — the number of test cases. Then t test cases follow.
The first line of the test case contains two integers n and k (2 ≤ n ≤ 2 ⋅ 10^5; 1 ≤ k < n) — the number of vertices in the tree and the number of leaves you remove in one move, respectively. The next n-1 lines describe edges. The i-th edge is represented as two integers x_i and y_i (1 ≤ x_i, y_i ≤ n), where x_i and y_i are vertices the i-th edge connects. It is guaranteed that the given set of edges forms a tree.
It is guaranteed that the sum of n does not exceed 2 ⋅ 10^5 (∑ n ≤ 2 ⋅ 10^5).
Output
For each test case, print the answer — the maximum number of moves you can perform if you remove leaves optimally.
Example
Input
4
8 3
1 2
1 5
7 6
6 8
3 1
6 4
6 1
10 3
1 2
1 10
2 3
1 5
1 6
2 4
7 10
10 9
8 10
7 2
3 1
4 5
3 6
7 4
1 2
1 4
5 1
1 2
2 3
4 3
5 3
Output
2
3
3
4
Note
The picture corresponding to the first test case of the example:
<image>
There you can remove vertices 2, 5 and 3 during the first move and vertices 1, 7 and 4 during the second move.
The picture corresponding to the second test case of the example:
<image>
There you can remove vertices 7, 8 and 9 during the first move, then vertices 5, 6 and 10 during the second move and vertices 1, 3 and 4 during the third move.
The picture corresponding to the third test case of the example:
<image>
There you can remove vertices 5 and 7 during the first move, then vertices 2 and 4 during the second move and vertices 1 and 6 during the third move.
|
import os
import sys
from io import BytesIO, IOBase
# region fastio
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
# ------------------------------
def RL(): return map(int, sys.stdin.readline().rstrip().split())
def RLL(): return list(map(int, sys.stdin.readline().rstrip().split()))
def N(): return int(input())
def comb(n, m): return factorial(n) / (factorial(m) * factorial(n - m)) if n >= m else 0
def perm(n, m): return factorial(n) // (factorial(n - m)) if n >= m else 0
def mdis(x1, y1, x2, y2): return abs(x1 - x2) + abs(y1 - y2)
mod = 998244353
INF = float('inf')
from math import factorial
from collections import Counter, defaultdict, deque
from heapq import heapify, heappop, heappush
# ------------------------------
# f = open('../input.txt')
# sys.stdin = f
def main():
for _ in range(N()):
n, k = RL()
gp = [[] for _ in range(n+1)]
ind = [0]*(n+1)
for _ in range(n-1):
a, b = RL()
gp[a].append(b)
gp[b].append(a)
ind[a]+=1
ind[b]+=1
if k==1:
print(n-1)
continue
q = []
vis = [0]*(n+1)
for i in range(1, n+1):
if ind[i]==1:
q.append(i)
vis[i] = 1
num = [0]*(n+1)
res = 0
while q:
nd = q.pop()
ind[nd]-=1
for nex in gp[nd]:
if vis[nex]==1: continue
ind[nex]-=1
num[nex]+=1
if num[nex]%k==0:
res+=1
if ind[nex]==1:
q.append(nex)
vis[nex] = 1
print(res)
if __name__ == "__main__":
main()
|
{
"input": [
"4\n8 3\n1 2\n1 5\n7 6\n6 8\n3 1\n6 4\n6 1\n10 3\n1 2\n1 10\n2 3\n1 5\n1 6\n2 4\n7 10\n10 9\n8 10\n7 2\n3 1\n4 5\n3 6\n7 4\n1 2\n1 4\n5 1\n1 2\n2 3\n4 3\n5 3\n",
"4\n8 3\n1 2\n1 5\n7 6\n6 8\n3 1\n6 4\n6 1\n10 3\n1 2\n1 10\n2 3\n1 5\n1 6\n2 4\n7 10\n10 9\n8 10\n7 2\n3 1\n2 5\n3 6\n7 4\n1 2\n1 4\n5 1\n1 2\n2 3\n4 3\n5 3\n",
"4\n8 3\n1 2\n1 5\n7 6\n6 8\n3 1\n6 4\n6 1\n10 3\n1 2\n1 10\n2 3\n1 5\n1 6\n2 4\n7 10\n10 9\n8 10\n7 2\n3 1\n4 5\n3 6\n7 4\n1 2\n1 4\n5 1\n1 4\n2 3\n4 3\n5 3\n",
"4\n8 3\n1 2\n1 5\n7 6\n6 8\n3 1\n6 4\n6 1\n10 3\n1 4\n1 10\n2 3\n1 5\n1 6\n2 4\n7 10\n10 9\n8 10\n7 2\n3 1\n4 5\n3 6\n7 4\n1 2\n1 4\n5 1\n1 2\n2 3\n4 3\n5 3\n",
"4\n8 3\n1 2\n1 5\n7 6\n6 8\n3 1\n7 4\n6 1\n10 3\n1 2\n1 10\n2 3\n1 5\n1 6\n2 4\n7 10\n10 9\n8 10\n7 2\n3 1\n2 5\n3 6\n7 4\n1 2\n1 4\n5 1\n1 2\n2 3\n4 3\n5 3\n",
"4\n8 3\n1 2\n1 5\n7 6\n6 8\n3 1\n6 4\n4 1\n10 3\n1 2\n1 10\n2 3\n1 5\n1 6\n2 4\n7 10\n10 9\n8 10\n7 2\n3 1\n4 5\n3 6\n7 4\n1 2\n1 4\n5 1\n1 4\n2 3\n4 3\n5 3\n",
"4\n8 3\n1 2\n1 5\n7 6\n6 8\n3 1\n6 4\n6 1\n10 3\n1 4\n1 10\n2 3\n1 5\n2 6\n2 4\n7 10\n10 9\n8 10\n7 2\n3 1\n4 5\n3 6\n7 4\n1 2\n1 4\n5 1\n1 2\n2 3\n4 3\n5 3\n",
"4\n8 6\n1 2\n1 5\n7 6\n6 8\n3 1\n6 4\n4 1\n10 3\n1 2\n1 10\n2 3\n1 5\n1 6\n2 4\n7 10\n10 9\n8 10\n7 2\n3 1\n4 5\n3 6\n7 4\n1 2\n1 4\n5 1\n1 4\n2 3\n4 3\n5 3\n",
"4\n8 3\n1 2\n1 5\n7 6\n6 8\n3 1\n7 4\n6 1\n10 3\n1 2\n1 10\n2 3\n1 5\n1 6\n2 4\n7 10\n6 9\n8 10\n7 2\n3 1\n2 5\n3 6\n7 4\n1 2\n1 4\n5 1\n1 2\n2 3\n4 3\n5 3\n",
"4\n8 3\n1 2\n1 5\n7 3\n6 8\n3 1\n6 4\n6 1\n10 3\n1 2\n1 10\n2 3\n1 5\n1 6\n2 4\n7 10\n10 9\n8 10\n7 2\n3 1\n2 5\n3 6\n7 4\n1 2\n1 4\n5 1\n1 2\n2 3\n4 3\n5 3\n",
"4\n8 3\n1 2\n1 5\n7 6\n6 8\n3 1\n6 4\n4 1\n10 6\n1 2\n1 10\n2 3\n1 5\n1 6\n2 4\n7 10\n10 9\n8 10\n7 2\n3 1\n4 5\n3 6\n7 4\n1 2\n1 4\n5 1\n1 4\n2 3\n4 3\n5 3\n",
"4\n8 3\n1 2\n1 5\n7 2\n6 8\n3 1\n6 4\n6 1\n10 3\n1 4\n1 10\n4 3\n1 5\n2 6\n2 4\n7 10\n10 9\n8 10\n7 2\n3 1\n4 5\n1 6\n7 4\n1 2\n1 4\n5 1\n1 2\n2 3\n4 3\n5 3\n",
"4\n8 3\n1 2\n1 5\n7 6\n6 8\n3 1\n6 4\n6 1\n10 3\n1 4\n1 10\n2 3\n1 5\n2 6\n2 4\n7 10\n10 9\n8 10\n7 2\n3 1\n4 5\n3 6\n7 4\n1 2\n1 7\n5 1\n1 2\n2 3\n4 3\n5 3\n",
"4\n8 6\n1 2\n1 5\n7 6\n6 8\n3 1\n6 4\n4 1\n10 3\n1 2\n1 10\n2 3\n1 5\n1 6\n2 4\n7 10\n10 9\n8 7\n7 2\n3 1\n4 5\n3 6\n7 4\n1 2\n1 4\n5 1\n1 4\n2 3\n4 3\n5 3\n",
"4\n8 3\n1 2\n1 5\n7 3\n6 8\n3 1\n6 4\n6 1\n10 1\n1 2\n1 10\n2 3\n1 5\n1 6\n2 4\n7 10\n10 9\n8 10\n7 2\n3 1\n2 5\n3 6\n7 4\n1 2\n1 4\n5 1\n1 2\n2 3\n4 3\n5 3\n",
"4\n8 3\n1 2\n1 5\n7 6\n6 8\n3 1\n6 4\n6 1\n10 3\n1 2\n1 10\n2 3\n1 5\n1 6\n2 4\n7 10\n10 9\n8 5\n7 2\n3 1\n4 5\n3 6\n7 4\n1 2\n1 4\n5 1\n1 2\n2 3\n4 3\n5 3\n",
"4\n8 3\n1 2\n1 5\n7 6\n6 8\n3 1\n6 4\n6 1\n10 3\n1 2\n1 10\n2 3\n1 5\n1 6\n2 4\n7 10\n10 9\n8 5\n7 2\n3 1\n4 5\n3 6\n7 6\n1 2\n1 4\n5 1\n1 2\n2 3\n4 3\n5 3\n",
"4\n8 3\n1 2\n1 5\n7 6\n6 8\n3 1\n6 4\n6 1\n10 2\n1 4\n1 10\n2 3\n1 5\n2 6\n2 4\n7 10\n10 9\n8 10\n7 2\n3 1\n4 5\n3 6\n7 4\n1 2\n1 4\n5 2\n1 2\n2 3\n4 3\n5 3\n",
"4\n8 3\n1 2\n1 5\n7 6\n6 8\n3 1\n7 4\n6 1\n10 3\n1 2\n1 10\n4 3\n1 5\n1 6\n2 4\n7 10\n10 9\n8 10\n7 2\n3 1\n2 5\n3 6\n7 4\n1 2\n1 4\n5 1\n1 2\n2 3\n4 3\n5 3\n",
"4\n8 10\n1 2\n1 5\n7 6\n6 8\n3 1\n8 4\n7 1\n10 1\n1 2\n1 10\n2 3\n1 5\n1 6\n2 4\n7 10\n10 9\n8 10\n7 2\n3 1\n1 5\n4 6\n7 4\n1 2\n1 4\n5 1\n1 4\n2 1\n4 3\n5 3\n",
"4\n8 1\n1 2\n1 5\n7 6\n6 8\n3 1\n6 4\n6 1\n10 2\n1 4\n1 10\n2 3\n1 5\n2 6\n2 4\n7 10\n10 9\n8 10\n7 2\n3 1\n4 5\n3 6\n7 4\n1 2\n1 4\n5 1\n1 2\n2 3\n4 3\n5 3\n",
"4\n8 3\n1 2\n1 5\n7 8\n6 8\n3 1\n6 4\n6 1\n10 3\n1 4\n1 10\n2 3\n1 5\n2 6\n2 4\n7 10\n10 9\n8 10\n7 2\n3 1\n4 5\n3 6\n7 4\n1 2\n1 4\n5 1\n1 2\n2 3\n4 3\n5 3\n",
"4\n8 3\n1 2\n1 5\n7 6\n6 8\n3 1\n6 4\n6 1\n10 3\n1 4\n1 10\n4 3\n1 5\n2 6\n2 4\n7 10\n10 9\n8 10\n7 2\n3 1\n4 5\n3 6\n7 4\n1 2\n1 4\n5 1\n1 2\n2 3\n4 3\n5 3\n",
"4\n8 3\n1 2\n1 5\n7 6\n6 8\n3 1\n6 4\n6 1\n10 3\n1 4\n1 10\n4 3\n1 5\n2 6\n2 4\n7 10\n10 9\n8 10\n7 2\n3 1\n4 5\n1 6\n7 4\n1 2\n1 4\n5 1\n1 2\n2 3\n4 3\n5 3\n",
"4\n8 6\n1 2\n1 5\n7 6\n6 8\n3 1\n6 4\n4 1\n10 3\n1 2\n1 10\n2 3\n1 5\n1 6\n2 4\n7 10\n10 9\n8 10\n7 2\n3 1\n4 5\n3 6\n7 4\n1 2\n1 4\n5 1\n1 4\n2 1\n4 3\n5 3\n",
"4\n8 3\n1 2\n1 5\n7 6\n6 8\n3 1\n6 4\n6 1\n10 3\n1 4\n1 10\n4 3\n1 5\n2 6\n2 4\n7 10\n10 9\n8 10\n7 2\n3 1\n4 5\n3 6\n7 4\n1 2\n1 4\n5 1\n1 2\n1 3\n4 3\n5 3\n",
"4\n8 3\n1 2\n1 5\n7 6\n6 8\n3 1\n6 4\n6 1\n10 3\n1 2\n1 10\n2 3\n1 5\n1 6\n2 4\n7 10\n10 9\n8 10\n7 4\n3 1\n4 5\n3 6\n7 4\n1 2\n1 4\n5 1\n1 4\n2 3\n4 3\n5 3\n",
"4\n8 6\n1 2\n1 5\n7 6\n6 8\n3 1\n6 4\n4 1\n10 3\n1 2\n1 10\n2 3\n1 5\n1 6\n2 4\n7 10\n10 9\n8 10\n7 2\n3 1\n4 5\n4 6\n7 4\n1 2\n1 4\n5 1\n1 4\n2 1\n4 3\n5 3\n",
"4\n8 6\n1 2\n1 5\n7 6\n6 8\n3 1\n8 4\n4 1\n10 3\n1 2\n1 10\n2 3\n1 5\n1 6\n2 4\n7 10\n10 9\n8 10\n7 2\n3 1\n4 5\n4 6\n7 4\n1 2\n1 4\n5 1\n1 4\n2 1\n4 3\n5 3\n",
"4\n8 10\n1 2\n1 5\n7 6\n6 8\n3 1\n8 4\n4 1\n10 3\n1 2\n1 10\n2 3\n1 5\n1 6\n2 4\n7 10\n10 9\n8 10\n7 2\n3 1\n4 5\n4 6\n7 4\n1 2\n1 4\n5 1\n1 4\n2 1\n4 3\n5 3\n",
"4\n8 10\n1 2\n1 5\n7 6\n6 8\n3 1\n8 4\n7 1\n10 3\n1 2\n1 10\n2 3\n1 5\n1 6\n2 4\n7 10\n10 9\n8 10\n7 2\n3 1\n4 5\n4 6\n7 4\n1 2\n1 4\n5 1\n1 4\n2 1\n4 3\n5 3\n",
"4\n8 3\n1 2\n1 5\n7 6\n6 8\n3 1\n6 4\n6 1\n10 3\n1 2\n1 10\n2 3\n1 5\n1 6\n2 4\n7 10\n2 9\n8 10\n7 2\n3 1\n4 5\n3 6\n7 4\n1 2\n1 4\n5 1\n1 2\n2 3\n4 3\n5 3\n",
"4\n8 10\n1 2\n1 5\n7 6\n6 8\n3 1\n8 4\n7 1\n10 3\n1 2\n1 10\n2 3\n1 5\n1 6\n2 4\n7 10\n10 9\n8 10\n7 2\n3 1\n1 5\n4 6\n7 4\n1 2\n1 4\n5 1\n1 4\n2 1\n4 3\n5 3\n",
"4\n8 3\n1 2\n1 5\n7 6\n6 8\n3 1\n6 4\n6 1\n10 3\n1 4\n1 10\n4 3\n1 5\n2 6\n2 4\n7 10\n10 9\n8 10\n7 2\n3 1\n4 5\n3 6\n7 4\n1 2\n1 7\n5 1\n1 2\n2 3\n4 3\n5 3\n",
"4\n8 3\n1 2\n1 5\n7 3\n6 8\n3 1\n6 4\n6 1\n10 1\n1 3\n1 10\n2 3\n1 5\n1 6\n2 4\n7 10\n10 9\n8 10\n7 2\n3 1\n2 5\n3 6\n7 4\n1 2\n1 4\n5 1\n1 2\n2 3\n4 3\n5 3\n",
"4\n8 10\n1 2\n1 5\n7 6\n3 8\n3 1\n8 4\n7 1\n10 3\n1 2\n1 10\n2 3\n1 5\n1 6\n2 4\n7 10\n10 9\n8 10\n7 2\n3 1\n1 5\n4 6\n7 4\n1 2\n1 4\n5 1\n1 4\n2 1\n4 3\n5 3\n",
"4\n8 3\n1 2\n1 5\n7 6\n6 8\n3 1\n6 4\n6 1\n10 2\n1 4\n1 10\n2 3\n1 5\n2 6\n2 4\n7 10\n10 9\n8 10\n7 2\n3 1\n4 5\n3 6\n7 4\n1 2\n1 4\n5 1\n1 2\n2 3\n4 3\n5 3\n",
"4\n8 3\n1 2\n1 5\n7 6\n6 8\n3 1\n6 4\n6 2\n10 3\n1 2\n1 10\n2 3\n1 5\n1 6\n2 4\n7 10\n10 9\n8 10\n7 4\n3 1\n4 5\n3 6\n7 4\n1 2\n1 4\n5 1\n1 4\n2 3\n4 3\n5 3\n",
"4\n8 6\n1 2\n1 5\n7 6\n6 8\n3 1\n8 4\n4 1\n10 3\n1 2\n1 10\n2 3\n1 5\n1 6\n2 4\n7 10\n10 9\n8 10\n7 2\n3 1\n4 5\n4 6\n7 4\n1 2\n1 4\n5 1\n1 4\n2 1\n2 3\n5 3\n",
"4\n8 3\n1 2\n1 5\n7 6\n6 8\n3 1\n6 4\n4 1\n10 6\n1 2\n1 10\n1 3\n1 5\n1 6\n2 4\n7 10\n10 9\n8 10\n7 2\n3 1\n4 5\n3 6\n7 4\n1 2\n1 4\n5 1\n1 4\n2 3\n4 3\n5 3\n",
"4\n8 6\n1 2\n1 5\n7 6\n6 8\n3 1\n6 4\n4 1\n10 3\n1 2\n1 10\n2 3\n2 5\n1 6\n2 4\n7 10\n10 9\n8 7\n7 2\n3 1\n4 5\n3 6\n7 4\n1 2\n1 4\n5 1\n1 4\n2 3\n4 3\n5 3\n",
"4\n8 10\n1 2\n1 5\n7 6\n6 8\n3 1\n5 4\n7 1\n10 3\n1 2\n1 10\n2 3\n1 5\n1 6\n2 4\n7 10\n10 9\n8 10\n7 2\n3 1\n1 5\n4 6\n7 4\n1 2\n1 4\n5 1\n1 4\n2 1\n4 3\n5 3\n",
"4\n8 3\n1 2\n1 5\n7 6\n6 8\n3 1\n6 4\n6 1\n10 2\n1 4\n1 10\n4 3\n1 5\n2 6\n2 4\n7 10\n10 9\n8 10\n7 2\n3 1\n4 5\n3 6\n7 4\n1 2\n1 7\n5 1\n1 2\n2 3\n4 3\n5 3\n",
"4\n8 3\n1 2\n1 5\n7 6\n6 8\n3 1\n6 4\n6 1\n10 2\n1 4\n1 10\n4 3\n1 5\n2 6\n2 8\n7 10\n10 9\n8 10\n7 2\n3 1\n4 5\n3 6\n7 4\n1 2\n1 7\n5 1\n1 2\n2 3\n4 3\n5 3\n",
"4\n8 6\n1 2\n1 5\n7 6\n6 8\n3 1\n6 4\n4 1\n10 3\n1 2\n1 10\n2 3\n1 5\n1 6\n2 4\n7 10\n10 9\n8 10\n7 3\n3 1\n4 5\n3 6\n7 4\n1 2\n1 4\n5 1\n1 4\n2 1\n4 3\n5 3\n",
"4\n8 3\n1 2\n1 5\n7 6\n6 8\n3 1\n6 4\n6 1\n10 3\n1 2\n1 10\n2 3\n1 5\n1 6\n2 4\n7 10\n5 9\n8 10\n7 4\n3 1\n4 5\n3 6\n7 4\n1 2\n1 4\n5 1\n1 4\n2 3\n4 3\n5 3\n",
"4\n8 3\n1 2\n1 5\n7 6\n6 8\n3 1\n7 4\n6 1\n10 3\n1 2\n1 10\n2 3\n1 5\n1 6\n2 4\n7 10\n6 9\n8 10\n7 2\n3 1\n2 5\n3 6\n7 3\n1 2\n1 4\n5 1\n1 2\n2 3\n4 3\n5 3\n",
"4\n8 10\n1 2\n1 5\n7 6\n6 8\n3 1\n8 4\n2 1\n10 3\n1 2\n1 10\n2 3\n1 5\n1 6\n2 4\n7 10\n10 9\n8 10\n7 2\n3 1\n4 5\n4 6\n7 4\n1 2\n1 4\n5 1\n1 4\n2 1\n4 3\n5 3\n",
"4\n8 3\n1 2\n1 5\n7 6\n6 8\n3 1\n6 4\n6 1\n10 3\n1 2\n1 10\n2 3\n1 5\n1 6\n2 4\n7 10\n2 9\n8 10\n7 2\n3 1\n4 5\n3 6\n7 4\n1 2\n1 4\n5 1\n1 3\n2 3\n4 3\n5 3\n",
"4\n8 3\n1 2\n1 5\n7 6\n6 8\n3 1\n6 4\n6 1\n10 5\n1 4\n1 10\n2 3\n1 5\n2 6\n2 4\n7 10\n10 9\n8 10\n7 2\n3 1\n4 5\n3 6\n7 4\n1 2\n1 7\n5 1\n1 2\n2 3\n4 3\n5 3\n",
"4\n8 6\n1 2\n1 5\n7 6\n6 8\n3 1\n6 4\n4 1\n10 3\n2 2\n1 10\n2 3\n1 5\n1 6\n2 4\n7 10\n10 9\n8 7\n7 2\n3 1\n4 5\n3 6\n7 4\n1 2\n1 4\n5 1\n1 4\n2 3\n4 3\n5 3\n",
"4\n8 6\n1 2\n1 5\n7 6\n6 8\n3 1\n8 4\n4 1\n10 3\n1 2\n1 10\n2 3\n1 5\n1 6\n2 4\n7 10\n10 9\n8 10\n7 2\n3 1\n4 5\n4 6\n7 4\n1 2\n1 4\n5 1\n2 4\n2 1\n2 3\n5 3\n",
"4\n8 10\n1 2\n1 5\n7 6\n6 8\n3 1\n5 4\n7 1\n10 3\n1 2\n2 10\n2 3\n1 5\n1 6\n2 4\n7 10\n10 9\n8 10\n7 2\n3 1\n1 5\n4 6\n7 4\n1 2\n1 4\n5 1\n1 4\n2 1\n4 3\n5 3\n",
"4\n8 3\n1 2\n1 5\n7 6\n6 8\n3 1\n6 4\n6 1\n10 3\n1 2\n1 10\n2 3\n1 5\n1 6\n2 4\n7 10\n10 9\n8 5\n7 2\n3 1\n4 5\n3 6\n7 6\n1 2\n1 4\n5 1\n1 3\n2 3\n4 3\n5 3\n",
"4\n8 6\n1 2\n1 5\n7 6\n6 8\n3 1\n6 4\n4 1\n10 3\n1 2\n1 10\n2 3\n1 5\n1 6\n2 4\n7 10\n10 9\n8 10\n7 3\n3 1\n4 5\n3 6\n7 4\n1 2\n1 4\n5 1\n1 4\n2 1\n2 3\n5 3\n",
"4\n8 3\n1 2\n1 5\n7 6\n6 8\n3 2\n7 4\n6 1\n10 3\n1 2\n1 10\n2 3\n1 5\n1 6\n2 4\n7 10\n6 9\n8 10\n7 2\n3 1\n2 5\n3 6\n7 3\n1 2\n1 4\n5 1\n1 2\n2 3\n4 3\n5 3\n",
"4\n8 6\n1 2\n1 5\n7 6\n6 8\n3 1\n6 4\n4 1\n10 3\n1 2\n1 10\n2 3\n1 5\n1 6\n2 4\n7 10\n10 9\n8 10\n7 3\n3 2\n4 5\n3 6\n7 4\n1 2\n1 4\n5 1\n1 4\n2 1\n2 3\n5 3\n",
"4\n8 4\n1 2\n1 5\n7 6\n6 8\n3 2\n7 4\n6 1\n10 3\n1 2\n1 10\n2 3\n1 5\n1 6\n2 4\n7 10\n6 9\n8 10\n7 2\n3 1\n2 5\n3 6\n7 3\n1 2\n1 4\n5 1\n1 2\n2 3\n4 3\n5 3\n",
"4\n8 6\n1 2\n2 5\n7 6\n6 8\n3 1\n6 4\n4 1\n10 3\n1 2\n1 10\n2 3\n1 5\n1 6\n2 4\n7 10\n10 9\n8 10\n7 3\n3 2\n4 5\n3 6\n7 4\n1 2\n1 4\n5 1\n1 4\n2 1\n2 3\n5 3\n",
"4\n8 3\n1 2\n1 5\n7 6\n6 8\n3 1\n6 4\n6 1\n10 3\n1 4\n1 10\n4 3\n1 5\n2 6\n2 4\n7 10\n10 9\n8 10\n7 2\n3 1\n4 5\n2 6\n7 4\n1 2\n1 4\n5 1\n1 2\n2 3\n4 3\n5 3\n"
],
"output": [
"2\n3\n3\n4\n",
"2\n3\n0\n4\n",
"2\n3\n3\n4\n",
"2\n2\n3\n4\n",
"1\n3\n0\n4\n",
"1\n3\n3\n4\n",
"2\n1\n3\n4\n",
"0\n3\n3\n4\n",
"1\n0\n0\n4\n",
"0\n3\n0\n4\n",
"1\n0\n3\n4\n",
"0\n1\n3\n4\n",
"2\n1\n0\n4\n",
"0\n0\n3\n4\n",
"0\n9\n0\n4\n",
"2\n0\n3\n4\n",
"2\n0\n0\n4\n",
"2\n2\n3\n2\n",
"1\n2\n0\n4\n",
"0\n9\n3\n4\n",
"7\n2\n3\n4\n",
"1\n1\n3\n4\n",
"2\n1\n3\n4\n",
"2\n1\n3\n4\n",
"0\n3\n3\n4\n",
"2\n1\n3\n4\n",
"2\n3\n0\n4\n",
"0\n3\n3\n4\n",
"0\n3\n3\n4\n",
"0\n3\n3\n4\n",
"0\n3\n3\n4\n",
"2\n3\n3\n4\n",
"0\n3\n3\n4\n",
"2\n1\n0\n4\n",
"0\n9\n0\n4\n",
"0\n3\n3\n4\n",
"2\n2\n3\n4\n",
"1\n3\n0\n4\n",
"0\n3\n3\n4\n",
"1\n0\n3\n4\n",
"0\n1\n3\n4\n",
"0\n3\n3\n4\n",
"2\n1\n0\n4\n",
"2\n1\n0\n4\n",
"0\n3\n0\n4\n",
"2\n0\n0\n4\n",
"1\n0\n3\n4\n",
"0\n3\n3\n4\n",
"2\n3\n3\n4\n",
"2\n0\n0\n4\n",
"0\n0\n3\n4\n",
"0\n3\n3\n4\n",
"0\n3\n3\n4\n",
"2\n0\n0\n4\n",
"0\n3\n0\n4\n",
"0\n0\n3\n4\n",
"0\n3\n0\n4\n",
"0\n0\n3\n4\n",
"0\n3\n0\n4\n",
"2\n1\n3\n4\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You are given a tree (connected graph without cycles) consisting of n vertices. The tree is unrooted — it is just a connected undirected graph without cycles.
In one move, you can choose exactly k leaves (leaf is such a vertex that is connected to only one another vertex) connected to the same vertex and remove them with edges incident to them. I.e. you choose such leaves u_1, u_2, ..., u_k that there are edges (u_1, v), (u_2, v), ..., (u_k, v) and remove these leaves and these edges.
Your task is to find the maximum number of moves you can perform if you remove leaves optimally.
You have to answer t independent test cases.
Input
The first line of the input contains one integer t (1 ≤ t ≤ 2 ⋅ 10^4) — the number of test cases. Then t test cases follow.
The first line of the test case contains two integers n and k (2 ≤ n ≤ 2 ⋅ 10^5; 1 ≤ k < n) — the number of vertices in the tree and the number of leaves you remove in one move, respectively. The next n-1 lines describe edges. The i-th edge is represented as two integers x_i and y_i (1 ≤ x_i, y_i ≤ n), where x_i and y_i are vertices the i-th edge connects. It is guaranteed that the given set of edges forms a tree.
It is guaranteed that the sum of n does not exceed 2 ⋅ 10^5 (∑ n ≤ 2 ⋅ 10^5).
Output
For each test case, print the answer — the maximum number of moves you can perform if you remove leaves optimally.
Example
Input
4
8 3
1 2
1 5
7 6
6 8
3 1
6 4
6 1
10 3
1 2
1 10
2 3
1 5
1 6
2 4
7 10
10 9
8 10
7 2
3 1
4 5
3 6
7 4
1 2
1 4
5 1
1 2
2 3
4 3
5 3
Output
2
3
3
4
Note
The picture corresponding to the first test case of the example:
<image>
There you can remove vertices 2, 5 and 3 during the first move and vertices 1, 7 and 4 during the second move.
The picture corresponding to the second test case of the example:
<image>
There you can remove vertices 7, 8 and 9 during the first move, then vertices 5, 6 and 10 during the second move and vertices 1, 3 and 4 during the third move.
The picture corresponding to the third test case of the example:
<image>
There you can remove vertices 5 and 7 during the first move, then vertices 2 and 4 during the second move and vertices 1 and 6 during the third move.
### Input:
4
8 3
1 2
1 5
7 6
6 8
3 1
6 4
6 1
10 3
1 2
1 10
2 3
1 5
1 6
2 4
7 10
10 9
8 10
7 2
3 1
4 5
3 6
7 4
1 2
1 4
5 1
1 2
2 3
4 3
5 3
### Output:
2
3
3
4
### Input:
4
8 3
1 2
1 5
7 6
6 8
3 1
6 4
6 1
10 3
1 2
1 10
2 3
1 5
1 6
2 4
7 10
10 9
8 10
7 2
3 1
2 5
3 6
7 4
1 2
1 4
5 1
1 2
2 3
4 3
5 3
### Output:
2
3
0
4
### Code:
import os
import sys
from io import BytesIO, IOBase
# region fastio
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
# ------------------------------
def RL(): return map(int, sys.stdin.readline().rstrip().split())
def RLL(): return list(map(int, sys.stdin.readline().rstrip().split()))
def N(): return int(input())
def comb(n, m): return factorial(n) / (factorial(m) * factorial(n - m)) if n >= m else 0
def perm(n, m): return factorial(n) // (factorial(n - m)) if n >= m else 0
def mdis(x1, y1, x2, y2): return abs(x1 - x2) + abs(y1 - y2)
mod = 998244353
INF = float('inf')
from math import factorial
from collections import Counter, defaultdict, deque
from heapq import heapify, heappop, heappush
# ------------------------------
# f = open('../input.txt')
# sys.stdin = f
def main():
for _ in range(N()):
n, k = RL()
gp = [[] for _ in range(n+1)]
ind = [0]*(n+1)
for _ in range(n-1):
a, b = RL()
gp[a].append(b)
gp[b].append(a)
ind[a]+=1
ind[b]+=1
if k==1:
print(n-1)
continue
q = []
vis = [0]*(n+1)
for i in range(1, n+1):
if ind[i]==1:
q.append(i)
vis[i] = 1
num = [0]*(n+1)
res = 0
while q:
nd = q.pop()
ind[nd]-=1
for nex in gp[nd]:
if vis[nex]==1: continue
ind[nex]-=1
num[nex]+=1
if num[nex]%k==0:
res+=1
if ind[nex]==1:
q.append(nex)
vis[nex] = 1
print(res)
if __name__ == "__main__":
main()
|
1407_D. Discrete Centrifugal Jumps_10523
|
There are n beautiful skyscrapers in New York, the height of the i-th one is h_i. Today some villains have set on fire first n - 1 of them, and now the only safety building is n-th skyscraper.
Let's call a jump from i-th skyscraper to j-th (i < j) discrete, if all skyscrapers between are strictly lower or higher than both of them. Formally, jump is discrete, if i < j and one of the following conditions satisfied:
* i + 1 = j
* max(h_{i + 1}, …, h_{j - 1}) < min(h_i, h_j)
* max(h_i, h_j) < min(h_{i + 1}, …, h_{j - 1}).
At the moment, Vasya is staying on the first skyscraper and wants to live a little longer, so his goal is to reach n-th skyscraper with minimal count of discrete jumps. Help him with calcualting this number.
Input
The first line contains a single integer n (2 ≤ n ≤ 3 ⋅ 10^5) — total amount of skyscrapers.
The second line contains n integers h_1, h_2, …, h_n (1 ≤ h_i ≤ 10^9) — heights of skyscrapers.
Output
Print single number k — minimal amount of discrete jumps. We can show that an answer always exists.
Examples
Input
5
1 3 1 4 5
Output
3
Input
4
4 2 2 4
Output
1
Input
2
1 1
Output
1
Input
5
100 1 100 1 100
Output
2
Note
In the first testcase, Vasya can jump in the following way: 1 → 2 → 4 → 5.
In the second and third testcases, we can reach last skyscraper in one jump.
Sequence of jumps in the fourth testcase: 1 → 3 → 5.
|
n = int(input())
a = list(map(int, input().split()))
dp = [10**9]*n
dp[0] = 0
s1 = [0]
s2 = [0]
for i in range(1, n):
dp[i] = dp[i-1] + 1
f1, f2 = True, True
while s1 and a[i] >= a[s1[-1]]:
if a[i] == a[s1[-1]]:
f1 = False
dp[i] = min(dp[i], dp[s1[-1]] + 1)
s1.pop()
while s2 and a[i] <= a[s2[-1]]:
if a[i] == a[s2[-1]]:
f2 = False
dp[i] = min(dp[i], dp[s2[-1]] + 1)
s2.pop()
if s1 and f1:
dp[i] = min(dp[i], dp[s1[-1]] + 1)
if s2 and f2:
dp[i] = min(dp[i], dp[s2[-1]] + 1)
s1.append(i)
s2.append(i)
print(dp[n-1])
|
{
"input": [
"5\n1 3 1 4 5\n",
"5\n100 1 100 1 100\n",
"4\n4 2 2 4\n",
"2\n1 1\n",
"4\n2 3 4 2\n",
"4\n2 1 3 3\n",
"8\n4 2 5 5 1 2 5 2\n",
"5\n1 5 5 1 4\n",
"4\n1 3 4 2\n",
"4\n2 1 5 3\n",
"8\n7 2 5 5 1 2 5 2\n",
"5\n1 3 1 4 7\n",
"8\n7 2 5 5 1 2 2 2\n",
"5\n0 5 5 1 4\n",
"4\n4 2 2 7\n",
"2\n1 2\n",
"4\n1 3 8 2\n",
"4\n2 2 5 3\n",
"8\n7 2 5 5 2 2 5 2\n",
"5\n0 5 6 1 4\n",
"5\n2 3 1 4 7\n",
"4\n4 2 0 7\n",
"2\n1 4\n",
"4\n1 4 8 2\n",
"4\n3 2 5 3\n",
"5\n0 10 6 1 4\n",
"5\n2 3 0 4 7\n",
"4\n4 2 0 3\n",
"2\n1 0\n",
"4\n0 4 8 2\n",
"4\n3 1 5 3\n",
"5\n0 10 6 1 8\n",
"4\n2 2 0 3\n",
"4\n-1 4 8 2\n",
"4\n3 0 5 3\n",
"5\n0 10 6 1 3\n",
"4\n2 4 0 3\n",
"4\n-1 4 8 3\n",
"4\n3 1 5 1\n",
"5\n1 10 6 1 3\n",
"4\n1 4 0 3\n",
"4\n-1 4 8 5\n",
"4\n3 0 5 1\n",
"5\n1 19 6 1 3\n",
"4\n1 7 0 3\n",
"4\n-1 5 8 5\n",
"5\n1 19 10 1 3\n",
"4\n1 7 0 0\n",
"4\n-1 3 8 5\n",
"5\n1 16 10 1 3\n",
"5\n1 16 10 0 3\n",
"5\n1 30 10 0 3\n",
"5\n1 30 10 0 0\n",
"5\n1 2 10 0 0\n",
"5\n0 2 10 0 0\n",
"5\n0 2 6 0 0\n",
"5\n0 2 6 0 1\n",
"5\n0 2 5 0 1\n",
"5\n0 2 8 0 1\n",
"5\n-1 2 8 0 1\n",
"5\n-1 4 8 0 1\n",
"4\n2 3 4 4\n",
"4\n2 2 3 3\n",
"8\n4 3 5 5 1 2 5 2\n",
"5\n1 5 5 1 1\n",
"5\n1 1 1 4 5\n",
"5\n110 1 100 1 100\n",
"4\n3 2 2 4\n",
"2\n0 0\n",
"4\n1 3 4 0\n",
"4\n2 1 5 6\n",
"5\n0 5 2 1 4\n",
"5\n2 3 1 7 7\n",
"4\n1 2 2 7\n",
"2\n2 2\n",
"4\n1 4 0 2\n",
"4\n2 0 5 3\n",
"8\n7 2 5 5 3 2 5 2\n",
"5\n0 5 6 1 1\n",
"5\n2 3 1 4 3\n",
"4\n4 2 0 5\n",
"4\n1 4 8 3\n",
"4\n3 3 5 3\n",
"5\n-1 10 6 1 4\n",
"5\n2 6 0 4 7\n",
"4\n4 2 1 3\n",
"4\n-1 8 8 3\n"
],
"output": [
"3",
"2",
"1",
"1",
"1",
"2",
"4",
"2",
"1\n",
"2\n",
"4\n",
"3\n",
"5\n",
"2\n",
"1\n",
"1\n",
"1\n",
"2\n",
"4\n",
"2\n",
"3\n",
"1\n",
"1\n",
"1\n",
"2\n",
"2\n",
"3\n",
"1\n",
"1\n",
"1\n",
"2\n",
"2\n",
"2\n",
"1\n",
"2\n",
"2\n",
"2\n",
"1\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"3\n",
"3\n",
"4\n",
"2\n",
"4\n",
"2\n",
"1\n",
"1\n",
"1\n",
"2\n",
"2\n",
"3\n",
"3\n",
"1\n",
"2\n",
"2\n",
"3\n",
"2\n",
"2\n",
"1\n",
"1\n",
"2\n",
"2\n",
"2\n",
"1\n",
"1\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
There are n beautiful skyscrapers in New York, the height of the i-th one is h_i. Today some villains have set on fire first n - 1 of them, and now the only safety building is n-th skyscraper.
Let's call a jump from i-th skyscraper to j-th (i < j) discrete, if all skyscrapers between are strictly lower or higher than both of them. Formally, jump is discrete, if i < j and one of the following conditions satisfied:
* i + 1 = j
* max(h_{i + 1}, …, h_{j - 1}) < min(h_i, h_j)
* max(h_i, h_j) < min(h_{i + 1}, …, h_{j - 1}).
At the moment, Vasya is staying on the first skyscraper and wants to live a little longer, so his goal is to reach n-th skyscraper with minimal count of discrete jumps. Help him with calcualting this number.
Input
The first line contains a single integer n (2 ≤ n ≤ 3 ⋅ 10^5) — total amount of skyscrapers.
The second line contains n integers h_1, h_2, …, h_n (1 ≤ h_i ≤ 10^9) — heights of skyscrapers.
Output
Print single number k — minimal amount of discrete jumps. We can show that an answer always exists.
Examples
Input
5
1 3 1 4 5
Output
3
Input
4
4 2 2 4
Output
1
Input
2
1 1
Output
1
Input
5
100 1 100 1 100
Output
2
Note
In the first testcase, Vasya can jump in the following way: 1 → 2 → 4 → 5.
In the second and third testcases, we can reach last skyscraper in one jump.
Sequence of jumps in the fourth testcase: 1 → 3 → 5.
### Input:
5
1 3 1 4 5
### Output:
3
### Input:
5
100 1 100 1 100
### Output:
2
### Code:
n = int(input())
a = list(map(int, input().split()))
dp = [10**9]*n
dp[0] = 0
s1 = [0]
s2 = [0]
for i in range(1, n):
dp[i] = dp[i-1] + 1
f1, f2 = True, True
while s1 and a[i] >= a[s1[-1]]:
if a[i] == a[s1[-1]]:
f1 = False
dp[i] = min(dp[i], dp[s1[-1]] + 1)
s1.pop()
while s2 and a[i] <= a[s2[-1]]:
if a[i] == a[s2[-1]]:
f2 = False
dp[i] = min(dp[i], dp[s2[-1]] + 1)
s2.pop()
if s1 and f1:
dp[i] = min(dp[i], dp[s1[-1]] + 1)
if s2 and f2:
dp[i] = min(dp[i], dp[s2[-1]] + 1)
s1.append(i)
s2.append(i)
print(dp[n-1])
|
1428_B. Belted Rooms_10527
|
In the snake exhibition, there are n rooms (numbered 0 to n - 1) arranged in a circle, with a snake in each room. The rooms are connected by n conveyor belts, and the i-th conveyor belt connects the rooms i and (i+1) mod n. In the other words, rooms 0 and 1, 1 and 2, …, n-2 and n-1, n-1 and 0 are connected with conveyor belts.
The i-th conveyor belt is in one of three states:
* If it is clockwise, snakes can only go from room i to (i+1) mod n.
* If it is anticlockwise, snakes can only go from room (i+1) mod n to i.
* If it is off, snakes can travel in either direction.
<image>
Above is an example with 4 rooms, where belts 0 and 3 are off, 1 is clockwise, and 2 is anticlockwise.
Each snake wants to leave its room and come back to it later. A room is returnable if the snake there can leave the room, and later come back to it using the conveyor belts. How many such returnable rooms are there?
Input
Each test contains multiple test cases. The first line contains a single integer t (1 ≤ t ≤ 1000): the number of test cases. The description of the test cases follows.
The first line of each test case description contains a single integer n (2 ≤ n ≤ 300 000): the number of rooms.
The next line of each test case description contains a string s of length n, consisting of only '<', '>' and '-'.
* If s_{i} = '>', the i-th conveyor belt goes clockwise.
* If s_{i} = '<', the i-th conveyor belt goes anticlockwise.
* If s_{i} = '-', the i-th conveyor belt is off.
It is guaranteed that the sum of n among all test cases does not exceed 300 000.
Output
For each test case, output the number of returnable rooms.
Example
Input
4
4
-><-
5
>>>>>
3
<--
2
<>
Output
3
5
3
0
Note
In the first test case, all rooms are returnable except room 2. The snake in the room 2 is trapped and cannot exit. This test case corresponds to the picture from the problem statement.
In the second test case, all rooms are returnable by traveling on the series of clockwise belts.
|
from sys import stdin
import sys
tt = int(stdin.readline())
for loop in range(tt):
n = int(stdin.readline())
s = stdin.readline()[:-1]
if ("<" not in s) or (">" not in s):
print (n)
continue
ans = 0
for i in range(n):
if s[(i-1)%n] == "-" or s[i] == "-":
ans += 1
print (ans)
|
{
"input": [
"4\n4\n-><-\n5\n>>>>>\n3\n<--\n2\n<>\n",
"1\n6\n->>-<-\n",
"1\n7\n->>-<<-\n",
"1\n15\n--->>>---<<<---\n",
"1\n5\n>-<<-\n",
"1\n4\n--<>\n",
"1\n6\n-<<<->\n",
"1\n12\n--->>>---<<<\n",
"1\n5\n<<->-\n",
"1\n7\n-->>-<-\n",
"1\n5\n<<->>\n",
"1\n8\n>>>-<---\n",
"1\n6\n<<->>-\n",
"4\n5\n->>-<\n4\n-><-\n5\n>>>>>\n3\n<--\n",
"3\n3\n->>\n11\n><<>---><>-\n7\n-<<<<-<\n",
"4\n4\n-><-\n5\n>>>>>\n3\n<--\n2\n<>\n",
"1\n5\n-<<->\n",
"1\n7\n-->>--<\n",
"1\n10\n->>>>-<<--\n",
"1\n6\n->-<<<\n",
"1\n6\n->-<<-\n",
"1\n7\n>--<<--\n",
"1\n15\n-->>>>---<<<---\n",
"1\n8\n>>--<<--\n",
"1\n8\n<<-->>--\n",
"1\n6\n>>>-<-\n",
"1\n7\n-<<->>-\n",
"1\n5\n->>-<\n",
"1\n5\n->-<<\n",
"1\n24\n>>>----->>>>----<<<<----\n",
"1\n8\n--<<-->>\n",
"1\n6\n-<->>-\n",
"1\n5\n<->>-\n",
"6\n5\n>-<<-\n5\n<->-<\n6\n>>-<<-\n6\n>-<<->\n7\n>>-<-<-\n7\n>>-<->-\n",
"1\n11\n-->--<<<<--\n",
"1\n9\n->>>-<<<-\n",
"1\n6\n>-<->>\n",
"36\n2\n--\n2\n>-\n2\n<-\n2\n->\n2\n>>\n2\n<>\n2\n-<\n2\n><\n2\n<<\n3\n---\n3\n>--\n3\n<--\n3\n->-\n3\n>>-\n3\n<>-\n3\n-<-\n3\n><-\n3\n<<-\n3\n-->\n3\n>->\n3\n<->\n3\n->>\n3\n>>>\n3\n<>>\n3\n-<>\n3\n><>\n3\n<<>\n3\n--<\n3\n>-<\n3\n<-<\n3\n-><\n3\n>><\n3\n<><\n3\n-<<\n3\n><<\n3\n<<<\n",
"1\n5\n>>-<-\n",
"1\n12\n->>>>--<<<<-\n",
"1\n8\n>>>-<<<-\n",
"1\n6\n>>-<<-\n",
"1\n12\n<<->>-<<->>-\n",
"1\n5\n-<<>-\n",
"1\n8\n---<->>>\n",
"3\n3\n->>\n11\n><<>---><>-\n5\n-<<<<-<\n",
"1\n6\n->--<<\n",
"1\n11\n--<<<<-->--\n",
"4\n7\n-><-\n5\n>>>>>\n3\n<--\n2\n<>\n",
"3\n3\n->>\n11\n><<>->-><--\n5\n-<<<<-<\n",
"1\n12\n->><<<->>--<\n",
"4\n7\n-><-\n5\n>>>>>\n3\n<,-\n4\nft;&;tl&\n",
"4\n7\n-><-\n3\n>>>>>\n3\n-,;tl&\n4\nft;&;tl&\n",
"4\n9\n-><-\n3\n>>>>>\n3\n-,;tl&\n4\nft;&;tl&\n",
"4\n3\n-><-\n3\n>>>>>\n3\n-,;tl&\n4\nft;&;ul&\n",
"1\n6\n<>-><-\n",
"4\n4\n-><-\n5\n>>>>>\n3\n<--\n0\n<>\n",
"4\n7\n-><-\n0\n>>>>>\n3\n<,-\n2\n<&ft;\n",
"4\n7\n-><-\n5\n>>>>>\n3\n<,-\n0\n;tf&;tl&\n",
"4\n7\n-><-\n7\n>>>>>\n3\n<,-\n2\nft;&;tl&\n",
"4\n7\n-><-\n8\n>>>>>\n3\n<,-\n4\nft;&;tl&\n",
"4\n10\n-><-\n5\n>>>>>\n3\n-,;tl&\n4\nft;&;tl&\n",
"4\n9\n-><-\n5\n>>>>>\n3\n-,;tl&\n4\nft;&;ul&\n",
"4\n6\n-'gt;<-\n3\n>>>>>\n3\n-,;tl&\n4\nft;&;ul&\n",
"4\n3\n-;tl&;tg'-\n3\n;tg&;tg&;tg&;tg&;tg&\n3\n-,;ul&\n0\nft;u;&m&\n",
"4\n3\n-;tl&;tg'-\n3\n>>>>>\n2\n-,:ul&\n4\nft;u;&m&\n",
"4\n4\n-><-\n9\n>>>>>\n3\n<--\n0\n<>\n",
"4\n7\n-≷&tt;-\n5\n>>>>>\n6\n<--\n2\n<&ft;\n",
"4\n9\n-><-\n8\n>>>>>\n3\n<,-\n4\nft;&;tl&\n",
"4\n9\n-><-\n3\n>>>>>\n3\n<,-\n3\nft;&;tl&\n",
"4\n6\n-'gt;<-\n6\n>>>>>\n3\n-,;tl&\n4\nft;&;ul&\n",
"4\n7\n-><-\n7\n>>>>>\n2\n-,;tl&\n2\nft;&;tl&\n",
"4\n3\n-><-\n3\n>>>>>\n3\n<,-\n3\nft;&;tl&\n",
"4\n6\n-'gt;<-\n10\n>>>>>\n3\n-,;tl&\n4\nft;&;ul&\n",
"4\n6\n-'gt;<-\n3\n>>%gt;>>\n3\n-,;ul&\n0\nft;&;um&\n",
"1\n12\n->>-<<->>-<<\n",
"4\n7\n-><-\n5\n>>>>>\n3\n<--\n2\n<&ft;\n",
"4\n7\n-><-\n5\n>>>>>\n3\n<,-\n2\n<&ft;\n",
"4\n7\n-><-\n5\n>>>>>\n3\n<,-\n2\n;tf&;tl&\n",
"4\n7\n-><-\n5\n>>>>>\n3\n<,-\n2\nft;&;tl&\n",
"4\n7\n-><-\n5\n>>>>>\n3\n-,;tl&\n4\nft;&;tl&\n",
"4\n9\n-><-\n3\n>>>>>\n3\n-,;tl&\n4\nft;&;ul&\n",
"4\n3\n-'gt;<-\n3\n>>>>>\n3\n-,;tl&\n4\nft;&;ul&\n",
"4\n3\n-'gt;<-\n3\n>>>>>\n3\n-,;tl&\n4\nft;&;um&\n",
"4\n3\n-'gt;<-\n3\n>>>>>\n3\n-,;ul&\n4\nft;&;um&\n",
"4\n3\n-'gt;<-\n3\n;tg&;tg&;tg&;tg&;tg&\n3\n-,;ul&\n4\nft;&;um&\n",
"4\n3\n-;tl&;tg'-\n3\n;tg&;tg&;tg&;tg&;tg&\n3\n-,;ul&\n4\nft;&;um&\n",
"4\n3\n-;tl&;tg'-\n3\n;tg&;tg&;tg&;tg&;tg&\n3\n-,;ul&\n4\nft;u;&m&\n",
"4\n3\n-;tl&;tg'-\n3\n;tg&;tg&;tg&;tg&;tg&\n3\n-,:ul&\n4\nft;u;&m&\n",
"4\n3\n-;tl&;tg'-\n3\n>>>>>\n3\n-,:ul&\n4\nft;u;&m&\n",
"1\n12\n--<>>>---<<-\n",
"1\n8\n><>->---\n",
"1\n6\n-><<<-\n",
"1\n7\n--<<-->\n",
"1\n8\n-->>--<<\n",
"1\n7\n-><-<>-\n",
"1\n9\n-<<<->>>-\n",
"1\n5\n-><<-\n",
"4\n7\n-><-\n5\n>>>>>\n3\n<.-\n2\n<>\n",
"3\n3\n->>\n11\n>-<>-><><--\n5\n-<<<<-<\n",
"4\n7\n-≷&tt;-\n5\n>>>>>\n3\n<--\n2\n<&ft;\n",
"4\n9\n-><-\n3\n>>>>>\n3\n<,-\n4\nft;&;tl&\n",
"4\n3\n-'gt;<-\n3\n>>>>>\n3\n-,:tl&\n4\nft;&;um&\n",
"4\n3\n-'gt;<-\n3\n>>%gt;>>\n3\n-,;ul&\n4\nft;&;um&\n",
"4\n3\n-'gt;<-\n3\n;tg&&tg&;tg&;tg&;tg;\n3\n-,;ul&\n4\nft;&;um&\n",
"4\n3\n-;tl&;tg'-\n3\n>>>>>\n3\n-,;ul&\n4\nft;&;um&\n",
"4\n3\n-;tl&;tg'-\n3\n;tg&;tg&;tg&;tg&;tg&\n3\n-,:ul'\n4\nft;u;&m&\n",
"1\n8\n--->-><>\n",
"4\n7\n-><-\n0\n>>>>>\n3\n&ls;,-\n2\n<&ft;\n",
"4\n7\n-><-\n7\n>>>>>\n3\n-,;tl&\n2\nft;&;tl&\n",
"4\n9\n-><-\n5\n>>>>>\n3\n-,;tl&\n4\nft;&;ul%\n",
"4\n3\n-'gt;<-\n3\n>>>>>\n2\n-,:tl&\n4\nft;&;um&\n",
"4\n3\n-'gt;<-\n3\n>>%gt;>>\n3\n-,;ul&\n0\nft;&;um&\n",
"4\n3\n.'gt;<-\n3\n;tg&&tg&;tg&;tg&;tg;\n3\n-,;ul&\n4\nft;&;um&\n",
"4\n3\n-'gt;<-\n3\n>>>>>\n3\n&lu;,-\n4\nft;&;um&\n",
"4\n3\n-;tl&;tg'-\n3\n:tg&;tg&;tg&;tg&;tg&\n3\n-,;ul&\n0\nft;u;&m&\n",
"4\n3\n-;tl&;tg'-\n3\n;tg&;tg&;tg&;tg&;tg%\n3\n-,:ul'\n4\nft;u;&m&\n",
"4\n3\n-;tl&;tg'-\n3\n>>>>>\n2\n&lu:,-\n4\nft;u;&m&\n",
"4\n7\n-><-\n0\n>>&ht;>>\n3\n&ls;,-\n2\n<&ft;\n",
"4\n9\n.><-\n5\n>>>>>\n3\n-,;tl&\n4\nft;&;ul%\n",
"4\n3\n-'gt;&mt;-\n3\n>>>>>\n2\n-,:tl&\n4\nft;&;um&\n",
"4\n3\n.'gt;<-\n3\n;tg&&tg&;tg&;tg&;tg;\n3\n-,;ul&\n4\nft;&<um&\n",
"4\n3\n-;tl&;tg'-\n3\n:tg&;tg&;tg&;tg&;tg&\n3\n&lu;,-\n0\nft;u;&m&\n",
"4\n3\n-;tl&;tg'-\n3\n;tg&;tg&;tf&;tg&;tg%\n3\n-,:ul'\n4\nft;u;&m&\n"
],
"output": [
"4\n5\n3\n2\n",
"5\n",
"5\n",
"11\n",
"4\n",
"3\n",
"4\n",
"8\n",
"4\n",
"6\n",
"2\n",
"6\n",
"4\n",
"4\n3\n5\n3\n",
"3\n6\n7\n",
"3\n5\n3\n0\n",
"4\n",
"6\n",
"6\n",
"4\n",
"5\n",
"6\n",
"10\n",
"6\n",
"6\n",
"4\n",
"5\n",
"4\n",
"4\n",
"16\n",
"6\n",
"5\n",
"4\n",
"4\n4\n4\n4\n6\n6\n",
"8\n",
"5\n",
"4\n",
"2\n2\n2\n2\n2\n0\n2\n0\n2\n3\n3\n3\n3\n3\n2\n3\n2\n3\n3\n3\n2\n3\n3\n0\n2\n0\n0\n3\n2\n3\n2\n0\n0\n3\n0\n3\n",
"4\n",
"6\n",
"4\n",
"4\n",
"8\n",
"3\n",
"6\n",
"3\n6\n5\n",
"5\n",
"8\n",
"7\n5\n3\n2\n",
"3\n7\n5\n",
"7\n",
"7\n5\n3\n4\n",
"7\n3\n3\n4\n",
"9\n3\n3\n4\n",
"3\n3\n3\n4\n",
"4\n",
"4\n5\n3\n0\n",
"7\n0\n3\n2\n",
"7\n5\n3\n0\n",
"7\n7\n3\n2\n",
"7\n8\n3\n4\n",
"10\n5\n3\n4\n",
"9\n5\n3\n4\n",
"6\n3\n3\n4\n",
"3\n3\n3\n0\n",
"3\n3\n2\n4\n",
"4\n9\n3\n0\n",
"7\n5\n6\n2\n",
"9\n8\n3\n4\n",
"9\n3\n3\n3\n",
"6\n6\n3\n4\n",
"7\n7\n2\n2\n",
"3\n3\n3\n3\n",
"6\n10\n3\n4\n",
"6\n3\n3\n0\n",
"8\n",
"7\n5\n3\n2\n",
"7\n5\n3\n2\n",
"7\n5\n3\n2\n",
"7\n5\n3\n2\n",
"7\n5\n3\n4\n",
"9\n3\n3\n4\n",
"3\n3\n3\n4\n",
"3\n3\n3\n4\n",
"3\n3\n3\n4\n",
"3\n3\n3\n4\n",
"3\n3\n3\n4\n",
"3\n3\n3\n4\n",
"3\n3\n3\n4\n",
"3\n3\n3\n4\n",
"8\n",
"6\n",
"3\n",
"6\n",
"6\n",
"5\n",
"5\n",
"3\n",
"7\n5\n3\n2\n",
"3\n7\n5\n",
"7\n5\n3\n2\n",
"9\n3\n3\n4\n",
"3\n3\n3\n4\n",
"3\n3\n3\n4\n",
"3\n3\n3\n4\n",
"3\n3\n3\n4\n",
"3\n3\n3\n4\n",
"6\n",
"7\n0\n3\n2\n",
"7\n7\n3\n2\n",
"9\n5\n3\n4\n",
"3\n3\n2\n4\n",
"3\n3\n3\n0\n",
"3\n3\n3\n4\n",
"3\n3\n3\n4\n",
"3\n3\n3\n0\n",
"3\n3\n3\n4\n",
"3\n3\n2\n4\n",
"7\n0\n3\n2\n",
"9\n5\n3\n4\n",
"3\n3\n2\n4\n",
"3\n3\n3\n4\n",
"3\n3\n3\n0\n",
"3\n3\n3\n4\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
In the snake exhibition, there are n rooms (numbered 0 to n - 1) arranged in a circle, with a snake in each room. The rooms are connected by n conveyor belts, and the i-th conveyor belt connects the rooms i and (i+1) mod n. In the other words, rooms 0 and 1, 1 and 2, …, n-2 and n-1, n-1 and 0 are connected with conveyor belts.
The i-th conveyor belt is in one of three states:
* If it is clockwise, snakes can only go from room i to (i+1) mod n.
* If it is anticlockwise, snakes can only go from room (i+1) mod n to i.
* If it is off, snakes can travel in either direction.
<image>
Above is an example with 4 rooms, where belts 0 and 3 are off, 1 is clockwise, and 2 is anticlockwise.
Each snake wants to leave its room and come back to it later. A room is returnable if the snake there can leave the room, and later come back to it using the conveyor belts. How many such returnable rooms are there?
Input
Each test contains multiple test cases. The first line contains a single integer t (1 ≤ t ≤ 1000): the number of test cases. The description of the test cases follows.
The first line of each test case description contains a single integer n (2 ≤ n ≤ 300 000): the number of rooms.
The next line of each test case description contains a string s of length n, consisting of only '<', '>' and '-'.
* If s_{i} = '>', the i-th conveyor belt goes clockwise.
* If s_{i} = '<', the i-th conveyor belt goes anticlockwise.
* If s_{i} = '-', the i-th conveyor belt is off.
It is guaranteed that the sum of n among all test cases does not exceed 300 000.
Output
For each test case, output the number of returnable rooms.
Example
Input
4
4
-><-
5
>>>>>
3
<--
2
<>
Output
3
5
3
0
Note
In the first test case, all rooms are returnable except room 2. The snake in the room 2 is trapped and cannot exit. This test case corresponds to the picture from the problem statement.
In the second test case, all rooms are returnable by traveling on the series of clockwise belts.
### Input:
4
4
-><-
5
>>>>>
3
<--
2
<>
### Output:
4
5
3
2
### Input:
1
6
->>-<-
### Output:
5
### Code:
from sys import stdin
import sys
tt = int(stdin.readline())
for loop in range(tt):
n = int(stdin.readline())
s = stdin.readline()[:-1]
if ("<" not in s) or (">" not in s):
print (n)
continue
ans = 0
for i in range(n):
if s[(i-1)%n] == "-" or s[i] == "-":
ans += 1
print (ans)
|
1451_B. Non-Substring Subsequence_10531
|
Hr0d1y has q queries on a binary string s of length n. A binary string is a string containing only characters '0' and '1'.
A query is described by a pair of integers l_i, r_i (1 ≤ l_i < r_i ≤ n).
For each query, he has to determine whether there exists a good subsequence in s that is equal to the substring s[l_i… r_i].
* A substring s[i… j] of a string s is the string formed by characters s_i s_{i+1} … s_j.
* String a is said to be a subsequence of string b if a can be obtained from b by deleting some characters without changing the order of the remaining characters.
* A subsequence is said to be good if it is not contiguous and has length ≥ 2. For example, if s is "1100110", then the subsequences s_1s_2s_4 ("1100110") and s_1s_5s_7 ("1100110") are good, while s_1s_2s_3 ("1100110") is not good.
Can you help Hr0d1y answer each query?
Input
The first line of the input contains a single integer t (1≤ t ≤ 100) — the number of test cases. The description of each test case is as follows.
The first line contains two integers n (2 ≤ n ≤ 100) and q (1≤ q ≤ 100) — the length of the string and the number of queries.
The second line contains the string s.
The i-th of the next q lines contains two integers l_i and r_i (1 ≤ l_i < r_i ≤ n).
Output
For each test case, output q lines. The i-th line of the output of each test case should contain "YES" if there exists a good subsequence equal to the substring s[l_i...r_i], and "NO" otherwise.
You may print each letter in any case (upper or lower).
Example
Input
2
6 3
001000
2 4
1 3
3 5
4 2
1111
1 4
2 3
Output
YES
NO
YES
NO
YES
Note
In the first test case,
* s[2… 4] = "010". In this case s_1s_3s_5 ("001000") and s_2s_3s_6 ("001000") are good suitable subsequences, while s_2s_3s_4 ("001000") is not good.
* s[1… 3] = "001". No suitable good subsequence exists.
* s[3… 5] = "100". Here s_3s_5s_6 ("001000") is a suitable good subsequence.
|
# Problem: B. Non-Substring Subsequence
# Contest: Codeforces - Codeforces Round #685 (Div. 2)
# URL: https://codeforces.com/contest/1451/problem/B
# Memory Limit: 256 MB
# Time Limit: 1000 ms
#
# KAPOOR'S
from sys import stdin, stdout
def INI():
return int(stdin.readline())
def INL():
return [int(_) for _ in stdin.readline().split()]
def INS():
return stdin.readline()
def MOD():
return pow(10,9)+7
def OPS(ans):
stdout.write(str(ans)+"\n")
def OPL(ans):
[stdout.write(str(_)+" ") for _ in ans]
stdout.write("\n")
if __name__=="__main__":
for _ in range(INI()):
n,q=INL()
S=INS()
for _ in range(q):
l,r=INL()
P=S[l-1:r]
if S[l-1] in S[:l-1] or S[r-1] in S[r:]:
OPS("YES")
else:
OPS("NO")
|
{
"input": [
"2\n6 3\n001000\n2 4\n1 3\n3 5\n4 2\n1111\n1 4\n2 3\n",
"2\n6 3\n001000\n2 4\n1 3\n3 5\n4 2\n1111\n1 4\n1 3\n",
"2\n6 3\n001000\n2 5\n1 3\n3 5\n4 2\n1111\n1 4\n1 3\n",
"2\n6 3\n001000\n2 5\n1 3\n3 5\n4 2\n1011\n1 4\n1 3\n",
"2\n6 3\n001000\n2 5\n1 3\n3 4\n4 2\n1011\n1 4\n1 3\n",
"2\n6 3\n001000\n4 5\n1 3\n3 5\n4 2\n1011\n1 4\n1 3\n",
"2\n6 3\n001000\n4 5\n1 3\n3 5\n4 2\n1111\n1 4\n1 3\n",
"2\n6 3\n001000\n2 5\n1 3\n3 4\n4 2\n1111\n1 4\n1 3\n",
"2\n6 3\n001000\n2 5\n1 3\n3 4\n4 2\n0011\n1 4\n1 3\n",
"2\n6 3\n001000\n3 5\n1 3\n3 4\n4 2\n0011\n1 4\n1 3\n",
"2\n6 3\n001000\n2 5\n1 3\n3 4\n4 2\n0111\n1 4\n1 3\n",
"2\n6 3\n001000\n4 5\n1 6\n3 5\n4 2\n1011\n1 4\n1 3\n",
"2\n6 3\n001000\n3 5\n1 3\n3 5\n4 2\n1111\n1 4\n1 3\n",
"2\n6 3\n001000\n2 5\n1 3\n3 4\n4 2\n1011\n2 4\n1 3\n",
"2\n6 3\n001000\n2 4\n1 3\n3 4\n4 2\n0011\n1 4\n1 3\n",
"2\n6 3\n001000\n2 6\n1 3\n3 5\n4 2\n1111\n1 4\n1 3\n",
"2\n6 3\n001000\n2 5\n1 3\n3 4\n4 2\n0111\n2 4\n1 3\n",
"2\n6 3\n001000\n2 4\n1 3\n1 5\n4 2\n1111\n1 4\n2 3\n",
"2\n6 3\n101000\n2 4\n1 3\n3 5\n4 2\n1111\n1 4\n1 3\n",
"2\n6 3\n001000\n1 5\n1 3\n3 5\n4 2\n1111\n1 4\n1 3\n",
"2\n6 3\n001000\n2 6\n1 3\n3 5\n4 2\n1111\n1 4\n2 3\n",
"2\n6 3\n001000\n2 6\n1 3\n3 5\n4 2\n0111\n1 4\n2 3\n",
"2\n6 3\n001000\n2 5\n1 6\n3 4\n4 2\n1011\n2 4\n1 3\n",
"2\n6 3\n001000\n2 5\n1 3\n1 5\n4 2\n1111\n1 4\n2 3\n",
"2\n6 3\n101000\n2 5\n1 3\n3 5\n4 2\n1111\n1 4\n1 3\n",
"2\n6 3\n111000\n2 5\n1 3\n3 5\n4 2\n1111\n1 4\n1 3\n",
"2\n6 3\n111000\n2 5\n1 3\n3 5\n4 2\n1011\n1 4\n1 3\n",
"2\n6 3\n001000\n2 5\n1 3\n3 5\n4 2\n1111\n1 4\n1 2\n",
"2\n6 3\n001000\n1 5\n1 3\n3 5\n4 2\n1011\n1 4\n1 3\n",
"2\n6 3\n001000\n4 5\n1 3\n2 5\n4 2\n1011\n1 4\n1 3\n",
"2\n6 3\n011000\n2 5\n1 3\n3 4\n4 2\n0111\n1 4\n1 3\n",
"2\n6 3\n001000\n4 5\n1 6\n3 5\n4 2\n0011\n1 4\n1 3\n",
"2\n6 3\n011000\n1 5\n1 3\n3 5\n4 2\n1111\n1 4\n1 3\n",
"2\n6 3\n001000\n2 4\n1 3\n3 5\n4 2\n1011\n1 4\n2 3\n",
"2\n6 3\n001000\n1 5\n1 3\n3 4\n4 2\n1011\n1 4\n1 3\n",
"2\n6 3\n001000\n2 5\n1 3\n2 4\n4 2\n1111\n1 4\n1 3\n",
"2\n6 3\n001000\n3 5\n1 3\n3 4\n4 2\n1011\n2 4\n1 3\n",
"2\n6 3\n001000\n2 4\n1 3\n1 5\n4 2\n1011\n1 4\n2 3\n",
"2\n6 3\n101000\n2 4\n1 3\n3 6\n4 2\n1111\n1 4\n1 3\n",
"2\n6 3\n001000\n2 5\n1 6\n1 4\n4 2\n1011\n2 4\n1 3\n",
"2\n6 3\n001000\n2 5\n1 3\n1 5\n4 2\n1101\n1 4\n2 3\n",
"2\n6 3\n111000\n2 5\n1 3\n3 5\n4 2\n1111\n1 4\n2 3\n",
"2\n6 3\n111000\n2 5\n1 3\n3 5\n4 2\n1011\n2 4\n1 3\n",
"2\n6 3\n001000\n1 5\n1 3\n1 5\n4 2\n1011\n1 4\n1 3\n",
"2\n6 3\n011000\n1 5\n2 3\n3 5\n4 2\n1111\n1 4\n1 3\n",
"2\n6 3\n111000\n1 5\n1 3\n3 5\n4 2\n1011\n2 4\n1 3\n",
"2\n6 3\n001000\n2 5\n1 3\n3 5\n4 2\n1111\n1 4\n2 3\n",
"2\n6 3\n001000\n2 5\n1 3\n4 5\n4 2\n1011\n1 4\n1 3\n",
"2\n6 3\n001000\n4 5\n1 3\n3 4\n4 2\n1111\n1 4\n1 3\n",
"2\n6 3\n011000\n2 5\n1 3\n3 4\n4 2\n1011\n2 4\n1 3\n",
"2\n6 3\n001000\n1 5\n1 3\n1 5\n4 2\n1111\n1 4\n2 3\n",
"2\n6 3\n101000\n2 5\n1 3\n3 6\n4 2\n1111\n1 4\n1 3\n",
"2\n6 3\n001000\n3 5\n1 3\n3 4\n4 2\n1011\n2 4\n2 3\n",
"2\n6 3\n101000\n2 4\n1 3\n5 6\n4 2\n1111\n1 4\n1 3\n",
"2\n6 3\n001000\n1 5\n1 3\n3 5\n4 2\n1111\n1 4\n2 3\n",
"2\n6 3\n001000\n2 4\n1 3\n3 4\n4 2\n1011\n1 4\n2 3\n",
"2\n6 3\n001000\n3 5\n1 3\n3 4\n4 2\n1111\n1 4\n1 3\n",
"2\n6 3\n101000\n2 5\n1 3\n3 4\n4 2\n0011\n1 4\n1 3\n",
"2\n6 3\n001000\n3 5\n1 3\n3 4\n4 2\n0111\n1 4\n1 3\n",
"2\n6 3\n001000\n2 3\n1 3\n3 4\n4 2\n0111\n2 4\n1 3\n",
"2\n6 3\n111000\n2 5\n1 3\n3 5\n4 2\n1111\n1 4\n1 2\n",
"2\n6 3\n001000\n1 4\n1 3\n3 5\n4 2\n1011\n1 4\n2 3\n",
"2\n6 3\n001000\n2 5\n1 3\n2 4\n4 2\n1111\n1 4\n1 2\n",
"2\n6 3\n011000\n1 5\n2 3\n3 5\n4 2\n0111\n1 4\n1 3\n",
"2\n6 3\n001000\n4 5\n1 3\n2 4\n4 2\n1111\n1 4\n1 3\n",
"2\n6 3\n101000\n2 4\n1 3\n5 6\n4 2\n0111\n1 4\n1 3\n",
"2\n6 3\n001000\n1 5\n1 3\n4 5\n4 2\n1111\n1 4\n2 3\n",
"2\n6 3\n001000\n2 4\n1 3\n3 4\n4 2\n0011\n1 4\n2 3\n",
"2\n6 3\n001000\n2 3\n1 3\n3 4\n4 2\n0111\n2 4\n2 3\n",
"2\n6 3\n101000\n2 5\n1 3\n3 5\n4 2\n1111\n1 4\n1 2\n",
"2\n6 3\n001000\n2 5\n1 3\n2 4\n4 2\n0111\n1 4\n1 2\n",
"2\n6 3\n011000\n1 5\n2 3\n3 5\n4 2\n0111\n1 4\n1 2\n",
"2\n6 3\n001000\n2 5\n1 3\n2 4\n4 2\n0111\n2 4\n1 2\n",
"2\n6 3\n011000\n1 5\n2 3\n3 5\n4 2\n0101\n1 4\n1 2\n",
"2\n6 3\n011000\n2 5\n2 3\n3 5\n4 2\n0101\n1 4\n1 2\n",
"2\n6 3\n001000\n2 5\n1 3\n3 4\n4 2\n1111\n1 4\n1 2\n",
"2\n6 3\n011000\n2 5\n1 3\n3 5\n4 2\n1011\n1 4\n1 3\n",
"2\n6 3\n111000\n2 5\n1 3\n3 4\n4 2\n0111\n1 4\n1 3\n",
"2\n6 3\n001000\n3 5\n1 3\n3 5\n4 2\n1011\n2 4\n1 3\n",
"2\n6 3\n111000\n2 4\n1 3\n3 6\n4 2\n1111\n1 4\n1 3\n",
"2\n6 3\n011000\n2 5\n1 6\n1 4\n4 2\n1011\n2 4\n1 3\n",
"2\n6 3\n001000\n2 5\n1 6\n3 5\n4 2\n1111\n1 4\n2 3\n",
"2\n6 3\n101000\n3 5\n1 3\n3 6\n4 2\n1111\n1 4\n1 3\n",
"2\n6 3\n101000\n1 4\n1 3\n5 6\n4 2\n1111\n1 4\n1 3\n",
"2\n6 3\n001000\n2 3\n1 3\n3 4\n4 2\n0111\n2 4\n1 2\n",
"2\n6 3\n011000\n1 5\n2 3\n4 5\n4 2\n0111\n1 4\n1 3\n",
"2\n6 3\n001000\n4 5\n1 3\n2 4\n4 2\n1111\n1 4\n2 3\n",
"2\n6 3\n011000\n1 5\n2 3\n3 5\n4 2\n1101\n1 4\n1 2\n",
"2\n6 3\n011000\n4 5\n2 3\n3 5\n4 2\n0101\n1 4\n1 2\n",
"2\n6 3\n011000\n1 5\n2 3\n4 5\n4 2\n0011\n1 4\n1 3\n",
"2\n6 3\n011000\n4 5\n2 3\n2 5\n4 2\n0101\n1 4\n1 2\n",
"2\n6 3\n011000\n2 5\n1 3\n3 4\n4 2\n0011\n1 4\n1 3\n",
"2\n6 3\n011000\n3 5\n1 3\n3 5\n4 2\n1111\n1 4\n1 3\n",
"2\n6 3\n001000\n2 4\n1 3\n1 5\n4 2\n1110\n1 4\n2 3\n",
"2\n6 3\n111000\n4 5\n1 3\n3 5\n4 2\n1011\n1 4\n1 3\n",
"2\n6 3\n011000\n2 5\n1 3\n3 5\n4 2\n1111\n1 4\n1 2\n",
"2\n6 3\n001000\n1 5\n1 3\n3 5\n4 2\n1011\n2 4\n1 3\n",
"2\n6 3\n001000\n4 5\n1 3\n4 5\n4 2\n1011\n1 4\n1 3\n",
"2\n6 3\n011000\n1 5\n1 3\n2 5\n4 2\n1111\n1 4\n1 3\n",
"2\n6 3\n111000\n1 5\n1 3\n3 5\n4 2\n1111\n1 4\n2 3\n",
"2\n6 3\n001000\n1 5\n1 3\n1 5\n4 2\n1011\n2 4\n1 3\n",
"2\n6 3\n001000\n1 5\n1 3\n1 4\n4 2\n1111\n1 4\n2 3\n",
"2\n6 3\n001000\n1 5\n1 3\n3 5\n4 2\n1011\n1 4\n2 3\n",
"2\n6 3\n001000\n4 5\n1 3\n2 4\n4 2\n0111\n1 4\n1 3\n",
"2\n6 3\n011000\n2 5\n2 3\n3 5\n4 2\n0111\n1 4\n1 2\n",
"2\n6 3\n001000\n4 5\n1 3\n2 4\n4 2\n0111\n2 4\n1 2\n",
"2\n6 3\n001000\n2 5\n1 6\n3 5\n4 2\n1111\n1 4\n1 3\n",
"2\n6 3\n011000\n1 5\n1 3\n2 5\n4 2\n1011\n1 4\n1 3\n",
"2\n6 3\n001000\n2 5\n1 3\n1 5\n4 2\n1111\n1 4\n1 3\n",
"2\n6 3\n001000\n4 5\n1 3\n3 5\n4 2\n1111\n1 4\n2 3\n",
"2\n6 3\n001000\n4 5\n1 6\n2 5\n4 2\n1011\n1 4\n1 3\n",
"2\n6 3\n001000\n2 5\n1 3\n2 4\n4 2\n0111\n2 4\n1 3\n",
"2\n6 3\n001000\n2 5\n1 6\n1 4\n4 2\n1011\n2 4\n2 3\n",
"2\n6 3\n001000\n2 5\n1 3\n2 5\n4 2\n1101\n1 4\n2 3\n",
"2\n6 3\n001000\n4 5\n1 3\n3 4\n4 2\n1111\n1 4\n1 2\n",
"2\n6 3\n101000\n1 5\n1 3\n1 5\n4 2\n1111\n1 4\n2 3\n",
"2\n6 3\n101000\n2 5\n1 3\n4 6\n4 2\n1111\n1 4\n1 3\n",
"2\n6 3\n001000\n3 4\n1 3\n3 4\n4 2\n1011\n1 4\n2 3\n",
"2\n6 3\n111000\n1 5\n1 3\n3 5\n4 2\n1111\n1 4\n1 2\n",
"2\n6 3\n001000\n1 4\n1 3\n3 5\n4 2\n1111\n1 4\n2 3\n",
"2\n6 3\n001000\n1 5\n1 3\n4 5\n4 2\n1011\n1 4\n2 3\n",
"2\n6 3\n101000\n2 4\n1 3\n3 4\n4 2\n0011\n1 4\n2 3\n",
"2\n6 3\n101000\n2 5\n1 3\n3 5\n4 2\n1101\n1 4\n1 2\n",
"2\n6 3\n001000\n2 5\n1 6\n2 4\n4 2\n0111\n1 4\n1 2\n",
"2\n6 3\n001000\n2 5\n1 3\n3 4\n4 2\n0111\n2 4\n1 2\n",
"2\n6 3\n001000\n2 5\n1 3\n3 5\n4 2\n1011\n2 4\n1 3\n",
"2\n6 3\n001000\n4 5\n1 3\n4 5\n4 2\n1011\n2 4\n1 3\n",
"2\n6 3\n001000\n2 5\n1 3\n1 4\n4 2\n1111\n1 4\n2 3\n",
"2\n6 3\n001000\n4 5\n1 3\n3 4\n4 2\n0111\n1 4\n1 2\n",
"2\n6 3\n101000\n2 5\n1 3\n5 6\n4 2\n1111\n1 4\n1 3\n",
"2\n6 3\n101000\n2 5\n2 3\n3 5\n4 2\n1101\n1 4\n1 2\n",
"2\n6 3\n001000\n4 5\n1 3\n3 5\n4 2\n0111\n1 4\n1 2\n",
"2\n6 3\n101000\n2 5\n2 3\n3 5\n4 2\n0101\n1 4\n1 2\n",
"2\n6 3\n101000\n2 5\n1 3\n3 5\n4 2\n0101\n1 4\n1 2\n",
"2\n6 3\n011000\n3 5\n1 3\n3 4\n4 2\n1111\n1 4\n1 3\n",
"2\n6 3\n001000\n2 4\n1 3\n1 5\n4 2\n0111\n1 4\n2 3\n",
"2\n6 3\n001000\n2 4\n1 3\n3 5\n4 2\n1011\n1 2\n2 3\n",
"2\n6 3\n001000\n1 5\n1 3\n1 5\n4 2\n1101\n1 4\n2 3\n",
"2\n6 3\n001000\n2 5\n1 3\n3 4\n4 2\n1111\n1 4\n2 3\n",
"2\n6 3\n001000\n1 5\n1 3\n4 5\n4 2\n0111\n1 4\n2 3\n",
"2\n6 3\n011000\n1 5\n2 3\n3 5\n4 2\n0110\n1 4\n1 2\n",
"2\n6 3\n001000\n2 3\n1 3\n3 4\n4 2\n1111\n1 4\n1 2\n",
"2\n6 3\n011000\n3 5\n1 3\n3 5\n4 2\n1011\n1 4\n1 3\n",
"2\n6 3\n001000\n2 3\n1 3\n3 4\n4 2\n0101\n2 4\n1 2\n",
"2\n6 3\n001000\n4 6\n1 3\n2 4\n4 2\n1111\n1 4\n1 3\n",
"2\n6 3\n011000\n2 5\n1 3\n3 4\n4 2\n0011\n1 4\n2 3\n",
"2\n6 3\n011000\n4 5\n1 3\n3 5\n4 2\n1011\n1 4\n1 3\n",
"2\n6 3\n001000\n1 5\n1 3\n1 2\n4 2\n1011\n2 4\n1 3\n",
"2\n6 3\n001000\n4 5\n1 6\n1 5\n4 2\n1011\n1 4\n1 3\n",
"2\n6 3\n101000\n1 5\n1 3\n1 5\n4 2\n1111\n1 4\n1 3\n",
"2\n6 3\n001000\n3 4\n1 3\n3 4\n4 2\n1011\n1 2\n2 3\n",
"2\n6 3\n101000\n2 5\n1 6\n2 4\n4 2\n0111\n1 4\n1 2\n",
"2\n6 3\n001000\n4 5\n1 3\n3 5\n4 2\n0110\n1 4\n1 2\n",
"2\n6 3\n101000\n2 5\n1 3\n3 5\n4 2\n0111\n1 4\n1 2\n",
"2\n6 3\n001000\n2 3\n1 3\n3 4\n4 2\n1110\n1 4\n1 2\n",
"2\n6 3\n011000\n4 5\n1 3\n3 5\n4 2\n0011\n1 4\n1 3\n",
"2\n6 3\n001000\n4 5\n1 3\n1 5\n4 2\n1011\n1 4\n1 3\n",
"2\n6 3\n001000\n4 6\n1 3\n3 5\n4 2\n1111\n1 4\n1 3\n",
"2\n6 3\n001000\n1 5\n1 3\n2 5\n4 2\n1111\n1 4\n1 3\n",
"2\n6 3\n011000\n2 5\n1 3\n1 5\n4 2\n1101\n1 4\n2 3\n",
"2\n6 3\n101000\n2 5\n1 3\n3 5\n4 2\n1011\n1 4\n1 3\n",
"2\n6 3\n001000\n4 5\n1 6\n3 4\n4 2\n0011\n1 4\n1 3\n",
"2\n6 3\n001000\n1 5\n1 3\n3 4\n4 2\n0011\n1 4\n1 3\n",
"2\n6 3\n001000\n2 5\n1 3\n2 4\n4 2\n1111\n1 4\n2 3\n",
"2\n6 3\n101000\n2 4\n2 3\n3 6\n4 2\n1111\n1 4\n1 3\n",
"2\n6 3\n101000\n2 5\n1 3\n4 5\n4 2\n1011\n1 4\n1 3\n",
"2\n6 3\n001000\n3 5\n1 3\n2 4\n4 2\n0111\n1 4\n1 3\n",
"2\n6 3\n111000\n2 5\n1 3\n3 5\n4 2\n1110\n1 4\n1 2\n",
"2\n6 3\n001000\n2 6\n1 3\n3 4\n4 2\n0011\n1 4\n2 3\n",
"2\n6 3\n001000\n2 5\n1 3\n2 4\n4 2\n0101\n1 4\n1 2\n",
"2\n6 3\n001000\n3 5\n1 3\n3 5\n4 2\n1011\n2 4\n2 3\n",
"2\n6 3\n011000\n4 5\n1 6\n1 4\n4 2\n1011\n2 4\n1 3\n",
"2\n6 3\n001000\n4 5\n1 3\n2 4\n4 2\n1011\n1 4\n2 3\n",
"2\n6 3\n011000\n4 5\n2 3\n1 5\n4 2\n0101\n1 4\n1 2\n",
"2\n6 3\n001000\n2 4\n1 6\n1 5\n4 2\n1110\n1 4\n2 3\n",
"2\n6 3\n011000\n1 5\n1 3\n4 5\n4 2\n1011\n1 4\n1 3\n"
],
"output": [
"\nYES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Hr0d1y has q queries on a binary string s of length n. A binary string is a string containing only characters '0' and '1'.
A query is described by a pair of integers l_i, r_i (1 ≤ l_i < r_i ≤ n).
For each query, he has to determine whether there exists a good subsequence in s that is equal to the substring s[l_i… r_i].
* A substring s[i… j] of a string s is the string formed by characters s_i s_{i+1} … s_j.
* String a is said to be a subsequence of string b if a can be obtained from b by deleting some characters without changing the order of the remaining characters.
* A subsequence is said to be good if it is not contiguous and has length ≥ 2. For example, if s is "1100110", then the subsequences s_1s_2s_4 ("1100110") and s_1s_5s_7 ("1100110") are good, while s_1s_2s_3 ("1100110") is not good.
Can you help Hr0d1y answer each query?
Input
The first line of the input contains a single integer t (1≤ t ≤ 100) — the number of test cases. The description of each test case is as follows.
The first line contains two integers n (2 ≤ n ≤ 100) and q (1≤ q ≤ 100) — the length of the string and the number of queries.
The second line contains the string s.
The i-th of the next q lines contains two integers l_i and r_i (1 ≤ l_i < r_i ≤ n).
Output
For each test case, output q lines. The i-th line of the output of each test case should contain "YES" if there exists a good subsequence equal to the substring s[l_i...r_i], and "NO" otherwise.
You may print each letter in any case (upper or lower).
Example
Input
2
6 3
001000
2 4
1 3
3 5
4 2
1111
1 4
2 3
Output
YES
NO
YES
NO
YES
Note
In the first test case,
* s[2… 4] = "010". In this case s_1s_3s_5 ("001000") and s_2s_3s_6 ("001000") are good suitable subsequences, while s_2s_3s_4 ("001000") is not good.
* s[1… 3] = "001". No suitable good subsequence exists.
* s[3… 5] = "100". Here s_3s_5s_6 ("001000") is a suitable good subsequence.
### Input:
2
6 3
001000
2 4
1 3
3 5
4 2
1111
1 4
2 3
### Output:
YES
NO
YES
NO
YES
### Input:
2
6 3
001000
2 4
1 3
3 5
4 2
1111
1 4
1 3
### Output:
YES
NO
YES
NO
YES
### Code:
# Problem: B. Non-Substring Subsequence
# Contest: Codeforces - Codeforces Round #685 (Div. 2)
# URL: https://codeforces.com/contest/1451/problem/B
# Memory Limit: 256 MB
# Time Limit: 1000 ms
#
# KAPOOR'S
from sys import stdin, stdout
def INI():
return int(stdin.readline())
def INL():
return [int(_) for _ in stdin.readline().split()]
def INS():
return stdin.readline()
def MOD():
return pow(10,9)+7
def OPS(ans):
stdout.write(str(ans)+"\n")
def OPL(ans):
[stdout.write(str(_)+" ") for _ in ans]
stdout.write("\n")
if __name__=="__main__":
for _ in range(INI()):
n,q=INL()
S=INS()
for _ in range(q):
l,r=INL()
P=S[l-1:r]
if S[l-1] in S[:l-1] or S[r-1] in S[r:]:
OPS("YES")
else:
OPS("NO")
|
1475_B. New Year's Number_10535
|
Polycarp remembered the 2020-th year, and he is happy with the arrival of the new 2021-th year. To remember such a wonderful moment, Polycarp wants to represent the number n as the sum of a certain number of 2020 and a certain number of 2021.
For example, if:
* n=4041, then the number n can be represented as the sum 2020 + 2021;
* n=4042, then the number n can be represented as the sum 2021 + 2021;
* n=8081, then the number n can be represented as the sum 2020 + 2020 + 2020 + 2021;
* n=8079, then the number n cannot be represented as the sum of the numbers 2020 and 2021.
Help Polycarp to find out whether the number n can be represented as the sum of a certain number of numbers 2020 and a certain number of numbers 2021.
Input
The first line contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases. Then t test cases follow.
Each test case contains one integer n (1 ≤ n ≤ 10^6) — the number that Polycarp wants to represent as the sum of the numbers 2020 and 2021.
Output
For each test case, output on a separate line:
* "YES" if the number n is representable as the sum of a certain number of 2020 and a certain number of 2021;
* "NO" otherwise.
You can output "YES" and "NO" in any case (for example, the strings yEs, yes, Yes and YES will be recognized as positive).
Example
Input
5
1
4041
4042
8081
8079
Output
NO
YES
YES
YES
NO
|
t=int(input())
for T in range(t):
n=int(input())
x=n//2020
if (n-x*2020)<=x:
print('YES')
else:
print('NO')
|
{
"input": [
"5\n1\n4041\n4042\n8081\n8079\n",
"1\n2021\n",
"1\n2020\n",
"3\n2020\n2021\n4040\n",
"1\n4040\n",
"1\n411\n",
"3\n2020\n2021\n4766\n",
"5\n1\n4041\n4042\n12391\n8079\n",
"3\n307\n2021\n4766\n",
"5\n1\n6831\n4042\n12391\n8079\n",
"5\n1\n6831\n3971\n12467\n2558\n",
"3\n2\n2097\n13304\n",
"3\n2020\n1279\n4040\n",
"5\n1\n4041\n4042\n8081\n4273\n",
"3\n3480\n1279\n4040\n",
"5\n1\n4041\n4462\n8081\n4273\n",
"1\n424\n",
"1\n2449\n",
"1\n84\n",
"1\n306\n",
"1\n522\n",
"1\n105\n",
"1\n159\n",
"3\n307\n2021\n8789\n",
"1\n905\n",
"5\n1\n6831\n4042\n12467\n8079\n",
"1\n127\n",
"1\n94\n",
"3\n307\n2021\n12194\n",
"1\n660\n",
"5\n1\n6831\n4042\n12467\n2558\n",
"1\n246\n",
"1\n155\n",
"3\n76\n2021\n12194\n",
"1\n717\n",
"1\n339\n",
"1\n239\n",
"3\n2\n2021\n12194\n",
"1\n235\n",
"5\n1\n6831\n7335\n12467\n2558\n",
"1\n46\n",
"1\n118\n",
"3\n2\n2021\n13304\n",
"1\n74\n",
"5\n1\n6831\n7335\n21103\n2558\n",
"1\n71\n",
"1\n93\n",
"1\n109\n",
"5\n1\n6831\n7335\n21103\n2858\n",
"1\n73\n",
"1\n7\n",
"3\n2\n2097\n10189\n",
"1\n69\n",
"5\n1\n6831\n7335\n21103\n3005\n",
"1\n85\n",
"1\n9\n",
"3\n2\n2317\n10189\n",
"5\n1\n6831\n548\n21103\n3005\n",
"1\n76\n",
"1\n15\n",
"3\n2\n123\n10189\n",
"5\n1\n12236\n548\n21103\n3005\n",
"1\n91\n",
"1\n28\n",
"3\n4\n123\n10189\n",
"5\n1\n12236\n548\n19262\n3005\n",
"1\n128\n",
"1\n55\n",
"3\n4\n156\n10189\n",
"5\n1\n12236\n548\n19288\n3005\n",
"1\n122\n",
"1\n11\n",
"3\n4\n156\n8198\n",
"5\n1\n10007\n548\n19288\n3005\n",
"1\n193\n",
"1\n8\n",
"3\n4\n250\n8198\n",
"5\n1\n10007\n548\n19288\n1884\n",
"1\n226\n",
"1\n12\n",
"3\n4\n492\n8198\n",
"5\n1\n9067\n548\n19288\n1884\n",
"1\n13\n",
"1\n10\n",
"3\n4\n923\n8198\n",
"5\n1\n9067\n536\n19288\n1884\n",
"1\n2\n",
"1\n20\n",
"3\n4\n679\n8198\n",
"5\n1\n9067\n536\n6504\n1884\n",
"1\n3\n",
"1\n6\n",
"3\n4\n679\n5360\n",
"5\n2\n9067\n536\n6504\n1884\n",
"3\n3\n679\n5360\n",
"5\n2\n9067\n536\n4454\n1884\n",
"3\n3\n679\n3631\n",
"5\n2\n9067\n132\n4454\n1884\n",
"3\n3\n679\n603\n",
"5\n2\n11051\n132\n4454\n1884\n",
"3\n3\n1285\n603\n",
"5\n2\n11051\n132\n4454\n382\n",
"3\n3\n1285\n644\n",
"5\n2\n11051\n132\n6658\n382\n",
"3\n4\n1285\n644\n",
"5\n2\n14444\n132\n6658\n382\n",
"3\n4\n1285\n1022\n",
"5\n2\n11465\n132\n6658\n382\n",
"3\n4\n1285\n1495\n",
"5\n1\n11465\n132\n6658\n382\n",
"3\n4\n1285\n2990\n",
"5\n2\n11465\n132\n3920\n382\n",
"3\n4\n1949\n2990\n",
"5\n2\n11465\n132\n3920\n2\n",
"3\n4\n2722\n2990\n",
"5\n2\n11465\n132\n6111\n2\n",
"3\n1\n2722\n2990\n",
"5\n2\n11465\n116\n6111\n2\n",
"3\n1\n1270\n2990\n",
"5\n2\n11465\n103\n6111\n2\n",
"3\n1\n780\n2990\n",
"5\n2\n11465\n110\n6111\n2\n",
"3\n1\n780\n5866\n",
"5\n2\n11465\n010\n6111\n2\n",
"3\n2\n780\n5866\n",
"5\n2\n11465\n010\n5053\n2\n",
"3\n2\n1560\n5866\n",
"5\n2\n5121\n010\n5053\n2\n",
"5\n2\n5121\n010\n5053\n1\n",
"1\n2397\n",
"1\n2591\n",
"1\n4304\n",
"1\n347\n",
"1\n157\n",
"3\n882\n2021\n4766\n",
"1\n1095\n",
"5\n1\n4041\n4042\n20009\n8079\n",
"1\n103\n",
"1\n4\n",
"3\n53\n2021\n4766\n",
"1\n385\n",
"5\n2\n6831\n4042\n12391\n8079\n",
"1\n149\n",
"1\n79\n",
"3\n307\n2021\n13578\n",
"1\n286\n",
"5\n1\n6831\n4042\n12467\n5215\n",
"1\n180\n",
"1\n87\n",
"1\n978\n",
"5\n1\n6831\n4042\n16712\n2558\n",
"1\n196\n",
"1\n26\n",
"3\n123\n2021\n12194\n",
"1\n1290\n",
"5\n1\n6831\n3971\n4515\n2558\n",
"1\n238\n",
"1\n332\n",
"3\n2\n2021\n24225\n",
"1\n163\n",
"5\n2\n6831\n7335\n12467\n2558\n",
"1\n30\n",
"1\n29\n",
"3\n2\n3187\n13304\n",
"1\n199\n",
"5\n1\n6831\n7335\n21103\n1985\n",
"1\n27\n",
"1\n62\n",
"3\n4\n2097\n13304\n",
"1\n116\n",
"5\n1\n6831\n7335\n21103\n1271\n",
"1\n67\n",
"1\n1\n",
"3\n2\n3799\n10189\n",
"1\n95\n",
"5\n1\n6831\n477\n21103\n3005\n",
"1\n14\n",
"1\n18\n",
"3\n1\n2317\n10189\n",
"5\n1\n6831\n65\n21103\n3005\n",
"1\n145\n",
"1\n17\n",
"3\n2\n123\n13162\n",
"5\n1\n12236\n548\n41686\n3005\n",
"1\n106\n",
"1\n36\n",
"3\n4\n163\n10189\n",
"1\n80\n",
"1\n5\n",
"3\n3\n156\n10189\n",
"1\n161\n",
"3\n4\n144\n8198\n",
"5\n1\n10007\n548\n15892\n3005\n",
"1\n81\n",
"3\n4\n13\n8198\n",
"5\n1\n10007\n548\n19288\n3486\n",
"1\n353\n",
"1\n22\n",
"3\n4\n492\n15801\n",
"5\n1\n9067\n316\n19288\n1884\n",
"1\n34\n",
"3\n4\n1765\n8198\n",
"5\n1\n9067\n302\n19288\n1884\n",
"1\n60\n",
"5\n2\n9067\n23\n6504\n1884\n"
],
"output": [
"\nNO\nYES\nYES\nYES\nNO\n",
"YES\n",
"YES\n",
"YES\nYES\nYES\n",
"YES\n",
"NO\n",
"YES\nYES\nNO\n",
"NO\nYES\nYES\nNO\nNO\n",
"NO\nYES\nNO\n",
"NO\nNO\nYES\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\n",
"YES\nNO\nYES\n",
"NO\nYES\nYES\nYES\nNO\n",
"NO\nNO\nYES\n",
"NO\nYES\nNO\nYES\nNO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\nYES\nNO\n",
"NO\n",
"NO\nNO\nYES\nNO\nNO\n",
"NO\n",
"NO\n",
"NO\nYES\nNO\n",
"NO\n",
"NO\nNO\nYES\nNO\nNO\n",
"NO\n",
"NO\n",
"NO\nYES\nNO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\nYES\nNO\n",
"NO\n",
"NO\nNO\nNO\nNO\nNO\n",
"NO\n",
"NO\n",
"NO\nYES\nNO\n",
"NO\n",
"NO\nNO\nNO\nNO\nNO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\nNO\nNO\nNO\nNO\n",
"NO\n",
"NO\n",
"NO\nNO\nNO\n",
"NO\n",
"NO\nNO\nNO\nNO\nNO\n",
"NO\n",
"NO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\n",
"NO\n",
"NO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\n",
"NO\n",
"NO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\n",
"NO\n",
"NO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\n",
"NO\n",
"NO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\n",
"NO\n",
"NO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\n",
"NO\n",
"NO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\n",
"NO\n",
"NO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\n",
"NO\n",
"NO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\n",
"NO\n",
"NO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\nYES\nNO\n",
"NO\n",
"NO\nYES\nYES\nNO\nNO\n",
"NO\n",
"NO\n",
"NO\nYES\nNO\n",
"NO\n",
"NO\nNO\nYES\nNO\nNO\n",
"NO\n",
"NO\n",
"NO\nYES\nNO\n",
"NO\n",
"NO\nNO\nYES\nNO\nNO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\nNO\nYES\nNO\nNO\n",
"NO\n",
"NO\n",
"NO\nYES\nNO\n",
"NO\n",
"NO\nNO\nNO\nNO\nNO\n",
"NO\n",
"NO\n",
"NO\nYES\nNO\n",
"NO\n",
"NO\nNO\nNO\nNO\nNO\n",
"NO\n",
"NO\n",
"NO\nNO\nNO\n",
"NO\n",
"NO\nNO\nNO\nNO\nNO\n",
"NO\n",
"NO\n",
"NO\nNO\nNO\n",
"NO\n",
"NO\nNO\nNO\nNO\nNO\n",
"NO\n",
"NO\n",
"NO\nNO\nNO\n",
"NO\n",
"NO\nNO\nNO\nNO\nNO\n",
"NO\n",
"NO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\n",
"NO\n",
"NO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\n",
"NO\n",
"NO\n",
"NO\nNO\nNO\n",
"NO\n",
"NO\n",
"NO\nNO\nNO\n",
"NO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\n",
"NO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\n",
"NO\n",
"NO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\n",
"NO\n",
"NO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\n",
"NO\n",
"NO\nNO\nNO\nNO\nNO\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Polycarp remembered the 2020-th year, and he is happy with the arrival of the new 2021-th year. To remember such a wonderful moment, Polycarp wants to represent the number n as the sum of a certain number of 2020 and a certain number of 2021.
For example, if:
* n=4041, then the number n can be represented as the sum 2020 + 2021;
* n=4042, then the number n can be represented as the sum 2021 + 2021;
* n=8081, then the number n can be represented as the sum 2020 + 2020 + 2020 + 2021;
* n=8079, then the number n cannot be represented as the sum of the numbers 2020 and 2021.
Help Polycarp to find out whether the number n can be represented as the sum of a certain number of numbers 2020 and a certain number of numbers 2021.
Input
The first line contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases. Then t test cases follow.
Each test case contains one integer n (1 ≤ n ≤ 10^6) — the number that Polycarp wants to represent as the sum of the numbers 2020 and 2021.
Output
For each test case, output on a separate line:
* "YES" if the number n is representable as the sum of a certain number of 2020 and a certain number of 2021;
* "NO" otherwise.
You can output "YES" and "NO" in any case (for example, the strings yEs, yes, Yes and YES will be recognized as positive).
Example
Input
5
1
4041
4042
8081
8079
Output
NO
YES
YES
YES
NO
### Input:
5
1
4041
4042
8081
8079
### Output:
NO
YES
YES
YES
NO
### Input:
1
2021
### Output:
YES
### Code:
t=int(input())
for T in range(t):
n=int(input())
x=n//2020
if (n-x*2020)<=x:
print('YES')
else:
print('NO')
|
14_E. Camels_10539
|
Bob likes to draw camels: with a single hump, two humps, three humps, etc. He draws a camel by connecting points on a coordinate plane. Now he's drawing camels with t humps, representing them as polylines in the plane. Each polyline consists of n vertices with coordinates (x1, y1), (x2, y2), ..., (xn, yn). The first vertex has a coordinate x1 = 1, the second — x2 = 2, etc. Coordinates yi might be any, but should satisfy the following conditions:
* there should be t humps precisely, i.e. such indexes j (2 ≤ j ≤ n - 1), so that yj - 1 < yj > yj + 1,
* there should be precisely t - 1 such indexes j (2 ≤ j ≤ n - 1), so that yj - 1 > yj < yj + 1,
* no segment of a polyline should be parallel to the Ox-axis,
* all yi are integers between 1 and 4.
For a series of his drawings of camels with t humps Bob wants to buy a notebook, but he doesn't know how many pages he will need. Output the amount of different polylines that can be drawn to represent camels with t humps for a given number n.
Input
The first line contains a pair of integers n and t (3 ≤ n ≤ 20, 1 ≤ t ≤ 10).
Output
Output the required amount of camels with t humps.
Examples
Input
6 1
Output
6
Input
4 2
Output
0
Note
In the first sample test sequences of y-coordinates for six camels are: 123421, 123431, 123432, 124321, 134321 и 234321 (each digit corresponds to one value of yi).
|
import sys
from array import array # noqa: F401
def input():
return sys.stdin.buffer.readline().decode('utf-8')
n, t = map(int, input().split())
dp = [[[0] * 5 for _ in range(2 * t + 1)] for _ in range(n)]
dp[0][0] = [0] + [1] * 4
for i in range(n - 1):
for j in range(min(2 * t, i + 1)):
if (j & 1) == 0:
for k in range(1, 4):
for l in range(k + 1, 5):
# //
dp[i + 1][j][l] += dp[i][j][k]
# /\
dp[i + 1][j + 1][l] += dp[i][j][k]
else:
for k in range(4, 1, -1):
for l in range(k - 1, 0, -1):
# \\
dp[i + 1][j][l] += dp[i][j][k]
# \/
dp[i + 1][j + 1][l] += dp[i][j][k]
print(sum(dp[-1][2 * t]))
|
{
"input": [
"6 1\n",
"4 2\n",
"19 10\n",
"19 4\n",
"20 9\n",
"19 7\n",
"4 9\n",
"19 9\n",
"4 1\n",
"20 1\n",
"19 1\n",
"20 10\n",
"3 2\n",
"5 5\n",
"5 10\n",
"19 6\n",
"6 10\n",
"3 3\n",
"4 3\n",
"5 3\n",
"20 4\n",
"20 8\n",
"19 2\n",
"6 2\n",
"20 5\n",
"6 3\n",
"3 10\n",
"19 8\n",
"6 4\n",
"5 9\n",
"20 7\n",
"20 2\n",
"5 1\n",
"20 6\n",
"3 1\n",
"5 2\n",
"19 5\n",
"19 3\n",
"20 3\n",
"17 9\n",
"7 1\n",
"9 3\n",
"12 4\n",
"10 3\n",
"15 4\n",
"13 5\n",
"17 3\n",
"14 4\n",
"11 3\n",
"13 4\n",
"7 3\n",
"8 2\n",
"10 2\n",
"17 6\n",
"11 2\n",
"6 9\n",
"8 1\n",
"2 2\n",
"10 5\n",
"4 10\n",
"13 8\n",
"2 3\n",
"7 8\n",
"12 8\n",
"8 4\n",
"3 9\n",
"4 7\n",
"5 4\n",
"7 6\n",
"4 4\n",
"8 9\n",
"10 6\n",
"7 10\n",
"8 8\n",
"8 5\n",
"3 7\n",
"2 6\n",
"9 5\n",
"2 7\n",
"9 7\n",
"13 1\n",
"11 6\n",
"11 9\n",
"4 6\n",
"2 4\n",
"3 4\n",
"2 5\n",
"8 6\n",
"6 19\n",
"3 5\n",
"9 6\n",
"10 1\n",
"10 7\n",
"11 1\n",
"10 10\n",
"8 10\n",
"13 2\n"
],
"output": [
"6\n",
"0\n",
"0\n",
"32632\n",
"90700276\n",
"197939352\n",
"0\n",
"5846414\n",
"22\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"69183464\n",
"0\n",
"0\n",
"0\n",
"0\n",
"12628\n",
"503245466\n",
"0\n",
"232\n",
"3715462\n",
"0\n",
"0\n",
"109824208\n",
"0\n",
"0\n",
"468541040\n",
"0\n",
"16\n",
"96046590\n",
"14\n",
"70\n",
"4594423\n",
"1\n",
"0\n",
"0\n",
"1\n",
"4500\n",
"92226\n",
"7414\n",
"201744\n",
"328222\n",
"96\n",
"195420\n",
"8849\n",
"152140\n",
"353\n",
"396\n",
"142\n",
"20852648\n",
"48\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"1\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Bob likes to draw camels: with a single hump, two humps, three humps, etc. He draws a camel by connecting points on a coordinate plane. Now he's drawing camels with t humps, representing them as polylines in the plane. Each polyline consists of n vertices with coordinates (x1, y1), (x2, y2), ..., (xn, yn). The first vertex has a coordinate x1 = 1, the second — x2 = 2, etc. Coordinates yi might be any, but should satisfy the following conditions:
* there should be t humps precisely, i.e. such indexes j (2 ≤ j ≤ n - 1), so that yj - 1 < yj > yj + 1,
* there should be precisely t - 1 such indexes j (2 ≤ j ≤ n - 1), so that yj - 1 > yj < yj + 1,
* no segment of a polyline should be parallel to the Ox-axis,
* all yi are integers between 1 and 4.
For a series of his drawings of camels with t humps Bob wants to buy a notebook, but he doesn't know how many pages he will need. Output the amount of different polylines that can be drawn to represent camels with t humps for a given number n.
Input
The first line contains a pair of integers n and t (3 ≤ n ≤ 20, 1 ≤ t ≤ 10).
Output
Output the required amount of camels with t humps.
Examples
Input
6 1
Output
6
Input
4 2
Output
0
Note
In the first sample test sequences of y-coordinates for six camels are: 123421, 123431, 123432, 124321, 134321 и 234321 (each digit corresponds to one value of yi).
### Input:
6 1
### Output:
6
### Input:
4 2
### Output:
0
### Code:
import sys
from array import array # noqa: F401
def input():
return sys.stdin.buffer.readline().decode('utf-8')
n, t = map(int, input().split())
dp = [[[0] * 5 for _ in range(2 * t + 1)] for _ in range(n)]
dp[0][0] = [0] + [1] * 4
for i in range(n - 1):
for j in range(min(2 * t, i + 1)):
if (j & 1) == 0:
for k in range(1, 4):
for l in range(k + 1, 5):
# //
dp[i + 1][j][l] += dp[i][j][k]
# /\
dp[i + 1][j + 1][l] += dp[i][j][k]
else:
for k in range(4, 1, -1):
for l in range(k - 1, 0, -1):
# \\
dp[i + 1][j][l] += dp[i][j][k]
# \/
dp[i + 1][j + 1][l] += dp[i][j][k]
print(sum(dp[-1][2 * t]))
|
1525_B. Permutation Sort_10543
|
You are given a permutation a consisting of n numbers 1, 2, ..., n (a permutation is an array in which each element from 1 to n occurs exactly once).
You can perform the following operation: choose some subarray (contiguous subsegment) of a and rearrange the elements in it in any way you want. But this operation cannot be applied to the whole array.
For example, if a = [2, 1, 4, 5, 3] and we want to apply the operation to the subarray a[2, 4] (the subarray containing all elements from the 2-nd to the 4-th), then after the operation, the array can become a = [2, 5, 1, 4, 3] or, for example, a = [2, 1, 5, 4, 3].
Your task is to calculate the minimum number of operations described above to sort the permutation a in ascending order.
Input
The first line contains a single integer t (1 ≤ t ≤ 2000) — the number of test cases.
The first line of the test case contains a single integer n (3 ≤ n ≤ 50) — the number of elements in the permutation.
The second line of the test case contains n distinct integers from 1 to n — the given permutation a.
Output
For each test case, output a single integer — the minimum number of operations described above to sort the array a in ascending order.
Example
Input
3
4
1 3 2 4
3
1 2 3
5
2 1 4 5 3
Output
1
0
2
Note
In the explanations, a[i, j] defines the subarray of a that starts from the i-th element and ends with the j-th element.
In the first test case of the example, you can select the subarray a[2, 3] and swap the elements in it.
In the second test case of the example, the permutation is already sorted, so you don't need to apply any operations.
In the third test case of the example, you can select the subarray a[3, 5] and reorder the elements in it so a becomes [2, 1, 3, 4, 5], and then select the subarray a[1, 2] and swap the elements in it, so a becomes [1, 2, 3, 4, 5].
|
k = int(input())
a = []
import math
def nhap():
r = input()
r = r.split()
r =[int(i) for i in r]
return r
def kq(a):
minn = min(a)
maxx = max(a)
b = sorted(a)
if(b == a): return 0
if(a[0]== maxx and a[-1]== minn): return 3
if(a[0]== minn or a[-1]== maxx): return 1
return 2
for i in range(k):
num = int(input())
a.append(nhap())
for i in a:
print(kq(i))
|
{
"input": [
"3\n4\n1 3 2 4\n3\n1 2 3\n5\n2 1 4 5 3\n",
"1\n8\n6 2 3 1 8 4 5 7\n",
"1\n8\n6 0 3 1 8 4 5 7\n",
"3\n4\n1 3 2 7\n3\n1 2 3\n5\n2 1 4 5 3\n",
"1\n8\n5 2 2 1 0 0 2 8\n",
"1\n6\n6 0 3 1 8 4 5 7\n",
"1\n8\n6 2 6 1 8 4 5 7\n",
"1\n8\n6 0 3 1 8 6 5 7\n",
"1\n6\n6 0 3 1 8 5 5 7\n",
"1\n8\n6 2 6 1 8 6 5 7\n",
"3\n4\n1 3 2 7\n3\n1 2 3\n5\n2 1 4 5 0\n",
"1\n8\n6 0 3 1 8 6 1 7\n",
"1\n8\n6 0 3 1 8 7 1 7\n",
"1\n8\n4 0 3 1 8 7 1 7\n",
"1\n8\n4 0 3 1 8 6 1 7\n",
"1\n8\n4 0 3 1 8 6 1 1\n",
"1\n8\n4 -1 3 1 8 6 1 1\n",
"1\n8\n4 -1 3 1 8 6 1 2\n",
"1\n8\n6 2 2 1 8 4 5 7\n",
"1\n8\n6 2 6 1 8 6 2 7\n",
"3\n4\n1 3 2 7\n3\n1 2 3\n5\n3 1 4 5 0\n",
"1\n8\n4 -1 3 1 8 4 1 2\n",
"1\n8\n6 2 2 1 8 4 4 7\n",
"1\n8\n4 -2 3 1 8 4 1 2\n",
"1\n8\n4 2 2 1 8 4 4 7\n",
"1\n8\n4 -2 3 1 8 4 1 4\n",
"1\n8\n6 2 3 1 8 4 3 7\n",
"1\n8\n6 0 3 1 8 5 5 7\n",
"1\n6\n6 2 6 1 8 4 5 7\n",
"3\n4\n1 3 2 7\n3\n1 2 3\n5\n2 1 1 5 3\n",
"1\n8\n6 1 3 1 8 6 5 7\n",
"1\n6\n12 0 3 1 8 5 5 7\n",
"1\n8\n6 2 6 1 8 8 5 7\n",
"1\n8\n6 0 3 1 8 6 1 0\n",
"1\n8\n6 0 3 1 8 7 1 0\n",
"1\n8\n4 0 3 1 8 6 0 1\n",
"1\n8\n4 -1 3 2 8 6 1 1\n",
"1\n8\n6 2 2 1 8 1 5 7\n",
"3\n4\n1 3 2 7\n3\n1 2 3\n5\n3 1 4 0 0\n",
"1\n8\n4 -1 3 1 8 4 2 2\n",
"1\n8\n4 -2 3 0 8 4 1 2\n",
"1\n8\n4 2 2 1 8 4 7 7\n",
"1\n8\n4 -2 3 0 8 4 1 4\n",
"1\n8\n6 2 3 1 15 4 3 7\n",
"1\n8\n6 0 3 1 8 5 5 2\n",
"3\n4\n1 3 2 7\n3\n1 2 3\n5\n2 0 1 5 3\n",
"1\n8\n6 1 3 1 8 6 6 7\n",
"1\n8\n6 2 6 1 0 8 5 7\n",
"1\n8\n6 0 3 1 8 6 0 0\n",
"1\n8\n6 0 3 1 6 7 1 0\n",
"1\n8\n4 0 3 1 8 4 0 1\n",
"1\n8\n4 -1 3 2 8 6 1 0\n",
"1\n8\n5 2 2 1 8 1 5 7\n",
"3\n4\n1 3 2 10\n3\n1 2 3\n5\n3 1 4 0 0\n",
"1\n8\n4 -2 3 1 8 4 2 2\n",
"1\n8\n4 2 2 1 10 4 7 7\n",
"1\n8\n6 2 3 1 15 4 1 7\n",
"1\n8\n6 0 3 1 8 5 5 3\n",
"1\n8\n6 1 3 0 8 6 6 7\n",
"1\n8\n6 2 2 1 0 8 5 7\n",
"1\n8\n6 0 3 1 8 6 0 1\n",
"1\n8\n6 0 3 0 6 7 1 0\n",
"1\n8\n5 2 2 1 8 1 5 2\n",
"1\n8\n6 2 3 2 15 4 1 7\n",
"1\n8\n12 0 3 1 8 5 5 3\n",
"1\n8\n5 2 2 1 6 1 5 2\n",
"1\n8\n6 2 3 2 15 3 1 7\n",
"1\n8\n5 2 2 1 6 1 5 0\n",
"1\n8\n6 2 0 2 15 3 1 7\n",
"1\n8\n5 2 2 1 6 0 5 0\n",
"1\n8\n6 2 3 1 13 4 5 7\n",
"3\n4\n1 3 2 4\n3\n1 2 3\n5\n2 1 4 1 3\n",
"1\n8\n11 0 3 1 8 4 5 7\n",
"1\n8\n11 0 3 1 8 6 5 7\n",
"1\n8\n6 2 6 1 8 6 0 7\n",
"3\n4\n1 3 2 7\n3\n1 2 3\n5\n2 1 4 5 -1\n",
"1\n8\n6 0 3 1 8 6 1 3\n",
"1\n8\n6 0 6 1 8 7 1 7\n",
"1\n8\n4 0 3 1 8 8 1 7\n",
"1\n8\n4 0 3 1 8 10 1 7\n",
"1\n8\n4 0 3 1 2 6 0 1\n",
"1\n8\n6 -1 3 1 8 6 1 1\n",
"1\n8\n6 2 6 1 8 6 2 5\n",
"1\n8\n4 -1 3 0 8 4 1 2\n",
"1\n8\n6 2 2 1 8 1 4 7\n",
"1\n8\n4 2 2 1 8 7 4 7\n",
"1\n8\n4 -2 3 1 8 4 1 5\n",
"1\n6\n6 0 6 1 8 4 5 7\n",
"1\n8\n6 1 5 1 8 6 5 7\n",
"1\n7\n6 0 3 1 8 7 1 0\n",
"1\n8\n4 0 3 1 8 6 -1 1\n",
"1\n8\n4 -1 2 2 8 6 1 1\n",
"1\n8\n6 2 0 1 8 1 5 7\n",
"1\n8\n4 -1 3 1 8 4 3 2\n",
"1\n8\n4 -3 3 0 8 4 1 2\n",
"1\n8\n8 2 2 1 8 4 7 7\n",
"1\n8\n3 0 3 1 8 5 5 2\n",
"1\n8\n6 2 6 1 0 8 5 0\n",
"1\n8\n4 0 3 1 8 4 -1 1\n",
"1\n8\n4 -1 3 0 8 6 1 0\n",
"1\n8\n5 1 2 1 8 1 5 7\n",
"1\n8\n4 1 2 1 10 4 7 7\n",
"1\n8\n6 2 3 1 15 4 1 1\n",
"1\n8\n6 0 3 1 8 5 8 3\n",
"1\n8\n6 1 1 0 8 6 6 7\n",
"1\n8\n6 -1 3 1 8 6 0 1\n",
"1\n8\n6 0 3 0 10 7 1 0\n",
"1\n8\n10 2 2 1 8 1 5 2\n",
"1\n8\n6 2 3 2 15 4 1 0\n",
"1\n8\n12 0 3 1 5 5 5 3\n",
"1\n8\n5 2 2 1 6 0 5 2\n",
"1\n8\n8 2 3 2 15 3 1 7\n",
"1\n8\n5 2 2 0 6 1 5 0\n",
"1\n8\n6 2 0 2 15 3 1 3\n",
"3\n4\n2 3 2 4\n3\n1 2 3\n5\n2 1 4 1 3\n",
"1\n8\n11 1 3 1 8 4 5 7\n",
"1\n8\n9 2 6 1 8 6 0 7\n",
"1\n8\n6 0 3 1 8 6 0 3\n",
"1\n8\n4 0 6 1 8 8 1 7\n",
"1\n8\n4 0 3 1 8 13 1 7\n",
"1\n8\n6 0 3 1 2 6 0 1\n",
"1\n8\n6 -1 3 1 8 6 2 1\n",
"1\n8\n6 2 6 1 8 6 2 3\n",
"1\n8\n4 -1 3 0 8 2 1 2\n",
"1\n8\n4 0 2 1 8 7 4 7\n",
"1\n8\n4 -2 3 1 8 4 1 0\n",
"1\n6\n6 0 6 1 8 5 5 7\n",
"1\n8\n6 1 5 1 15 6 5 7\n",
"1\n7\n6 1 3 1 8 7 1 0\n",
"1\n8\n4 1 3 1 8 6 -1 1\n",
"1\n8\n2 -1 2 2 8 6 1 1\n",
"1\n8\n6 2 0 1 8 1 2 7\n",
"1\n8\n4 -1 3 1 8 4 3 3\n",
"1\n8\n4 -3 3 -1 8 4 1 2\n",
"1\n8\n8 2 2 1 8 4 5 7\n",
"1\n8\n6 2 6 1 0 8 9 0\n",
"1\n6\n4 0 3 1 8 4 -1 1\n",
"1\n8\n3 -1 3 0 8 6 1 0\n",
"1\n8\n6 2 3 1 15 7 1 1\n",
"1\n8\n6 0 3 1 8 5 16 3\n",
"1\n8\n6 1 1 0 8 10 6 7\n",
"1\n8\n6 0 3 0 10 9 1 0\n",
"1\n8\n12 -1 3 1 5 5 5 3\n",
"1\n8\n5 4 2 1 6 0 5 2\n",
"1\n8\n5 2 2 0 6 1 5 1\n",
"1\n8\n6 2 0 4 15 3 1 3\n",
"3\n4\n2 6 2 4\n3\n1 2 3\n5\n2 1 4 1 3\n",
"1\n8\n9 2 6 1 8 6 -1 7\n",
"1\n8\n6 0 3 1 10 6 0 3\n",
"1\n8\n3 0 6 1 8 8 1 7\n",
"1\n8\n4 0 3 1 8 26 1 7\n",
"1\n8\n6 2 6 1 8 11 2 3\n",
"1\n8\n4 -1 3 0 8 3 1 2\n",
"1\n8\n4 0 2 1 8 9 4 7\n",
"1\n8\n4 -2 3 1 8 4 2 0\n",
"1\n6\n6 0 6 1 8 5 5 3\n",
"1\n8\n6 1 5 0 15 6 5 7\n",
"1\n7\n6 1 3 1 8 7 0 0\n",
"1\n8\n4 1 3 1 8 2 -1 1\n",
"1\n8\n2 -1 2 2 8 6 1 2\n",
"1\n8\n2 2 0 1 8 1 2 7\n",
"1\n8\n4 -3 3 -1 8 7 1 2\n",
"1\n8\n8 2 2 1 14 4 5 7\n",
"1\n8\n2 -1 3 0 8 6 1 0\n",
"1\n8\n6 0 3 1 8 5 16 4\n",
"1\n8\n6 1 1 0 8 15 6 7\n",
"1\n8\n6 0 3 0 10 9 1 -1\n",
"1\n8\n5 4 2 1 6 0 4 2\n",
"1\n8\n5 2 2 0 11 1 5 1\n",
"1\n8\n6 2 -1 4 15 3 1 3\n",
"3\n4\n2 6 3 4\n3\n1 2 3\n5\n2 1 4 1 3\n",
"1\n8\n9 2 6 1 8 6 -1 2\n",
"1\n8\n3 0 0 1 8 8 1 7\n",
"1\n8\n4 0 3 1 8 50 1 7\n",
"1\n8\n6 1 6 1 8 11 2 3\n",
"1\n8\n6 -1 3 0 8 3 1 2\n",
"1\n8\n4 0 2 1 4 9 4 7\n",
"1\n8\n4 -2 3 1 8 4 4 0\n",
"1\n8\n6 1 1 0 15 6 5 7\n",
"1\n7\n6 1 3 1 8 7 0 -1\n",
"1\n8\n3 1 3 1 8 2 -1 1\n",
"1\n8\n2 -1 2 2 8 1 1 2\n",
"1\n8\n4 -2 3 -1 8 7 1 2\n",
"1\n8\n8 4 2 1 14 4 5 7\n",
"1\n8\n2 0 3 0 8 6 1 0\n",
"1\n8\n6 0 3 1 8 5 5 4\n",
"1\n8\n6 1 1 1 8 15 6 7\n",
"1\n8\n6 0 6 0 10 9 1 -1\n",
"1\n8\n5 4 2 1 6 0 2 2\n",
"1\n8\n5 2 0 0 11 1 5 1\n",
"1\n8\n6 2 -2 4 15 3 1 3\n",
"1\n8\n9 2 6 1 11 6 -1 2\n",
"1\n8\n3 0 0 1 8 5 1 7\n",
"1\n8\n6 1 6 1 3 11 2 3\n",
"1\n8\n6 -1 3 0 2 3 1 2\n",
"1\n8\n6 1 2 0 15 6 5 7\n",
"1\n7\n6 1 5 1 8 7 0 -1\n",
"1\n8\n2 -1 2 2 8 1 0 2\n",
"1\n8\n8 6 2 1 14 4 5 7\n",
"1\n8\n2 0 3 0 8 6 1 -1\n",
"1\n8\n6 1 1 1 12 15 6 7\n",
"1\n8\n6 0 6 -1 10 9 1 -1\n"
],
"output": [
"\n1\n0\n2\n",
"2\n",
"2\n",
"1\n0\n2\n",
"1\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"1\n0\n2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"1\n0\n2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"1\n0\n2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"1\n0\n2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"1\n0\n2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"1\n0\n2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"1\n0\n2\n",
"2\n",
"2\n",
"2\n",
"1\n0\n2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
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"2\n",
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"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"1\n0\n2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"1\n0\n2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
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"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"1\n0\n2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You are given a permutation a consisting of n numbers 1, 2, ..., n (a permutation is an array in which each element from 1 to n occurs exactly once).
You can perform the following operation: choose some subarray (contiguous subsegment) of a and rearrange the elements in it in any way you want. But this operation cannot be applied to the whole array.
For example, if a = [2, 1, 4, 5, 3] and we want to apply the operation to the subarray a[2, 4] (the subarray containing all elements from the 2-nd to the 4-th), then after the operation, the array can become a = [2, 5, 1, 4, 3] or, for example, a = [2, 1, 5, 4, 3].
Your task is to calculate the minimum number of operations described above to sort the permutation a in ascending order.
Input
The first line contains a single integer t (1 ≤ t ≤ 2000) — the number of test cases.
The first line of the test case contains a single integer n (3 ≤ n ≤ 50) — the number of elements in the permutation.
The second line of the test case contains n distinct integers from 1 to n — the given permutation a.
Output
For each test case, output a single integer — the minimum number of operations described above to sort the array a in ascending order.
Example
Input
3
4
1 3 2 4
3
1 2 3
5
2 1 4 5 3
Output
1
0
2
Note
In the explanations, a[i, j] defines the subarray of a that starts from the i-th element and ends with the j-th element.
In the first test case of the example, you can select the subarray a[2, 3] and swap the elements in it.
In the second test case of the example, the permutation is already sorted, so you don't need to apply any operations.
In the third test case of the example, you can select the subarray a[3, 5] and reorder the elements in it so a becomes [2, 1, 3, 4, 5], and then select the subarray a[1, 2] and swap the elements in it, so a becomes [1, 2, 3, 4, 5].
### Input:
3
4
1 3 2 4
3
1 2 3
5
2 1 4 5 3
### Output:
1
0
2
### Input:
1
8
6 2 3 1 8 4 5 7
### Output:
2
### Code:
k = int(input())
a = []
import math
def nhap():
r = input()
r = r.split()
r =[int(i) for i in r]
return r
def kq(a):
minn = min(a)
maxx = max(a)
b = sorted(a)
if(b == a): return 0
if(a[0]== maxx and a[-1]== minn): return 3
if(a[0]== minn or a[-1]== maxx): return 1
return 2
for i in range(k):
num = int(input())
a.append(nhap())
for i in a:
print(kq(i))
|
156_D. Clues_10546
|
As Sherlock Holmes was investigating another crime, he found a certain number of clues. Also, he has already found direct links between some of those clues. The direct links between the clues are mutual. That is, the direct link between clues A and B and the direct link between clues B and A is the same thing. No more than one direct link can exist between two clues.
Of course Sherlock is able to find direct links between all clues. But it will take too much time and the criminals can use this extra time to hide. To solve the crime, Sherlock needs each clue to be linked to all other clues (maybe not directly, via some other clues). Clues A and B are considered linked either if there is a direct link between them or if there is a direct link between A and some other clue C which is linked to B.
Sherlock Holmes counted the minimum number of additional direct links that he needs to find to solve the crime. As it turns out, it equals T.
Please count the number of different ways to find exactly T direct links between the clues so that the crime is solved in the end. Two ways to find direct links are considered different if there exist two clues which have a direct link in one way and do not have a direct link in the other way.
As the number of different ways can turn out rather big, print it modulo k.
Input
The first line contains three space-separated integers n, m, k (1 ≤ n ≤ 105, 0 ≤ m ≤ 105, 1 ≤ k ≤ 109) — the number of clues, the number of direct clue links that Holmes has already found and the divisor for the modulo operation.
Each of next m lines contains two integers a and b (1 ≤ a, b ≤ n, a ≠ b), that represent a direct link between clues. It is guaranteed that any two clues are linked by no more than one direct link. Note that the direct links between the clues are mutual.
Output
Print the single number — the answer to the problem modulo k.
Examples
Input
2 0 1000000000
Output
1
Input
3 0 100
Output
3
Input
4 1 1000000000
1 4
Output
8
Note
The first sample only has two clues and Sherlock hasn't found any direct link between them yet. The only way to solve the crime is to find the link.
The second sample has three clues and Sherlock hasn't found any direct links between them. He has to find two of three possible direct links between clues to solve the crime — there are 3 ways to do it.
The third sample has four clues and the detective has already found one direct link between the first and the fourth clue. There are 8 ways to find two remaining clues to solve the crime.
|
def dfs(node, my_cc):
vis[node] = True
acc[my_cc]+=1
for i in adj[node]:
if not vis[i]:
dfs(i, my_cc)
def ittDfs(node):
queue = [node]
curr = 0
while(queue):
node = queue.pop()
if vis[node]:
continue
vis[node] = True
acc[cc] += 1
for i in adj[node]:
if not vis[i]:
queue.append(i)
def bfs(node):
vis[node] = True
cola = [node]
cur = 0
while (cur < len(cola)):
x = cola[cur]
acc[cc] += 1
cur += 1;
for i in adj[x]:
if not vis[i]:
vis[i] = True
cola.append(i)
if __name__ == '__main__':
_input = input().split()
n = int(_input[0])
m = int(_input[1])
k = int(_input[2])
adj = []
vis = []
acc = []
cc = 0
for i in range(n):
vis.append(False)
adj.append([])
acc.append(0)
for i in range(m):
_in2 = input().split()
v = int(_in2[0]) - 1
w = int(_in2[1]) - 1
adj[v].append(w)
adj[w].append(v)
for i in range(n):
if not vis[i]:
# dfs(i, cc)
ittDfs(i)
cc+=1
if cc == 1:
print(1 % k)
exit()
ans = 1
for i in range(cc - 2):
ans = ans * n
ans = ans % k
for i in range(cc):
ans = ans * acc[i]
ans = ans % k
print(ans)
|
{
"input": [
"4 1 1000000000\n1 4\n",
"3 0 100\n",
"2 0 1000000000\n",
"100000 0 1\n",
"2 1 100000\n1 2\n",
"2 1 819865995\n2 1\n",
"83 33 367711297\n14 74\n26 22\n55 19\n8 70\n6 42\n53 49\n54 56\n52 17\n62 44\n78 61\n76 4\n78 30\n51 2\n31 42\n33 67\n45 41\n64 62\n15 25\n33 35\n37 20\n38 65\n65 83\n61 14\n20 67\n62 47\n7 34\n78 41\n38 83\n26 69\n54 58\n11 62\n30 55\n15 74\n",
"8 4 17\n1 2\n2 3\n3 4\n4 1\n",
"10 45 220178113\n9 1\n8 1\n5 8\n1 5\n7 8\n6 7\n7 9\n6 2\n3 2\n1 4\n8 3\n8 9\n3 6\n4 5\n5 3\n10 4\n3 9\n9 6\n5 9\n2 9\n10 7\n1 10\n9 4\n3 10\n2 5\n7 1\n6 10\n6 5\n8 6\n8 4\n8 10\n1 6\n4 2\n9 10\n2 10\n7 3\n6 4\n7 5\n1 2\n4 3\n10 5\n4 7\n3 1\n7 2\n8 2\n",
"9 11 498920381\n2 8\n5 4\n1 8\n8 3\n4 9\n3 6\n8 9\n1 7\n5 1\n5 6\n9 6\n",
"2 1 1000\n1 2\n",
"30 18 918975816\n30 18\n23 1\n21 14\n14 8\n18 9\n23 29\n3 23\n29 19\n18 4\n27 19\n30 2\n9 10\n9 28\n16 15\n10 6\n18 12\n23 9\n19 14\n",
"3 2 11\n1 2\n2 3\n",
"2 0 753780649\n",
"3 3 975373207\n1 2\n1 3\n3 2\n",
"1 0 997185958\n",
"1 0 773734495\n",
"9 35 480175322\n6 3\n8 6\n7 5\n7 9\n3 4\n2 8\n5 3\n4 5\n4 6\n7 1\n7 6\n2 5\n8 3\n6 9\n8 4\n8 5\n6 1\n8 1\n3 2\n5 1\n8 9\n3 1\n8 7\n5 6\n5 9\n4 9\n7 4\n2 7\n3 9\n2 4\n7 3\n9 1\n2 9\n1 4\n1 2\n",
"1 0 10000\n",
"5 7 729985252\n2 3\n3 1\n2 5\n1 5\n1 2\n1 4\n4 3\n",
"57 28 776442742\n31 10\n25 28\n51 45\n14 40\n21 52\n53 51\n52 53\n4 6\n51 35\n53 15\n17 16\n40 44\n37 51\n33 43\n55 40\n42 16\n30 8\n19 45\n7 27\n31 8\n49 8\n43 44\n45 3\n16 22\n32 36\n52 36\n5 26\n2 23\n",
"10 5 1000000000\n1 2\n4 3\n5 6\n8 7\n10 9\n",
"24 68 862907549\n6 9\n16 22\n11 23\n12 17\n18 2\n15 5\n5 22\n16 4\n21 9\n7 11\n19 16\n9 13\n21 20\n5 24\n7 12\n17 1\n24 21\n23 7\n16 17\n16 18\n10 13\n18 7\n8 21\n13 5\n10 18\n4 11\n21 6\n15 13\n2 1\n20 16\n11 16\n22 19\n2 4\n21 1\n6 18\n24 12\n21 19\n6 14\n22 24\n11 20\n2 19\n1 11\n24 18\n14 8\n10 24\n5 3\n11 3\n17 4\n4 20\n2 10\n12 11\n24 7\n23 16\n2 3\n19 24\n22 1\n22 4\n4 6\n3 4\n11 13\n6 5\n18 23\n4 23\n22 13\n20 5\n2 5\n2 11\n9 5\n",
"10 0 766953983\n",
"67 2 818380264\n4 52\n15 44\n",
"3 2 21502109\n3 2\n1 2\n",
"47 51 283106191\n18 14\n30 26\n24 2\n18 41\n35 31\n16 24\n29 39\n6 12\n17 21\n7 19\n36 16\n27 39\n28 34\n22 35\n28 43\n40 5\n2 26\n18 16\n27 13\n21 6\n19 5\n35 30\n13 31\n7 10\n25 7\n44 42\n45 1\n35 47\n11 28\n47 46\n18 15\n27 16\n24 41\n10 8\n25 41\n4 40\n5 11\n24 6\n10 17\n41 38\n47 28\n8 29\n25 24\n35 37\n44 17\n24 47\n8 32\n33 11\n26 28\n23 9\n5 9\n",
"15 10 1\n1 2\n4 5\n6 3\n11 8\n8 5\n5 9\n9 1\n11 12\n12 1\n2 8\n",
"588 32 634894588\n535 26\n562 406\n70 368\n357 513\n108 361\n515 5\n159 56\n522 81\n169 229\n312 252\n492 43\n476 405\n524 555\n537 169\n142 149\n586 112\n7 159\n76 370\n295 376\n33 455\n278 225\n377 88\n526 308\n517 303\n300 576\n230 493\n588 525\n177 312\n356 215\n515 34\n196 236\n323 9\n",
"2 1 855341703\n2 1\n",
"100000 0 1000000000\n",
"2 1 719418546\n1 2\n",
"10 7 587143295\n1 10\n7 1\n1 8\n7 10\n8 10\n4 8\n6 8\n",
"10 30 407595309\n3 6\n6 10\n6 7\n7 10\n7 8\n3 10\n3 4\n1 4\n9 10\n8 4\n3 7\n5 1\n2 4\n6 2\n8 9\n10 5\n7 5\n10 4\n5 8\n8 2\n10 2\n1 6\n4 7\n2 3\n5 6\n8 10\n3 5\n1 8\n9 7\n1 9\n",
"5 10 93196990\n1 5\n1 4\n4 2\n1 3\n3 4\n1 2\n5 2\n5 4\n5 3\n2 3\n",
"1 0 21080115\n",
"7 7 302838679\n5 3\n4 1\n5 4\n6 5\n1 6\n3 2\n6 4\n",
"8 8 999999937\n1 2\n1 3\n1 4\n1 5\n1 6\n1 7\n1 8\n8 7\n",
"2 1 100\n1 2\n",
"1 0 1\n",
"1 0 10\n",
"6 4 100000\n1 4\n4 6\n6 1\n2 5\n",
"99 12 832839308\n66 23\n36 5\n16 57\n70 62\n94 96\n63 33\n99 23\n63 10\n6 85\n73 23\n69 46\n72 95\n",
"3 2 42\n1 2\n2 3\n",
"5 4 100000\n1 2\n2 3\n3 4\n4 5\n",
"3 3 100\n1 2\n2 3\n3 1\n",
"6 1 310732484\n4 2\n",
"9 33 321578376\n9 5\n6 3\n8 4\n4 1\n3 5\n2 6\n8 2\n7 6\n7 9\n8 6\n4 5\n1 6\n1 2\n5 6\n9 4\n7 8\n3 9\n9 6\n4 7\n7 2\n1 8\n4 6\n8 3\n3 7\n8 9\n5 7\n3 4\n7 1\n9 2\n5 1\n2 5\n9 1\n3 2\n",
"10 0 123456789\n",
"9 6 342597160\n1 2\n3 4\n4 5\n6 7\n7 8\n8 9\n",
"10 36 279447540\n10 7\n10 8\n1 8\n1 5\n4 5\n9 5\n3 9\n7 3\n10 4\n8 9\n2 10\n6 2\n4 8\n10 3\n1 4\n10 1\n10 6\n8 3\n3 6\n9 7\n10 5\n6 9\n3 1\n8 6\n4 9\n5 3\n9 10\n7 2\n2 4\n7 4\n5 6\n5 8\n7 5\n5 2\n6 7\n1 9\n",
"30 70 288262020\n27 18\n5 19\n23 17\n16 17\n29 17\n1 22\n23 5\n10 13\n22 26\n14 3\n8 3\n29 9\n9 1\n3 9\n16 4\n9 22\n10 22\n20 1\n3 7\n23 19\n26 8\n24 1\n5 7\n28 29\n20 11\n16 12\n6 9\n24 29\n30 4\n5 26\n18 21\n5 21\n30 6\n12 13\n16 23\n28 14\n30 1\n7 27\n7 19\n27 17\n5 30\n30 27\n28 30\n12 28\n27 9\n30 26\n20 18\n21 16\n8 30\n4 26\n13 22\n2 14\n12 30\n4 2\n6 12\n29 25\n19 29\n14 15\n3 23\n10 28\n7 1\n21 10\n4 12\n1 14\n7 21\n21 8\n17 26\n7 6\n26 29\n9 8\n",
"86 23 608266393\n62 78\n44 84\n42 37\n20 24\n40 36\n41 76\n14 38\n80 72\n39 52\n31 58\n71 17\n81 6\n32 65\n11 69\n43 86\n85 59\n28 77\n78 64\n15 19\n36 39\n53 49\n48 75\n33 85\n",
"2 1 110000\n1 2\n",
"8 4 17\n1 3\n2 3\n3 4\n4 1\n",
"30 18 918975816\n30 18\n23 1\n21 14\n14 8\n17 9\n23 29\n3 23\n29 19\n18 4\n27 19\n30 2\n9 10\n9 28\n16 15\n10 6\n18 12\n23 9\n19 14\n",
"57 28 776442742\n31 10\n25 28\n51 45\n14 40\n21 52\n53 51\n52 53\n4 6\n51 35\n53 15\n17 16\n40 44\n37 51\n33 43\n55 52\n42 16\n30 8\n19 45\n7 27\n31 8\n49 8\n43 44\n45 3\n16 22\n32 36\n52 36\n5 26\n2 23\n",
"10 5 1000000000\n1 2\n4 3\n5 2\n8 7\n10 9\n",
"10 0 56786793\n",
"15 10 1\n1 2\n4 5\n6 3\n11 8\n8 5\n5 2\n9 1\n11 12\n12 1\n2 8\n",
"588 32 634894588\n535 26\n562 406\n70 368\n357 513\n108 361\n515 5\n159 56\n522 81\n169 229\n312 252\n492 43\n476 405\n524 555\n537 11\n142 149\n586 112\n7 159\n76 370\n295 376\n33 455\n278 225\n377 88\n526 308\n517 303\n300 576\n230 493\n588 525\n177 312\n356 215\n515 34\n196 236\n323 9\n",
"2 1 855341703\n2 2\n",
"8 10 93196990\n1 5\n1 4\n4 2\n1 3\n3 4\n1 2\n5 2\n5 4\n5 3\n2 3\n",
"7 7 302838679\n5 3\n4 1\n5 4\n6 5\n1 6\n1 2\n6 4\n",
"99 12 832839308\n66 23\n36 5\n16 57\n70 62\n94 96\n63 33\n99 23\n63 10\n6 9\n73 23\n69 46\n72 95\n",
"6 1 310732484\n4 1\n",
"8 1 1000000000\n1 4\n",
"3 0 110\n",
"57 28 776442742\n31 10\n25 28\n51 45\n14 40\n21 52\n53 57\n52 53\n4 6\n51 35\n53 15\n17 16\n40 44\n37 51\n33 43\n55 52\n42 16\n30 8\n19 45\n7 27\n31 8\n49 8\n43 44\n45 3\n16 22\n32 36\n52 36\n5 26\n2 23\n",
"10 0 24779564\n",
"4 3 100\n1 2\n2 3\n3 1\n",
"14 36 279447540\n10 7\n10 8\n1 8\n1 5\n4 5\n9 5\n3 9\n7 3\n10 4\n8 9\n2 10\n6 2\n4 8\n8 3\n1 4\n10 1\n10 6\n8 3\n3 6\n9 7\n10 5\n6 9\n3 1\n8 6\n4 9\n5 3\n9 10\n7 2\n2 4\n7 4\n5 6\n5 8\n7 5\n5 2\n6 7\n1 9\n",
"16 1 1000000000\n1 4\n",
"2 1 989003834\n2 1\n",
"9 11 498920381\n2 8\n5 4\n1 8\n8 3\n4 9\n3 2\n8 9\n1 7\n5 1\n5 6\n9 6\n",
"2 1 1100\n1 2\n",
"3 3 975373207\n2 2\n1 3\n3 2\n",
"9 35 480175322\n5 3\n8 6\n7 5\n7 9\n3 4\n2 8\n5 3\n4 5\n4 6\n7 1\n7 6\n2 5\n8 3\n6 9\n8 4\n8 5\n6 1\n8 1\n3 2\n5 1\n8 9\n3 1\n8 7\n5 6\n5 9\n4 9\n7 4\n2 7\n3 9\n2 4\n7 3\n9 1\n2 9\n1 4\n1 2\n",
"1 0 10001\n",
"5 7 729985252\n2 3\n3 1\n2 5\n1 5\n1 2\n1 2\n4 3\n",
"24 68 862907549\n6 9\n16 22\n11 23\n12 17\n18 2\n15 5\n5 22\n16 4\n21 9\n7 11\n19 16\n9 13\n21 20\n5 24\n7 12\n17 1\n24 21\n23 7\n16 17\n16 18\n10 13\n18 7\n8 21\n13 5\n10 18\n4 11\n21 6\n15 13\n2 1\n20 16\n11 16\n22 19\n2 4\n21 1\n6 18\n24 12\n21 19\n6 14\n22 24\n11 20\n2 19\n1 11\n24 18\n14 8\n10 24\n5 3\n11 3\n17 4\n1 20\n2 10\n12 11\n24 7\n23 16\n2 3\n19 24\n22 1\n22 4\n4 6\n3 4\n11 13\n6 5\n18 23\n4 23\n22 13\n20 5\n2 5\n2 11\n9 5\n",
"3 2 31007477\n3 2\n1 2\n",
"10 30 566439979\n3 6\n6 10\n6 7\n7 10\n7 8\n3 10\n3 4\n1 4\n9 10\n8 4\n3 7\n5 1\n2 4\n6 2\n8 9\n10 5\n7 5\n10 4\n5 8\n8 2\n10 2\n1 6\n4 7\n2 3\n5 6\n8 10\n3 5\n1 8\n9 7\n1 9\n",
"2 0 21080115\n",
"2 1 100\n2 2\n",
"1 0 11\n",
"6 3 100\n1 2\n2 3\n3 1\n",
"9 33 321578376\n9 5\n6 3\n8 4\n4 1\n3 5\n2 6\n8 2\n7 6\n7 9\n8 6\n4 5\n1 6\n1 2\n5 6\n9 4\n7 8\n3 9\n9 9\n4 7\n7 2\n1 8\n4 6\n8 3\n3 7\n8 9\n5 7\n3 4\n7 1\n9 2\n5 1\n2 5\n9 1\n3 2\n",
"10 36 279447540\n10 7\n10 8\n1 8\n1 5\n4 5\n9 5\n3 9\n7 3\n10 4\n8 9\n2 10\n6 2\n4 8\n8 3\n1 4\n10 1\n10 6\n8 3\n3 6\n9 7\n10 5\n6 9\n3 1\n8 6\n4 9\n5 3\n9 10\n7 2\n2 4\n7 4\n5 6\n5 8\n7 5\n5 2\n6 7\n1 9\n",
"30 70 288262020\n27 18\n5 19\n23 17\n16 17\n29 17\n1 22\n23 5\n10 13\n22 26\n14 3\n8 3\n29 9\n9 1\n3 9\n16 4\n9 22\n10 22\n20 1\n3 7\n23 19\n26 8\n24 1\n5 7\n28 29\n20 11\n16 12\n6 9\n24 29\n30 4\n5 26\n18 21\n5 21\n30 6\n12 13\n16 23\n28 14\n30 1\n7 27\n7 19\n27 17\n5 30\n30 27\n28 30\n12 28\n27 9\n30 26\n20 18\n21 16\n8 30\n4 26\n23 22\n2 14\n12 30\n4 2\n6 12\n29 25\n19 29\n14 15\n3 23\n10 28\n7 1\n21 10\n4 12\n1 14\n7 21\n21 8\n17 26\n7 6\n26 29\n9 8\n",
"4 4 17\n1 3\n2 3\n3 4\n4 1\n",
"30 18 918975816\n30 18\n23 1\n21 9\n14 8\n17 9\n23 29\n3 23\n29 19\n18 4\n27 19\n30 2\n9 10\n9 28\n16 15\n10 6\n18 12\n23 9\n19 14\n",
"9 35 480175322\n5 3\n8 4\n7 5\n7 9\n3 4\n2 8\n5 3\n4 5\n4 6\n7 1\n7 6\n2 5\n8 3\n6 9\n8 4\n8 5\n6 1\n8 1\n3 2\n5 1\n8 9\n3 1\n8 7\n5 6\n5 9\n4 9\n7 4\n2 7\n3 9\n2 4\n7 3\n9 1\n2 9\n1 4\n1 2\n",
"5 7 729985252\n2 3\n5 1\n2 5\n1 5\n1 2\n1 2\n4 3\n",
"24 68 862907549\n6 9\n16 22\n11 23\n12 17\n18 2\n15 5\n5 22\n16 4\n21 9\n7 11\n19 16\n9 13\n21 20\n5 24\n7 12\n17 1\n24 21\n23 7\n16 17\n16 18\n10 13\n18 7\n8 21\n13 5\n10 18\n4 11\n21 6\n15 13\n2 1\n20 16\n11 16\n22 19\n2 4\n21 1\n6 18\n24 12\n21 19\n6 14\n22 24\n11 20\n2 19\n1 11\n24 18\n14 8\n10 24\n5 3\n11 3\n17 4\n1 20\n2 10\n12 11\n24 7\n23 22\n2 3\n19 24\n22 1\n22 4\n4 6\n3 4\n11 13\n6 5\n18 23\n4 23\n22 13\n20 5\n2 5\n2 11\n9 5\n",
"3 2 48180342\n3 2\n1 2\n",
"15 10 1\n1 2\n4 5\n6 3\n11 8\n6 5\n5 2\n9 1\n11 12\n12 1\n2 8\n",
"588 32 634894588\n535 26\n562 406\n70 368\n357 513\n108 361\n515 5\n159 54\n522 81\n169 229\n312 252\n492 43\n476 405\n524 555\n537 11\n142 149\n586 112\n7 159\n76 370\n295 376\n33 455\n278 225\n377 88\n526 308\n517 303\n300 576\n230 493\n588 525\n177 312\n356 215\n515 34\n196 236\n323 9\n",
"10 30 566439979\n3 6\n6 10\n6 7\n7 10\n7 8\n3 10\n3 4\n1 4\n9 10\n8 4\n3 7\n5 1\n2 4\n6 2\n8 9\n10 5\n7 5\n10 4\n5 8\n8 2\n8 2\n1 6\n4 7\n2 3\n5 6\n8 10\n3 5\n1 8\n9 7\n1 9\n",
"8 10 93196990\n1 1\n1 4\n4 2\n1 3\n3 4\n1 2\n5 2\n5 4\n5 3\n2 3\n",
"2 0 24022820\n",
"1 0 14\n",
"9 33 321578376\n9 5\n6 3\n8 4\n4 1\n3 5\n2 6\n8 2\n7 6\n7 9\n8 6\n4 5\n1 6\n1 2\n5 6\n9 4\n8 8\n3 9\n9 9\n4 7\n7 2\n1 8\n4 6\n8 3\n3 7\n8 9\n5 7\n3 4\n7 1\n9 2\n5 1\n2 5\n9 1\n3 2\n",
"30 70 288262020\n27 18\n5 19\n23 25\n16 17\n29 17\n1 22\n23 5\n10 13\n22 26\n14 3\n8 3\n29 9\n9 1\n3 9\n16 4\n9 22\n10 22\n20 1\n3 7\n23 19\n26 8\n24 1\n5 7\n28 29\n20 11\n16 12\n6 9\n24 29\n30 4\n5 26\n18 21\n5 21\n30 6\n12 13\n16 23\n28 14\n30 1\n7 27\n7 19\n27 17\n5 30\n30 27\n28 30\n12 28\n27 9\n30 26\n20 18\n21 16\n8 30\n4 26\n23 22\n2 14\n12 30\n4 2\n6 12\n29 25\n19 29\n14 15\n3 23\n10 28\n7 1\n21 10\n4 12\n1 14\n7 21\n21 8\n17 26\n7 6\n26 29\n9 8\n",
"9 35 480175322\n5 3\n8 4\n7 5\n7 9\n3 4\n2 8\n5 3\n4 5\n4 6\n7 2\n7 6\n2 5\n8 3\n6 9\n8 4\n8 5\n6 1\n8 1\n3 2\n5 1\n8 9\n3 1\n8 7\n5 6\n5 9\n4 9\n7 4\n2 7\n3 9\n2 4\n7 3\n9 1\n2 9\n1 4\n1 2\n"
],
"output": [
"8\n",
"3\n",
"1\n",
"0\n",
"1\n",
"1\n",
"131377693\n",
"8\n",
"1\n",
"1\n",
"1\n",
"782410104\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"135540294\n",
"32000\n",
"1\n",
"100000000\n",
"517849052\n",
"1\n",
"189974\n",
"0\n",
"478655040\n",
"1\n",
"0\n",
"1\n",
"6000\n",
"1\n",
"1\n",
"1\n",
"6\n",
"1\n",
"1\n",
"0\n",
"1\n",
"36\n",
"71450536\n",
"1\n",
"1\n",
"1\n",
"432\n",
"1\n",
"100000000\n",
"216\n",
"1\n",
"1\n",
"235915236\n",
"1\n",
"8\n",
"285778512\n",
"284121670\n",
"24000\n",
"43213207\n",
"0\n",
"3312132\n",
"1",
"320\n",
"6",
"71450536\n",
"432\n",
"65536\n",
"3\n",
"451800980\n",
"881744\n",
"3",
"27440\n",
"254740992\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1",
"1",
"1\n",
"8\n",
"1\n",
"1\n",
"1\n",
"1\n",
"285778512\n",
"1\n",
"1\n",
"1\n",
"1\n",
"0\n",
"3312132\n",
"1\n",
"320\n",
"1",
"1\n",
"1\n",
"1\n",
"1\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
As Sherlock Holmes was investigating another crime, he found a certain number of clues. Also, he has already found direct links between some of those clues. The direct links between the clues are mutual. That is, the direct link between clues A and B and the direct link between clues B and A is the same thing. No more than one direct link can exist between two clues.
Of course Sherlock is able to find direct links between all clues. But it will take too much time and the criminals can use this extra time to hide. To solve the crime, Sherlock needs each clue to be linked to all other clues (maybe not directly, via some other clues). Clues A and B are considered linked either if there is a direct link between them or if there is a direct link between A and some other clue C which is linked to B.
Sherlock Holmes counted the minimum number of additional direct links that he needs to find to solve the crime. As it turns out, it equals T.
Please count the number of different ways to find exactly T direct links between the clues so that the crime is solved in the end. Two ways to find direct links are considered different if there exist two clues which have a direct link in one way and do not have a direct link in the other way.
As the number of different ways can turn out rather big, print it modulo k.
Input
The first line contains three space-separated integers n, m, k (1 ≤ n ≤ 105, 0 ≤ m ≤ 105, 1 ≤ k ≤ 109) — the number of clues, the number of direct clue links that Holmes has already found and the divisor for the modulo operation.
Each of next m lines contains two integers a and b (1 ≤ a, b ≤ n, a ≠ b), that represent a direct link between clues. It is guaranteed that any two clues are linked by no more than one direct link. Note that the direct links between the clues are mutual.
Output
Print the single number — the answer to the problem modulo k.
Examples
Input
2 0 1000000000
Output
1
Input
3 0 100
Output
3
Input
4 1 1000000000
1 4
Output
8
Note
The first sample only has two clues and Sherlock hasn't found any direct link between them yet. The only way to solve the crime is to find the link.
The second sample has three clues and Sherlock hasn't found any direct links between them. He has to find two of three possible direct links between clues to solve the crime — there are 3 ways to do it.
The third sample has four clues and the detective has already found one direct link between the first and the fourth clue. There are 8 ways to find two remaining clues to solve the crime.
### Input:
4 1 1000000000
1 4
### Output:
8
### Input:
3 0 100
### Output:
3
### Code:
def dfs(node, my_cc):
vis[node] = True
acc[my_cc]+=1
for i in adj[node]:
if not vis[i]:
dfs(i, my_cc)
def ittDfs(node):
queue = [node]
curr = 0
while(queue):
node = queue.pop()
if vis[node]:
continue
vis[node] = True
acc[cc] += 1
for i in adj[node]:
if not vis[i]:
queue.append(i)
def bfs(node):
vis[node] = True
cola = [node]
cur = 0
while (cur < len(cola)):
x = cola[cur]
acc[cc] += 1
cur += 1;
for i in adj[x]:
if not vis[i]:
vis[i] = True
cola.append(i)
if __name__ == '__main__':
_input = input().split()
n = int(_input[0])
m = int(_input[1])
k = int(_input[2])
adj = []
vis = []
acc = []
cc = 0
for i in range(n):
vis.append(False)
adj.append([])
acc.append(0)
for i in range(m):
_in2 = input().split()
v = int(_in2[0]) - 1
w = int(_in2[1]) - 1
adj[v].append(w)
adj[w].append(v)
for i in range(n):
if not vis[i]:
# dfs(i, cc)
ittDfs(i)
cc+=1
if cc == 1:
print(1 % k)
exit()
ans = 1
for i in range(cc - 2):
ans = ans * n
ans = ans % k
for i in range(cc):
ans = ans * acc[i]
ans = ans % k
print(ans)
|
177_G1. Fibonacci Strings_10549
|
Fibonacci strings are defined as follows:
* f1 = «a»
* f2 = «b»
* fn = fn - 1 fn - 2, n > 2
Thus, the first five Fibonacci strings are: "a", "b", "ba", "bab", "babba".
You are given a Fibonacci string and m strings si. For each string si, find the number of times it occurs in the given Fibonacci string as a substring.
Input
The first line contains two space-separated integers k and m — the number of a Fibonacci string and the number of queries, correspondingly.
Next m lines contain strings si that correspond to the queries. It is guaranteed that strings si aren't empty and consist only of characters "a" and "b".
The input limitations for getting 30 points are:
* 1 ≤ k ≤ 3000
* 1 ≤ m ≤ 3000
* The total length of strings si doesn't exceed 3000
The input limitations for getting 100 points are:
* 1 ≤ k ≤ 1018
* 1 ≤ m ≤ 104
* The total length of strings si doesn't exceed 105
Please do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64d specifier.
Output
For each string si print the number of times it occurs in the given Fibonacci string as a substring. Since the numbers can be large enough, print them modulo 1000000007 (109 + 7). Print the answers for the strings in the order in which they are given in the input.
Examples
Input
6 5
a
b
ab
ba
aba
Output
3
5
3
3
1
|
F = ['', 'a', 'b', 'ba', 'bab', 'babba', 'babbabab', 'babbababbabba', 'babbababbabbababbabab', 'babbababbabbababbababbabbababbabba', 'babbababbabbababbababbabbababbabbababbababbabbababbabab', 'babbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabba', 'babbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabab', 'babbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabba', 'babbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabab', 'babbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabba', 'babbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabab', 'babbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabba', 'babbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabab', 'babbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabba', 'babbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabab']
d = 1000000007
def sqr(t):
return [[sum(t[i][k] * t[k][j] for k in range(4)) % d for j in range(4)] for i in range(4)]
def mul(a, b):
return [[sum(a[i][k] * b[k][j] for k in range(4)) % d for j in range(4)] for i in range(4)]
def fib(k):
s, p = format(k, 'b')[:: -1], [[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]]
t = [[[0, 1, 0, 0], [1, 1, 1, 0], [0, 0, 0, 1], [0, 0, 1, 0]]] + [0] * (len(s) - 1)
for i in range(1, len(s)):
t[i] = sqr(t[i - 1])
for i, k in enumerate(s):
if k == '1': p = mul(p, t[i])
return p
def cnt(t, p):
s, i = 0, p.find(t) + 1
while i > 0:
i = p.find(t, i) + 1
s += 1
return s
def f(t, p, k):
l = len(t) - 1
if l: x, y = cnt(t, F[k - 1][- l: ] + F[k][:l ]), cnt(t, F[k][- l: ] + F[k + 1][:l ])
else: x, y = 0, 0
a, b = cnt(t, F[k - 1]), cnt(t, F[k])
return (p[0] * a + p[1] * b + p[2] * y + p[3] * x) % d
k, m = map(int, input().split())
if k > 15:
a, b = fib(k - 7)[0], fib(k - 18)[0]
for i in range(m):
t = input()
if len(t) < len(F[7]): print(f(t, a, 8))
else: print(f(t, b, 19))
else:
p = F[k]
for i in range(m):
print(cnt(input(), p))
|
{
"input": [
"6 5\na\nb\nab\nba\naba\n",
"50 100\nbb\naa\nb\nbaa\nbbba\naa\nba\na\nabba\nbaa\naa\naab\nab\nbabb\naabb\nbaa\nbaaa\nbaa\naab\nbba\nbb\naba\naaba\nbab\naaba\naa\naaaa\nbabb\nbbb\naaba\naaa\nab\nbab\nb\nb\naa\naaab\naa\nbba\nbaa\nbabb\nbaba\nba\naaba\nbba\nba\nab\nabb\nb\nba\nbbb\nba\naaa\nbbb\nbaa\nbb\na\naaa\naaba\nab\nbba\nba\nb\nbbb\naaa\na\na\nb\nb\naba\nbb\nba\na\nb\nbaa\nb\naaaa\na\naaab\nbaba\nba\nbb\nbaba\nab\nbaaa\nbbbb\na\naabb\nab\nb\nb\naaa\nb\nb\nabab\nabb\nb\nb\nbb\nb\n",
"15 100\nb\na\nb\na\nb\na\nb\na\nb\na\nb\na\nb\na\nb\na\nb\na\nb\na\nb\na\nb\na\nb\na\nb\na\nb\na\nb\na\nb\na\nb\na\nb\na\nb\na\nb\na\nb\na\nb\na\nb\na\nb\na\nb\na\nb\na\nb\na\nb\na\nb\na\nb\na\nb\na\nb\na\nb\na\nb\na\nb\na\nb\na\nb\na\nb\na\nb\na\nb\na\nb\na\nb\na\nb\na\nb\na\nb\na\nb\na\nb\na\nb\na\nb\na\n",
"15 100\nbbb\nabb\nbab\naab\nbba\naba\nbaa\naaa\nbbb\nabb\nbab\naab\nbba\naba\nbaa\naaa\nbbb\nabb\nbab\naab\nbba\naba\nbaa\naaa\nbbb\nabb\nbab\naab\nbba\naba\nbaa\naaa\nbbb\nabb\nbab\naab\nbba\naba\nbaa\naaa\nbbb\nabb\nbab\naab\nbba\naba\nbaa\naaa\nbbb\nabb\nbab\naab\nbba\naba\nbaa\naaa\nbbb\nabb\nbab\naab\nbba\naba\nbaa\naaa\nbbb\nabb\nbab\naab\nbba\naba\nbaa\naaa\nbbb\nabb\nbab\naab\nbba\naba\nbaa\naaa\nbbb\nabb\nbab\naab\nbba\naba\nbaa\naaa\nbbb\nabb\nbab\naab\nbba\naba\nbaa\naaa\nbbb\nabb\nbab\naab\n",
"10 10\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\n",
"2 14\na\nb\naa\nab\nba\nbb\naaa\naab\naba\nabb\nbaa\nbab\nbba\nbbb\n",
"3 10\nbbb\nabb\nbab\naab\nbba\naba\nbaa\naaa\nbbb\nabb\n",
"50 100\nb\naab\nab\naaa\na\naab\naaa\nbb\na\na\nb\naab\nbbb\naa\nbbb\nb\nab\nab\nbbb\nb\nbaa\na\nbab\nbbb\na\naba\nab\na\nba\nb\nbba\naba\nba\nbba\nb\nb\nb\nb\nab\na\nabb\nab\nbb\nbba\nb\nbbb\nbb\nb\naba\naab\nba\nbb\na\na\nbb\nba\nbaa\nba\nba\na\nb\nbb\nb\nbaa\nbab\nbba\nb\nbb\nbbb\nb\naba\nbba\nbba\naaa\nab\na\nbbb\nab\nb\nba\nbab\nb\naab\nbb\naba\nb\na\naa\nbaa\nbbb\naa\naba\nb\nbb\nba\nb\nb\naaa\nab\nba\n",
"4 14\na\nb\naa\nab\nba\nbb\naaa\naab\naba\nabb\nbaa\nbab\nbba\nbbb\n",
"2 10\nb\na\nb\na\nb\na\nb\na\nb\na\n",
"10 10\nbbb\nabb\nbab\naab\nbba\naba\nbaa\naaa\nbbb\nabb\n",
"50 100\nb\naa\na\na\na\nb\na\nb\nbb\na\naa\naa\naa\nba\naa\na\na\naa\na\na\naa\nb\nbb\naa\naa\nbb\nb\nbb\na\naa\naa\naa\na\na\nb\nb\na\naa\nb\naa\nab\nb\nb\na\naa\nbb\nb\nb\na\nb\na\na\nb\na\nbb\nb\nab\nbb\na\naa\naa\nb\nb\na\nbb\nba\naa\nba\nbb\nba\nbb\na\nb\na\nba\na\nab\na\nbb\nab\na\nab\nbb\na\na\nb\na\nba\na\nbb\nb\nab\nab\naa\na\nab\nab\nbb\nab\nab\n",
"15 100\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\n",
"3 14\na\nb\naa\nab\nba\nbb\naaa\naab\naba\nabb\nbaa\nbab\nbba\nbbb\n",
"1 14\na\nb\naa\nab\nba\nbb\naaa\naab\naba\nabb\nbaa\nbab\nbba\nbbb\n",
"5 14\na\nb\naa\nab\nba\nbb\naaa\naab\naba\nabb\nbaa\nbab\nbba\nbbb\n",
"50 100\na\na\nb\na\na\nb\nb\nb\na\na\nb\nb\na\na\na\na\nb\nb\na\nb\nb\nb\na\na\na\na\na\na\nb\nb\na\nb\na\nb\na\nb\na\nb\nb\nb\na\na\nb\na\na\na\nb\na\nb\na\na\na\nb\na\nb\na\na\nb\na\na\nb\na\na\na\na\nb\na\nb\na\nb\nb\na\nb\nb\nb\na\nb\nb\nb\nb\nb\nb\nb\nb\nb\nb\na\na\na\nb\nb\nb\nb\na\na\na\nb\nb\nb\na\n",
"1 10\nb\na\nb\na\nb\na\nb\na\nb\na\n",
"50 100\nbb\naa\nb\nbaa\nbbba\naa\nba\na\nabba\nbaa\naa\naab\nab\nbabb\naabb\nbaa\nbaaa\nbaa\naab\nbba\nbb\naba\naaba\nbab\naaaa\naa\naaaa\nbabb\nbbb\naaba\naaa\nab\nbab\nb\nb\naa\naaab\naa\nbba\nbaa\nbabb\nbaba\nba\naaba\nbba\nba\nab\nabb\nb\nba\nbbb\nba\naaa\nbbb\nbaa\nbb\na\naaa\naaba\nab\nbba\nba\nb\nbbb\naaa\na\na\nb\nb\naba\nbb\nba\na\nb\nbaa\nb\naaaa\na\naaab\nbaba\nba\nbb\nbaba\nab\nbaaa\nbbbb\na\naabb\nab\nb\nb\naaa\nb\nb\nabab\nabb\nb\nb\nbb\nb\n",
"10 10\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\naa\n",
"2 14\na\nb\naa\nab\nba\nbb\naaa\naab\naba\nabb\naab\nbab\nbba\nbbb\n",
"50 100\nb\naab\nab\naaa\na\naab\naba\nbb\na\na\nb\naab\nbbb\naa\nbbb\nb\nab\nab\nbbb\nb\nbaa\na\nbab\nbbb\na\naba\nab\na\nba\nb\nbba\naba\nba\nbba\nb\nb\nb\nb\nab\na\nabb\nab\nbb\nbba\nb\nbbb\nbb\nb\naba\naab\nba\nbb\na\na\nbb\nba\nbaa\nba\nba\na\nb\nbb\nb\nbaa\nbab\nbba\nb\nbb\nbbb\nb\naba\nbba\nbba\naaa\nab\na\nbbb\nab\nb\nba\nbab\nb\naab\nbb\naba\nb\na\naa\nbaa\nbbb\naa\naba\nb\nbb\nba\nb\nb\naaa\nab\nba\n",
"4 14\na\nb\naa\nab\nba\nbb\naaa\naab\naba\nbba\nbaa\nbab\nbba\nbbb\n",
"15 100\nbb\nab\nbb\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\n",
"3 14\na\nb\naa\nab\nab\nbb\naaa\naab\naba\nabb\nbaa\nbab\nbba\nbbb\n",
"5 14\na\nb\naa\nab\nbb\nbb\naaa\naab\naba\nabb\nbaa\nbab\nbba\nbbb\n",
"50 100\na\na\nb\na\na\nb\nb\nb\na\na\nb\nb\na\na\na\na\nb\nb\na\nb\nb\nb\na\na\na\na\na\na\nb\nb\na\nb\na\nb\na\nb\na\nb\nb\nb\na\na\nb\na\na\na\nb\na\nb\na\na\na\na\na\nb\na\na\nb\na\na\nb\na\na\na\na\nb\na\nb\na\nb\nb\na\nb\nb\nb\na\nb\nb\nb\nb\nb\nb\nb\nb\nb\nb\na\na\na\nb\nb\nb\nb\na\na\na\nb\nb\nb\na\n",
"6 4\na\nb\nab\nba\naba\n",
"50 100\nb\naab\nab\naaa\na\naab\naba\nbb\na\na\nb\naab\nbbb\naa\nbbb\nb\nab\nab\nbbb\nb\nbaa\na\nbab\nbbb\na\naba\nab\na\nba\nb\nbba\naba\nba\nbba\nb\na\nb\nb\nab\na\nabb\nab\nbb\nbba\nb\nbbb\nbb\nb\naba\naab\nba\nbb\na\na\nbb\nba\nbaa\nba\nba\na\nb\nbb\nb\nbaa\nbab\nbba\nb\nbb\nbbb\nb\naba\nbba\nbba\naaa\nab\na\nbbb\nab\nb\nba\nbab\nb\naab\nbb\naba\nb\na\naa\nbaa\nbbb\naa\naba\nb\nbb\nba\nb\nb\naaa\nab\nba\n",
"15 100\nbb\nab\nbb\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nab\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\n",
"1 14\na\nb\naa\nab\nab\nbb\naaa\naab\naba\nabb\nbaa\nbab\nbba\nbbb\n",
"6 4\na\nb\nab\nbb\naba\n",
"10 8\nbb\nab\nab\naa\nbb\nab\nba\naa\nbb\naa\n",
"50 100\nb\naab\nab\naaa\na\naab\naba\nbb\na\na\nb\naab\nbbb\naa\nbbb\nb\nab\nab\nbbb\na\nbaa\na\nbab\nbbb\na\naba\nab\na\nba\nb\nbba\naba\nba\nbba\nb\na\nb\nb\nab\na\nabb\nab\nbb\nbba\nb\nbbb\nbb\nb\naba\naab\nba\nbb\na\na\nbb\nba\nbaa\nba\nba\na\nb\nbb\nb\nbaa\nbab\nbba\nb\nbb\nbbb\nb\naba\nbba\nbba\naaa\nab\na\nbbb\nab\nb\nba\nbab\nb\naab\nbb\naba\nb\na\naa\nbaa\nbbb\naa\naba\nb\nbb\nba\nb\nb\naaa\nab\nba\n",
"15 100\nbb\nab\nbb\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nab\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nbb\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\n",
"5 14\na\nb\nab\nab\nbb\nbb\naaa\naab\naba\nbba\nbaa\nbab\nbba\nbbb\n",
"6 1\na\nb\nab\nba\naba\n",
"50 100\nb\naab\nab\naaa\na\naab\naba\nbb\na\na\nb\naab\nbbb\naa\nbbb\nb\nab\nab\nbbb\na\nbaa\na\nbab\nbbb\na\naba\nab\na\nba\nb\nbba\naba\nba\nbba\nb\na\nb\nb\nab\na\nabb\nab\nbb\nbba\nb\nbbb\nbb\nb\naba\naab\nba\nbb\na\na\nbb\nba\nbaa\nba\nba\na\nb\nbb\nb\nbaa\nbab\nbba\nb\nbb\nbbb\nb\naba\nbba\nbba\naaa\nab\na\nbbb\nab\nb\nba\nbbb\nb\naab\nbb\naba\nb\na\naa\nbaa\nbbb\naa\naba\nb\nbb\nba\nb\nb\naaa\nab\nba\n",
"15 100\nbb\nab\nbb\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nab\nab\nab\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nbb\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\n",
"50 100\nb\naab\nab\naaa\na\naab\naba\nbb\na\na\nb\naab\nbbb\naa\nbbb\nb\nab\nab\nbbb\na\nbaa\na\nbab\nbbb\na\naba\nab\na\nba\nb\nbba\naba\nba\nbba\nb\na\nb\nb\nab\na\nabb\nab\nbb\nbba\nb\nbbb\nbb\nb\naba\naab\nba\nbb\na\na\nbb\nba\nbaa\nba\nba\na\nb\nbb\nb\nbaa\nbab\nbba\nb\nbb\nbbb\nb\naba\nbba\nbba\naaa\nab\na\nbbb\nab\nb\nba\nbbb\nb\naab\nbb\naba\nb\na\naa\nbaa\nbba\naa\naba\nb\nbb\nba\nb\nb\naaa\nab\nba\n",
"15 100\nbb\nab\nbb\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\nab\nab\nab\nab\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nbb\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\n",
"50 100\nb\naab\nab\naaa\na\naab\naba\nbb\na\na\nb\naab\nbbb\naa\nbbb\nb\nab\nab\nbbb\na\nbaa\na\nbab\nbbb\na\naba\nab\na\nba\nb\nbba\naba\nba\nbba\nb\na\nb\nb\nab\na\nabb\nab\nbb\nbba\nb\nbbb\nbb\nb\naba\naab\nba\nbb\na\na\nbb\nba\nbaa\nba\nba\na\nb\nbb\nb\nbaa\nbab\nbba\nb\nbb\nbbb\nb\naba\nbba\nbba\naaa\nab\na\nbbb\nab\nb\nba\nbbb\nb\naab\nbb\naba\nb\nb\naa\nbaa\nbba\naa\naba\nb\nbb\nba\nb\nb\naaa\nab\nba\n",
"15 100\nbb\nab\nbb\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\nab\nab\nab\nab\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nbb\nba\naa\nbb\nab\nba\naa\nbb\nab\nab\naa\n",
"15 100\nbb\nab\nbb\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\nab\nab\nab\nab\naa\nbb\nab\nba\naa\nbb\naa\nba\naa\nbb\nab\nba\naa\nbb\nbb\nba\naa\nbb\nab\nba\naa\nbb\nab\nab\naa\n",
"5 1\na\nb\nba\nab\nbab\n",
"15 100\nbbb\nabb\nbab\naab\nbba\naba\nbaa\naaa\nbbb\nabb\nbab\naab\nbba\naba\nbaa\naaa\nbbb\nabb\nbab\naab\nbba\naba\nbaa\naaa\nbbb\nabb\nbab\nbaa\nbba\naba\nbaa\naaa\nbbb\nabb\nbab\naab\nbba\naba\nbaa\naaa\nbbb\nabb\nbab\naab\nbba\naba\nbaa\naaa\nbbb\nabb\nbab\naab\nbba\naba\nbaa\naaa\nbbb\nabb\nbab\naab\nbba\naba\nbaa\naaa\nbbb\nabb\nbab\naab\nbba\naba\nbaa\naaa\nbbb\nabb\nbab\naab\nbba\naba\nbaa\naaa\nbbb\nabb\nbab\naab\nbba\naba\nbaa\naaa\nbbb\nabb\nbab\naab\nbba\naba\nbaa\naaa\nbbb\nabb\nbab\naab\n",
"10 10\nba\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\n",
"3 10\nbbb\nabb\nbab\naab\nbab\naba\nbaa\naaa\nbbb\nabb\n",
"50 100\nb\naab\nab\naaa\na\naab\naaa\nbb\na\na\nb\naab\nbbb\naa\nbbb\nb\nab\nab\nbbb\nb\nbaa\na\nbab\nbbb\na\naba\nab\na\nba\nb\nbba\naba\nba\nbba\nb\nb\nb\nb\nab\na\nabb\nab\nbb\nbba\nb\nbbb\nbb\nb\naba\naab\nba\nbb\na\na\nbb\nba\nbaa\nba\nba\na\nb\nbb\nb\nbaa\nbab\nbba\nb\nbb\nbbb\nb\naba\nbba\nbba\naaa\nab\na\nbbb\nab\nb\nba\nbab\nb\nabb\nbb\naba\nb\na\naa\nbaa\nbbb\naa\naba\nb\nbb\nba\nb\nb\naaa\nab\nba\n",
"17 10\nbbb\nabb\nbab\naab\nbba\naba\nbaa\naaa\nbbb\nabb\n",
"15 100\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nab\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\nbb\nab\nba\naa\n",
"3 14\nb\nb\naa\nab\nba\nbb\naaa\naab\naba\nabb\nbaa\nbab\nbba\nbbb\n",
"10 10\nbb\nab\nab\naa\nbb\nab\nba\naa\nbb\naa\n",
"2 14\na\nb\naa\nab\nba\nbb\naaa\naab\naba\nabb\naab\nabb\nbba\nbbb\n",
"5 14\na\nb\naa\nab\nbb\nbb\naaa\naab\naba\nbba\nbaa\nbab\nbba\nbbb\n",
"6 1\na\nb\nab\nba\naab\n",
"6 1\na\nb\nab\nab\naab\n",
"6 1\na\nb\nab\nab\nbab\n",
"50 100\nb\naab\nab\naaa\na\naab\naba\nbb\na\na\nb\naab\nbbb\naa\nbbb\nb\nab\nab\nbbb\na\nbaa\na\nbab\nbbb\na\naba\nab\na\nba\nb\nbba\naba\nba\nbba\nb\na\nb\nb\nab\na\nabb\nab\nbb\nbba\nb\nbbb\nbb\nb\naba\naab\nba\nbb\na\na\nbb\nba\nbaa\nba\nba\na\nb\nbb\nb\nbaa\nbab\nbba\nb\nbb\nbbb\nb\naba\nbba\nbba\naaa\nba\na\nbbb\nab\nb\nba\nbbb\nb\naab\nbb\naba\nb\nb\naa\nbaa\nbba\naa\naba\nb\nbb\nba\nb\nb\naaa\nab\nba\n",
"6 1\na\nb\nba\nab\nbab\n",
"5 1\na\nb\nba\nab\naab\n",
"5 1\na\nb\nba\nba\naab\n",
"4 14\na\nb\naa\nab\nba\nbb\naaa\naab\naab\nabb\nbaa\nbab\nbba\nbbb\n"
],
"output": [
"3\n5\n3\n3\n1\n",
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"377\n233\n377\n233\n377\n233\n377\n233\n377\n233\n377\n233\n377\n233\n377\n233\n377\n233\n377\n233\n377\n233\n377\n233\n377\n233\n377\n233\n377\n233\n377\n233\n377\n233\n377\n233\n377\n233\n377\n233\n377\n233\n377\n233\n377\n233\n377\n233\n377\n233\n377\n233\n377\n233\n377\n233\n377\n233\n377\n233\n377\n233\n377\n233\n377\n233\n377\n233\n377\n233\n377\n233\n377\n233\n377\n233\n377\n233\n377\n233\n377\n233\n377\n233\n377\n233\n377\n233\n377\n233\n377\n233\n377\n233\n377\n233\n377\n233\n377\n233\n",
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"12\n21\n21\n0\n12\n21\n21\n0\n12\n21\n",
"0\n1\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n",
"0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n",
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"1\n2\n0\n1\n1\n0\n0\n0\n0\n0\n0\n1\n0\n0\n",
"1\n0\n1\n0\n1\n0\n1\n0\n1\n0\n",
"0\n12\n21\n0\n12\n8\n0\n0\n0\n12\n",
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"144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n",
"1\n1\n0\n0\n1\n0\n0\n0\n0\n0\n0\n0\n0\n0\n",
"1\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n",
"2\n3\n0\n1\n2\n1\n0\n0\n0\n1\n0\n1\n1\n0\n",
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"0\n1\n0\n1\n0\n1\n0\n1\n0\n1\n",
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"12\n21\n21\n0\n12\n21\n21\n0\n12\n0\n",
"0\n1\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n",
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"1\n2\n0\n1\n1\n0\n0\n0\n0\n0\n0\n1\n0\n0\n",
"144\n232\n144\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n",
"1\n1\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n",
"2\n3\n0\n1\n1\n1\n0\n0\n0\n1\n0\n1\n1\n0\n",
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"3\n5\n3\n3\n",
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"3\n5\n3\n1\n",
"12\n21\n21\n0\n12\n21\n21\n0\n",
"778742000\n0\n807526948\n0\n807526948\n0\n836311896\n971215058\n807526948\n807526948\n778742000\n0\n0\n0\n0\n778742000\n807526948\n807526948\n0\n807526948\n0\n807526948\n807526948\n0\n807526948\n836311896\n807526948\n807526948\n807526948\n778742000\n971215058\n836311896\n807526948\n971215058\n778742000\n807526948\n778742000\n778742000\n807526948\n807526948\n971215058\n807526948\n971215058\n971215058\n778742000\n0\n971215058\n778742000\n836311896\n0\n807526948\n971215058\n807526948\n807526948\n971215058\n807526948\n0\n807526948\n807526948\n807526948\n778742000\n971215058\n778742000\n0\n807526948\n971215058\n778742000\n971215058\n0\n778742000\n836311896\n971215058\n971215058\n0\n807526948\n807526948\n0\n807526948\n778742000\n807526948\n807526948\n778742000\n0\n971215058\n836311896\n778742000\n807526948\n0\n0\n0\n0\n836311896\n778742000\n971215058\n807526948\n778742000\n778742000\n0\n807526948\n807526948\n",
"144\n232\n144\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n232\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n144\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n",
"2\n3\n1\n1\n1\n1\n0\n0\n0\n1\n0\n1\n1\n0\n",
"3\n",
"778742000\n0\n807526948\n0\n807526948\n0\n836311896\n971215058\n807526948\n807526948\n778742000\n0\n0\n0\n0\n778742000\n807526948\n807526948\n0\n807526948\n0\n807526948\n807526948\n0\n807526948\n836311896\n807526948\n807526948\n807526948\n778742000\n971215058\n836311896\n807526948\n971215058\n778742000\n807526948\n778742000\n778742000\n807526948\n807526948\n971215058\n807526948\n971215058\n971215058\n778742000\n0\n971215058\n778742000\n836311896\n0\n807526948\n971215058\n807526948\n807526948\n971215058\n807526948\n0\n807526948\n807526948\n807526948\n778742000\n971215058\n778742000\n0\n807526948\n971215058\n778742000\n971215058\n0\n778742000\n836311896\n971215058\n971215058\n0\n807526948\n807526948\n0\n807526948\n778742000\n807526948\n0\n778742000\n0\n971215058\n836311896\n778742000\n807526948\n0\n0\n0\n0\n836311896\n778742000\n971215058\n807526948\n778742000\n778742000\n0\n807526948\n807526948\n",
"144\n232\n144\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n232\n232\n232\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n144\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n",
"778742000\n0\n807526948\n0\n807526948\n0\n836311896\n971215058\n807526948\n807526948\n778742000\n0\n0\n0\n0\n778742000\n807526948\n807526948\n0\n807526948\n0\n807526948\n807526948\n0\n807526948\n836311896\n807526948\n807526948\n807526948\n778742000\n971215058\n836311896\n807526948\n971215058\n778742000\n807526948\n778742000\n778742000\n807526948\n807526948\n971215058\n807526948\n971215058\n971215058\n778742000\n0\n971215058\n778742000\n836311896\n0\n807526948\n971215058\n807526948\n807526948\n971215058\n807526948\n0\n807526948\n807526948\n807526948\n778742000\n971215058\n778742000\n0\n807526948\n971215058\n778742000\n971215058\n0\n778742000\n836311896\n971215058\n971215058\n0\n807526948\n807526948\n0\n807526948\n778742000\n807526948\n0\n778742000\n0\n971215058\n836311896\n778742000\n807526948\n0\n0\n971215058\n0\n836311896\n778742000\n971215058\n807526948\n778742000\n778742000\n0\n807526948\n807526948\n",
"144\n232\n144\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n232\n232\n232\n232\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n144\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n",
"778742000\n0\n807526948\n0\n807526948\n0\n836311896\n971215058\n807526948\n807526948\n778742000\n0\n0\n0\n0\n778742000\n807526948\n807526948\n0\n807526948\n0\n807526948\n807526948\n0\n807526948\n836311896\n807526948\n807526948\n807526948\n778742000\n971215058\n836311896\n807526948\n971215058\n778742000\n807526948\n778742000\n778742000\n807526948\n807526948\n971215058\n807526948\n971215058\n971215058\n778742000\n0\n971215058\n778742000\n836311896\n0\n807526948\n971215058\n807526948\n807526948\n971215058\n807526948\n0\n807526948\n807526948\n807526948\n778742000\n971215058\n778742000\n0\n807526948\n971215058\n778742000\n971215058\n0\n778742000\n836311896\n971215058\n971215058\n0\n807526948\n807526948\n0\n807526948\n778742000\n807526948\n0\n778742000\n0\n971215058\n836311896\n778742000\n778742000\n0\n0\n971215058\n0\n836311896\n778742000\n971215058\n807526948\n778742000\n778742000\n0\n807526948\n807526948\n",
"144\n232\n144\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n232\n232\n232\n232\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n144\n233\n0\n144\n232\n233\n0\n144\n232\n232\n0\n",
"144\n232\n144\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n232\n232\n232\n232\n0\n144\n232\n233\n0\n144\n0\n233\n0\n144\n232\n233\n0\n144\n144\n233\n0\n144\n232\n233\n0\n144\n232\n232\n0\n",
"2\n",
"0\n144\n232\n0\n144\n88\n0\n0\n0\n144\n232\n0\n144\n88\n0\n0\n0\n144\n232\n0\n144\n88\n0\n0\n0\n144\n232\n0\n144\n88\n0\n0\n0\n144\n232\n0\n144\n88\n0\n0\n0\n144\n232\n0\n144\n88\n0\n0\n0\n144\n232\n0\n144\n88\n0\n0\n0\n144\n232\n0\n144\n88\n0\n0\n0\n144\n232\n0\n144\n88\n0\n0\n0\n144\n232\n0\n144\n88\n0\n0\n0\n144\n232\n0\n144\n88\n0\n0\n0\n144\n232\n0\n144\n88\n0\n0\n0\n144\n232\n0\n",
"21\n21\n21\n0\n12\n21\n21\n0\n12\n21\n",
"0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n",
"778742000\n0\n807526948\n0\n807526948\n0\n0\n971215058\n807526948\n807526948\n778742000\n0\n0\n0\n0\n778742000\n807526948\n807526948\n0\n778742000\n0\n807526948\n807526948\n0\n807526948\n836311896\n807526948\n807526948\n807526948\n778742000\n971215058\n836311896\n807526948\n971215058\n778742000\n778742000\n778742000\n778742000\n807526948\n807526948\n971215058\n807526948\n971215058\n971215058\n778742000\n0\n971215058\n778742000\n836311896\n0\n807526948\n971215058\n807526948\n807526948\n971215058\n807526948\n0\n807526948\n807526948\n807526948\n778742000\n971215058\n778742000\n0\n807526948\n971215058\n778742000\n971215058\n0\n778742000\n836311896\n971215058\n971215058\n0\n807526948\n807526948\n0\n807526948\n778742000\n807526948\n807526948\n778742000\n971215058\n971215058\n836311896\n778742000\n807526948\n0\n0\n0\n0\n836311896\n778742000\n971215058\n807526948\n778742000\n778742000\n0\n807526948\n807526948\n",
"0\n377\n609\n0\n377\n232\n0\n0\n0\n377\n",
"144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n232\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n144\n232\n233\n0\n",
"1\n1\n0\n0\n1\n0\n0\n0\n0\n0\n0\n0\n0\n0\n",
"12\n21\n21\n0\n12\n21\n21\n0\n12\n0\n",
"0\n1\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n",
"2\n3\n0\n1\n1\n1\n0\n0\n0\n1\n0\n1\n1\n0\n",
"3\n",
"3\n",
"3\n",
"778742000\n0\n807526948\n0\n807526948\n0\n836311896\n971215058\n807526948\n807526948\n778742000\n0\n0\n0\n0\n778742000\n807526948\n807526948\n0\n807526948\n0\n807526948\n807526948\n0\n807526948\n836311896\n807526948\n807526948\n807526948\n778742000\n971215058\n836311896\n807526948\n971215058\n778742000\n807526948\n778742000\n778742000\n807526948\n807526948\n971215058\n807526948\n971215058\n971215058\n778742000\n0\n971215058\n778742000\n836311896\n0\n807526948\n971215058\n807526948\n807526948\n971215058\n807526948\n0\n807526948\n807526948\n807526948\n778742000\n971215058\n778742000\n0\n807526948\n971215058\n778742000\n971215058\n0\n778742000\n836311896\n971215058\n971215058\n0\n807526948\n807526948\n0\n807526948\n778742000\n807526948\n0\n778742000\n0\n971215058\n836311896\n778742000\n778742000\n0\n0\n971215058\n0\n836311896\n778742000\n971215058\n807526948\n778742000\n778742000\n0\n807526948\n807526948\n",
"3\n",
"2\n",
"2\n",
"1\n2\n0\n1\n1\n0\n0\n0\n0\n0\n0\n1\n0\n0\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Fibonacci strings are defined as follows:
* f1 = «a»
* f2 = «b»
* fn = fn - 1 fn - 2, n > 2
Thus, the first five Fibonacci strings are: "a", "b", "ba", "bab", "babba".
You are given a Fibonacci string and m strings si. For each string si, find the number of times it occurs in the given Fibonacci string as a substring.
Input
The first line contains two space-separated integers k and m — the number of a Fibonacci string and the number of queries, correspondingly.
Next m lines contain strings si that correspond to the queries. It is guaranteed that strings si aren't empty and consist only of characters "a" and "b".
The input limitations for getting 30 points are:
* 1 ≤ k ≤ 3000
* 1 ≤ m ≤ 3000
* The total length of strings si doesn't exceed 3000
The input limitations for getting 100 points are:
* 1 ≤ k ≤ 1018
* 1 ≤ m ≤ 104
* The total length of strings si doesn't exceed 105
Please do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use cin, cout streams or the %I64d specifier.
Output
For each string si print the number of times it occurs in the given Fibonacci string as a substring. Since the numbers can be large enough, print them modulo 1000000007 (109 + 7). Print the answers for the strings in the order in which they are given in the input.
Examples
Input
6 5
a
b
ab
ba
aba
Output
3
5
3
3
1
### Input:
6 5
a
b
ab
ba
aba
### Output:
3
5
3
3
1
### Input:
50 100
bb
aa
b
baa
bbba
aa
ba
a
abba
baa
aa
aab
ab
babb
aabb
baa
baaa
baa
aab
bba
bb
aba
aaba
bab
aaba
aa
aaaa
babb
bbb
aaba
aaa
ab
bab
b
b
aa
aaab
aa
bba
baa
babb
baba
ba
aaba
bba
ba
ab
abb
b
ba
bbb
ba
aaa
bbb
baa
bb
a
aaa
aaba
ab
bba
ba
b
bbb
aaa
a
a
b
b
aba
bb
ba
a
b
baa
b
aaaa
a
aaab
baba
ba
bb
baba
ab
baaa
bbbb
a
aabb
ab
b
b
aaa
b
b
abab
abb
b
b
bb
b
### Output:
971215058
0
778742000
0
0
0
807526948
807526948
971215058
0
0
0
807526948
971215058
0
0
0
0
0
971215058
971215058
836311896
0
807526948
0
0
0
971215058
0
0
0
807526948
807526948
778742000
778742000
0
0
0
971215058
0
971215058
836311896
807526948
0
971215058
807526948
807526948
971215058
778742000
807526948
0
807526948
0
0
0
971215058
807526948
0
0
807526948
971215058
807526948
778742000
0
0
807526948
807526948
778742000
778742000
836311896
971215058
807526948
807526948
778742000
0
778742000
0
807526948
0
836311896
807526948
971215058
836311896
807526948
0
0
807526948
0
807526948
778742000
778742000
0
778742000
778742000
836311896
971215058
778742000
778742000
971215058
778742000
### Code:
F = ['', 'a', 'b', 'ba', 'bab', 'babba', 'babbabab', 'babbababbabba', 'babbababbabbababbabab', 'babbababbabbababbababbabbababbabba', 'babbababbabbababbababbabbababbabbababbababbabbababbabab', 'babbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabba', 'babbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabab', 'babbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabba', 'babbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabab', 'babbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabba', 'babbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabab', 'babbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabba', 'babbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabab', 'babbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabba', 'babbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabbababbababbabbababbababbabbababbabbababbababbabbababbabab']
d = 1000000007
def sqr(t):
return [[sum(t[i][k] * t[k][j] for k in range(4)) % d for j in range(4)] for i in range(4)]
def mul(a, b):
return [[sum(a[i][k] * b[k][j] for k in range(4)) % d for j in range(4)] for i in range(4)]
def fib(k):
s, p = format(k, 'b')[:: -1], [[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]]
t = [[[0, 1, 0, 0], [1, 1, 1, 0], [0, 0, 0, 1], [0, 0, 1, 0]]] + [0] * (len(s) - 1)
for i in range(1, len(s)):
t[i] = sqr(t[i - 1])
for i, k in enumerate(s):
if k == '1': p = mul(p, t[i])
return p
def cnt(t, p):
s, i = 0, p.find(t) + 1
while i > 0:
i = p.find(t, i) + 1
s += 1
return s
def f(t, p, k):
l = len(t) - 1
if l: x, y = cnt(t, F[k - 1][- l: ] + F[k][:l ]), cnt(t, F[k][- l: ] + F[k + 1][:l ])
else: x, y = 0, 0
a, b = cnt(t, F[k - 1]), cnt(t, F[k])
return (p[0] * a + p[1] * b + p[2] * y + p[3] * x) % d
k, m = map(int, input().split())
if k > 15:
a, b = fib(k - 7)[0], fib(k - 18)[0]
for i in range(m):
t = input()
if len(t) < len(F[7]): print(f(t, a, 8))
else: print(f(t, b, 19))
else:
p = F[k]
for i in range(m):
print(cnt(input(), p))
|
223_A. Bracket Sequence_10554
|
A bracket sequence is a string, containing only characters "(", ")", "[" and "]".
A correct bracket sequence is a bracket sequence that can be transformed into a correct arithmetic expression by inserting characters "1" and "+" between the original characters of the sequence. For example, bracket sequences "()[]", "([])" are correct (the resulting expressions are: "(1)+[1]", "([1+1]+1)"), and "](" and "[" are not. The empty string is a correct bracket sequence by definition.
A substring s[l... r] (1 ≤ l ≤ r ≤ |s|) of string s = s1s2... s|s| (where |s| is the length of string s) is the string slsl + 1... sr. The empty string is a substring of any string by definition.
You are given a bracket sequence, not necessarily correct. Find its substring which is a correct bracket sequence and contains as many opening square brackets «[» as possible.
Input
The first and the only line contains the bracket sequence as a string, consisting only of characters "(", ")", "[" and "]". It is guaranteed that the string is non-empty and its length doesn't exceed 105 characters.
Output
In the first line print a single integer — the number of brackets «[» in the required bracket sequence. In the second line print the optimal sequence. If there are more than one optimal solutions print any of them.
Examples
Input
([])
Output
1
([])
Input
(((
Output
0
|
import sys
from math import gcd,sqrt,ceil,log2
from collections import defaultdict,Counter,deque
from bisect import bisect_left,bisect_right
import math
import heapq
from itertools import permutations
# input=sys.stdin.readline
# def print(x):
# sys.stdout.write(str(x)+"\n")
# sys.stdin = open('input.txt', 'r')
# sys.stdout = open('output.txt', 'w')
import os
import sys
from io import BytesIO, IOBase
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
# import sys
# import io, os
# input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
def get_sum(bit,i):
s = 0
i+=1
while i>0:
s+=bit[i]
i-=i&(-i)
return s
def update(bit,n,i,v):
i+=1
while i<=n:
bit[i]+=v
i+=i&(-i)
def modInverse(b,m):
g = math.gcd(b, m)
if (g != 1):
return -1
else:
return pow(b, m - 2, m)
def primeFactors(n):
sa = set()
sa.add(n)
while n % 2 == 0:
sa.add(2)
n = n // 2
for i in range(3,int(math.sqrt(n))+1,2):
while n % i== 0:
sa.add(i)
n = n // i
# sa.add(n)
return sa
def seive(n):
pri = [True]*(n+1)
p = 2
while p*p<=n:
if pri[p] == True:
for i in range(p*p,n+1,p):
pri[i] = False
p+=1
return pri
def check_prim(n):
if n<0:
return False
for i in range(2,int(sqrt(n))+1):
if n%i == 0:
return False
return True
def getZarr(string, z):
n = len(string)
# [L,R] make a window which matches
# with prefix of s
l, r, k = 0, 0, 0
for i in range(1, n):
# if i>R nothing matches so we will calculate.
# Z[i] using naive way.
if i > r:
l, r = i, i
# R-L = 0 in starting, so it will start
# checking from 0'th index. For example,
# for "ababab" and i = 1, the value of R
# remains 0 and Z[i] becomes 0. For string
# "aaaaaa" and i = 1, Z[i] and R become 5
while r < n and string[r - l] == string[r]:
r += 1
z[i] = r - l
r -= 1
else:
# k = i-L so k corresponds to number which
# matches in [L,R] interval.
k = i - l
# if Z[k] is less than remaining interval
# then Z[i] will be equal to Z[k].
# For example, str = "ababab", i = 3, R = 5
# and L = 2
if z[k] < r - i + 1:
z[i] = z[k]
# For example str = "aaaaaa" and i = 2,
# R is 5, L is 0
else:
# else start from R and check manually
l = i
while r < n and string[r - l] == string[r]:
r += 1
z[i] = r - l
r -= 1
def search(text, pattern):
# Create concatenated string "P$T"
concat = pattern + "$" + text
l = len(concat)
z = [0] * l
getZarr(concat, z)
ha = []
for i in range(l):
if z[i] == len(pattern):
ha.append(i - len(pattern) - 1)
return ha
# n,k = map(int,input().split())
# l = list(map(int,input().split()))
#
# n = int(input())
# l = list(map(int,input().split()))
#
# hash = defaultdict(list)
# la = []
#
# for i in range(n):
# la.append([l[i],i+1])
#
# la.sort(key = lambda x: (x[0],-x[1]))
# ans = []
# r = n
# flag = 0
# lo = []
# ha = [i for i in range(n,0,-1)]
# yo = []
# for a,b in la:
#
# if a == 1:
# ans.append([r,b])
# # hash[(1,1)].append([b,r])
# lo.append((r,b))
# ha.pop(0)
# yo.append([r,b])
# r-=1
#
# elif a == 2:
# # print(yo,lo)
# # print(hash[1,1])
# if lo == []:
# flag = 1
# break
# c,d = lo.pop(0)
# yo.pop(0)
# if b>=d:
# flag = 1
# break
# ans.append([c,b])
# yo.append([c,b])
#
#
#
# elif a == 3:
#
# if yo == []:
# flag = 1
# break
# c,d = yo.pop(0)
# if b>=d:
# flag = 1
# break
# if ha == []:
# flag = 1
# break
#
# ka = ha.pop(0)
#
# ans.append([ka,b])
# ans.append([ka,d])
# yo.append([ka,b])
#
# if flag:
# print(-1)
# else:
# print(len(ans))
# for a,b in ans:
# print(a,b)
def mergeIntervals(arr):
# Sorting based on the increasing order
# of the start intervals
arr.sort(key = lambda x: x[0])
# array to hold the merged intervals
m = []
s = -10000
max = -100000
for i in range(len(arr)):
a = arr[i]
if a[0] > max:
if i != 0:
m.append([s,max])
max = a[1]
s = a[0]
else:
if a[1] >= max:
max = a[1]
#'max' value gives the last point of
# that particular interval
# 's' gives the starting point of that interval
# 'm' array contains the list of all merged intervals
if max != -100000 and [s, max] not in m:
m.append([s, max])
return m
s = input()
n = len(s)
stack = []
i = 0
ans = []
pre = [0]
for i in s:
if i == '[':
pre.append(pre[-1]+1)
else:
pre.append(pre[-1])
i = 0
while i<n:
if s[i] == '(' or s[i] == '[':
stack.append(i)
elif stack!=[] and s[i] == ')' and s[stack[-1]] == '(':
z = stack.pop()
ans.append((z,i))
elif stack!=[] and s[i] == ')' and s[stack[-1]] == '[':
stack = []
elif stack!=[] and s[i] == ']' and s[stack[-1]] == '[':
z = stack.pop()
ans.append((z,i))
elif stack!=[] and s[i] == ']' and s[stack[-1]] == '(':
stack = []
i+=1
ans.sort()
x,y = -1,-1
maxi = 0
lo = []
i = 1
# print(ans)
ans = mergeIntervals(ans)
if ans == []:
print(0)
print()
exit()
a,b = ans[i-1]
lo.append([a,b])
# print(ans)
while i<=len(ans):
a,b = ans[i-1]
while i<len(ans) and ans[i][0]-ans[i-1][1] == 1:
i+=1
lo.append([a,ans[i-1][1]])
i+=1
ans = lo
# print(lo)
for i in range(len(ans)):
a,b = ans[i]
a+=1
b+=1
z = pre[b] - pre[a-1]
if z>maxi:
maxi = z
a-=1
b-=1
x,y = a,b
if ans == []:
print(0)
print()
else:
print(maxi)
print(s[x:y+1])
|
{
"input": [
"(((\n",
"([])\n",
"(][)\n",
"[(()[])]()[()[]]\n",
"[[]\n",
"(()[))()[]\n",
"([]\n",
")[)][)))((([[)]((]][)[)((]([)[)(([)[)]][([\n",
"][([))][[))[[((]][([(([[)]]])([)][([([[[[([))]])][[[[[([)]]([[(((]([(](([([[)[(]])(][(((][)[[)][)(][[)[[)])))[)]))]])[([[))(([(]][))([(]]][(])]))))))[[[[[([[([)[[[)[(([)[[(][((([(([([(([))[[[[[[([(](])(][[)[)(](]])]]]((([))(])[[)[))[([[[[(]][)[([(]](([)([[)[[([))[)\n",
"[([[)[(()[])[()][]()[[[)()[][[[()[]]]()]][\n",
"((()))([]\n",
"()]])()()]\n",
"((])(]]))(](((()[[()[[[)([]()])[(]][)]])[]]()[()[[[[(([[)\n",
"((((([]((((((((((\n",
"(][](](][[(][\n",
"()()([]]\n",
"([[[]]))\n",
"[()][([[]])][[[]()]][()[]]()()([[][]][[]][](()))[[[(())]]][]()(([([])(([[[]]()])(()))]((())))([()]([()[[[]([][[[[][(())([[]()])]]][[(())]([])]()][[](())]()[])]()[][]]([[]])[]])[(()[()((()[][()]))][])[]()()([]())](()[][][])()()[]()))[]()[]\n",
"([])()[()]()()[(([])[]()[()([])()[][]()])]\n",
"[[])\n",
"(][(](][[(][(\n",
"(((((([](((((((\n",
"](]][)]()][[])[()(][)]))[)[]()()])[([((([[(([)][(])](][])([([)())))([(([][))[)()]][[])()[)](][[((]](](])]][(][[()(]][[)][])(][]))[])[)[(])[)()()[[))((()]]([([[(]))][(]())))))[[]]][][))[)])])()((((([[](([[()(([[()](([[([[(](]([)]())))[)]([]\n",
"[()][][][][]()[)])))[(]()[]([)(])[)(])()[))][)]()[][][]][][)(((([))))[)[))]]([[[)[())))[(][(()[()[(]())]])([[)[)[[())[()[]()[[[[])][))](()()())()](((((([(()]][[)([)([]]))(()[((]]())[]])][)()(][]][][(([])]]((]])([[][)])(][)][([[[[(][()(][[(\n",
"[]())])([)][[[]])))][])([]([]()]]))))())[[([))()(])))]][)[][[])(][()()]]](]][])[[))((]][)[)(]))([])((]([)([])]]]]]]][)[[[]]([[[]]][(][][])()[[([](])(]]((]([[)])]])([)(][([)(([))(]([)[[](([(](][[)()(][\n",
"(([])\n",
"[(()[](]()[()[]]\n",
"(()[[)())]\n",
"[([]])[)[(()[)[(](()[)[]]((])[[((()))[])[)\n",
"[([[)[(()Z])[()][]()[[[)()[][[[()[]]]()]][\n",
"((])(]]))(](((()[[()[][)([]()])[(]][)]])[[]()[()[[[[(([[)\n",
"[()][([[]])][[[]()]][()[]]()()([[][]][[]][](()))[[[(())]]][]()(([([])(([[[]]()])(()))]((())))([()]([()[[[]([][[[[][(())([[]()])]]][[(())](Z])]()][[](())]()[])]()[][]]([[]])[]])[(()[()((()[][()]))][])[]()()([]())](()[][][])()()[]()))[]()[]\n",
"([[]()([]([[[[([])[]()])[][[()]]((]])][(([][]][]()()[])]][))(]](([)(())]][()[()[[]])(([((((((])())()()((]))[])][[[[)(][)([))([[)[)[[()]]))(]([)([)(([]([))))([)[[[(]]))[)[))))[(((()[][]][][][)(])[]))[)()]()[)]()[(][)(]([)))])[)(][][][][])([\n",
"[]()()[[](]([((][[)[(]())[(()[([]()[()]])])[[(]((]]()](][([[)()][][]([]]][[[(]][[[)[]]]]]]])][()[(](()][())]()[)[]](())[[)][]](]]])()([]()][[][)[]])))]()())[([[))())))]])(][(][()][])))]][[[])[()]))(][\n",
"[([[)[(()Z])[()][](([[[)()[][[[')[]]]()]][\n",
")[[(([[[))([)(][[[]])[]]([)])(][()[][)([[)((((]())]]()]((\n",
"[()][][][][]()[)])))[(]()[]([)(])[)(])()[))][)]())][][]][][)(((([)[))[)[))]]([[[)[())))[(][(()[()[(]())]])([[)[)[[())[()[]()[[[[])][))](()()())()](((((([(()]][[)([)([]]))(()[((]]())[]])][)()(][]][][(([])]]((]])([[][)])(][)][([[[[(][()(][[(\n",
"(\\]\n",
"(())))([]\n",
"()]])((()]\n",
"((((([](((()(((((\n",
"[]([[](](][](\n",
"]][()()(\n",
"])])(][][)()][()([)(][)][(([)()(])([)()][(\n",
"([]([[](]([](\n",
"(((((((][((((((\n",
"'((\n",
"[(])\n",
"]))()[[)((\n",
"(][\n",
"[([(])[)[(()[)[(](()[)[]]((])[[((])))[])[)\n",
"[([[)[(()Z])[()][](([[[)()[][[[()[]]]()]][\n",
"(()))*([]\n",
"))]](((()]\n",
")[[(([[[[)([)(][[)]])[]]([)])(][()[][)([[)((((]())]]()]((\n",
"(((((Z]((((((((((\n",
"[]][[](](([](\n",
"]]Z()()(\n",
"[()][([[]])][[[]()]][()[]]()()([[][]][[]][](()))[[[(())]]][]()(([([])('[[[]]()])(()))]((())))([()]([()[[[]([][[[[][(())([[]()])]]][[(())](Z])]()][[](())]()[])]()[][]]([[]])[]])[(()[()((()[][()]))][])[]()()([]())](()[][][])()()[]()))[]()[]\n",
"])])(][][)()][()([)(][)][(([*()(])([)()][(\n",
"[[]([(](]([](\n",
"(((((((][()((((\n",
"([[]()([]([[[[([])[]()])[][[()]]((]])][(([][]][]()()[])]][))(]](([)(())]][()[()[[]])(([((((((])())()()((]))[])][[[[)(][)([))([[)[)[[()]]))(]([)([)(([]([))))([)[[[(]]))[)[))[)[(((()[][]][][]))(])[]))[)()]()[)]()[(][)(]([)))])[)(][][][][])([\n",
"('(\n",
"[(\\)\n",
"(]\\\n",
")()))*([]\n",
"])((((]]))\n",
"((((((((((]Z(((((\n",
"[]][[](]((Z](\n",
"()()(Z]]\n",
"[()][([[]])][[[]()]][()[]]()()([[][]][[]][](()))[[[(())]]][]()(([([])('[[[]]()])(()))]((())))([()]([()[[[]([][[[[][(())([[]()])]]][[(())](Z])]()][[](())]()[])]()[][]]([[]])[]])[(()[()((()[][()]*)][])[]()()([]())](()[][][])()()[]()))[]()[]\n",
"(][(](]([(][[\n",
"((([(((](()((((\n",
"Z(\\)\n",
"]\\(\n",
"))((((]]])\n",
")[[(([[[))([)(][[[]])[]]([)])(][()[^[)([[)((((]())]]()]((\n",
"]((((((((((Z(((((\n",
"](Z()()]\n",
"(([(](]][(][[\n",
"(((()((]((([(((\n",
")(\\Z\n"
],
"output": [
"0\n\n",
"1\n([])\n",
"0\n\n",
"4\n[(()[])]()[()[]]\n",
"1\n[]\n",
"1\n()[]\n",
"1\n[]\n",
"0\n\n",
"0\n\n",
"5\n()[][[[()[]]]()]\n",
"1\n[]\n",
"0\n\n",
"1\n[]\n",
"1\n[]\n",
"1\n[]\n",
"1\n[]\n",
"2\n[[]]\n",
"61\n[()][([[]])][[[]()]][()[]]()()([[][]][[]][](()))[[[(())]]][]()(([([])(([[[]]()])(()))]((())))([()]([()[[[]([][[[[][(())([[]()])]]][[(())]([])]()][[](())]()[])]()[][]]([[]])[]])[(()[()((()[][()]))][])[]()()([]())](()[][][])()()[]()))[]()[]\n",
"9\n([])()[()]()()[(([])[]()[()([])()[][]()])]\n",
"1\n[]\n",
"0\n\n",
"1\n[]\n",
"2\n[[]]\n",
"5\n[()][][][][]()\n",
"3\n[[[]]]\n",
"1\n([])\n",
"2\n()[()[]]\n",
"0\n\n",
"1\n[]\n",
"5\n()[][[[()[]]]()]\n",
"1\n()[]\n",
"19\n[()][([[]])][[[]()]][()[]]()()([[][]][[]][](()))[[[(())]]][]\n",
"4\n[][][][]\n",
"2\n[]()[()]\n",
"2\n[()][]\n",
"2\n[[]]\n",
"5\n[()][][][][]\n",
"0\n\n",
"1\n[]\n",
"0\n\n",
"1\n[]\n",
"1\n[]\n",
"0\n\n",
"1\n[]\n",
"1\n[]\n",
"0\n\n",
"0\n\n",
"0\n\n",
"0\n\n",
"0\n\n",
"1\n[]\n",
"5\n()[][[[()[]]]()]\n",
"1\n[]\n",
"0\n\n",
"1\n[]\n",
"0\n\n",
"1\n[]\n",
"0\n\n",
"19\n[()][([[]])][[[]()]][()[]]()()([[][]][[]][](()))[[[(())]]][]\n",
"1\n[]\n",
"1\n[]\n",
"0\n\n",
"4\n[][][][]\n",
"0\n\n",
"0\n\n",
"0\n\n",
"1\n[]\n",
"0\n\n",
"0\n\n",
"1\n[]\n",
"0\n\n",
"19\n[()][([[]])][[[]()]][()[]]()()([[][]][[]][](()))[[[(())]]][]\n",
"0\n\n",
"0\n\n",
"0\n\n",
"0\n\n",
"0\n\n",
"2\n[[]]\n",
"0\n\n",
"0\n\n",
"0\n\n",
"0\n\n",
"0\n\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
A bracket sequence is a string, containing only characters "(", ")", "[" and "]".
A correct bracket sequence is a bracket sequence that can be transformed into a correct arithmetic expression by inserting characters "1" and "+" between the original characters of the sequence. For example, bracket sequences "()[]", "([])" are correct (the resulting expressions are: "(1)+[1]", "([1+1]+1)"), and "](" and "[" are not. The empty string is a correct bracket sequence by definition.
A substring s[l... r] (1 ≤ l ≤ r ≤ |s|) of string s = s1s2... s|s| (where |s| is the length of string s) is the string slsl + 1... sr. The empty string is a substring of any string by definition.
You are given a bracket sequence, not necessarily correct. Find its substring which is a correct bracket sequence and contains as many opening square brackets «[» as possible.
Input
The first and the only line contains the bracket sequence as a string, consisting only of characters "(", ")", "[" and "]". It is guaranteed that the string is non-empty and its length doesn't exceed 105 characters.
Output
In the first line print a single integer — the number of brackets «[» in the required bracket sequence. In the second line print the optimal sequence. If there are more than one optimal solutions print any of them.
Examples
Input
([])
Output
1
([])
Input
(((
Output
0
### Input:
(((
### Output:
0
### Input:
([])
### Output:
1
([])
### Code:
import sys
from math import gcd,sqrt,ceil,log2
from collections import defaultdict,Counter,deque
from bisect import bisect_left,bisect_right
import math
import heapq
from itertools import permutations
# input=sys.stdin.readline
# def print(x):
# sys.stdout.write(str(x)+"\n")
# sys.stdin = open('input.txt', 'r')
# sys.stdout = open('output.txt', 'w')
import os
import sys
from io import BytesIO, IOBase
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
# import sys
# import io, os
# input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
def get_sum(bit,i):
s = 0
i+=1
while i>0:
s+=bit[i]
i-=i&(-i)
return s
def update(bit,n,i,v):
i+=1
while i<=n:
bit[i]+=v
i+=i&(-i)
def modInverse(b,m):
g = math.gcd(b, m)
if (g != 1):
return -1
else:
return pow(b, m - 2, m)
def primeFactors(n):
sa = set()
sa.add(n)
while n % 2 == 0:
sa.add(2)
n = n // 2
for i in range(3,int(math.sqrt(n))+1,2):
while n % i== 0:
sa.add(i)
n = n // i
# sa.add(n)
return sa
def seive(n):
pri = [True]*(n+1)
p = 2
while p*p<=n:
if pri[p] == True:
for i in range(p*p,n+1,p):
pri[i] = False
p+=1
return pri
def check_prim(n):
if n<0:
return False
for i in range(2,int(sqrt(n))+1):
if n%i == 0:
return False
return True
def getZarr(string, z):
n = len(string)
# [L,R] make a window which matches
# with prefix of s
l, r, k = 0, 0, 0
for i in range(1, n):
# if i>R nothing matches so we will calculate.
# Z[i] using naive way.
if i > r:
l, r = i, i
# R-L = 0 in starting, so it will start
# checking from 0'th index. For example,
# for "ababab" and i = 1, the value of R
# remains 0 and Z[i] becomes 0. For string
# "aaaaaa" and i = 1, Z[i] and R become 5
while r < n and string[r - l] == string[r]:
r += 1
z[i] = r - l
r -= 1
else:
# k = i-L so k corresponds to number which
# matches in [L,R] interval.
k = i - l
# if Z[k] is less than remaining interval
# then Z[i] will be equal to Z[k].
# For example, str = "ababab", i = 3, R = 5
# and L = 2
if z[k] < r - i + 1:
z[i] = z[k]
# For example str = "aaaaaa" and i = 2,
# R is 5, L is 0
else:
# else start from R and check manually
l = i
while r < n and string[r - l] == string[r]:
r += 1
z[i] = r - l
r -= 1
def search(text, pattern):
# Create concatenated string "P$T"
concat = pattern + "$" + text
l = len(concat)
z = [0] * l
getZarr(concat, z)
ha = []
for i in range(l):
if z[i] == len(pattern):
ha.append(i - len(pattern) - 1)
return ha
# n,k = map(int,input().split())
# l = list(map(int,input().split()))
#
# n = int(input())
# l = list(map(int,input().split()))
#
# hash = defaultdict(list)
# la = []
#
# for i in range(n):
# la.append([l[i],i+1])
#
# la.sort(key = lambda x: (x[0],-x[1]))
# ans = []
# r = n
# flag = 0
# lo = []
# ha = [i for i in range(n,0,-1)]
# yo = []
# for a,b in la:
#
# if a == 1:
# ans.append([r,b])
# # hash[(1,1)].append([b,r])
# lo.append((r,b))
# ha.pop(0)
# yo.append([r,b])
# r-=1
#
# elif a == 2:
# # print(yo,lo)
# # print(hash[1,1])
# if lo == []:
# flag = 1
# break
# c,d = lo.pop(0)
# yo.pop(0)
# if b>=d:
# flag = 1
# break
# ans.append([c,b])
# yo.append([c,b])
#
#
#
# elif a == 3:
#
# if yo == []:
# flag = 1
# break
# c,d = yo.pop(0)
# if b>=d:
# flag = 1
# break
# if ha == []:
# flag = 1
# break
#
# ka = ha.pop(0)
#
# ans.append([ka,b])
# ans.append([ka,d])
# yo.append([ka,b])
#
# if flag:
# print(-1)
# else:
# print(len(ans))
# for a,b in ans:
# print(a,b)
def mergeIntervals(arr):
# Sorting based on the increasing order
# of the start intervals
arr.sort(key = lambda x: x[0])
# array to hold the merged intervals
m = []
s = -10000
max = -100000
for i in range(len(arr)):
a = arr[i]
if a[0] > max:
if i != 0:
m.append([s,max])
max = a[1]
s = a[0]
else:
if a[1] >= max:
max = a[1]
#'max' value gives the last point of
# that particular interval
# 's' gives the starting point of that interval
# 'm' array contains the list of all merged intervals
if max != -100000 and [s, max] not in m:
m.append([s, max])
return m
s = input()
n = len(s)
stack = []
i = 0
ans = []
pre = [0]
for i in s:
if i == '[':
pre.append(pre[-1]+1)
else:
pre.append(pre[-1])
i = 0
while i<n:
if s[i] == '(' or s[i] == '[':
stack.append(i)
elif stack!=[] and s[i] == ')' and s[stack[-1]] == '(':
z = stack.pop()
ans.append((z,i))
elif stack!=[] and s[i] == ')' and s[stack[-1]] == '[':
stack = []
elif stack!=[] and s[i] == ']' and s[stack[-1]] == '[':
z = stack.pop()
ans.append((z,i))
elif stack!=[] and s[i] == ']' and s[stack[-1]] == '(':
stack = []
i+=1
ans.sort()
x,y = -1,-1
maxi = 0
lo = []
i = 1
# print(ans)
ans = mergeIntervals(ans)
if ans == []:
print(0)
print()
exit()
a,b = ans[i-1]
lo.append([a,b])
# print(ans)
while i<=len(ans):
a,b = ans[i-1]
while i<len(ans) and ans[i][0]-ans[i-1][1] == 1:
i+=1
lo.append([a,ans[i-1][1]])
i+=1
ans = lo
# print(lo)
for i in range(len(ans)):
a,b = ans[i]
a+=1
b+=1
z = pre[b] - pre[a-1]
if z>maxi:
maxi = z
a-=1
b-=1
x,y = a,b
if ans == []:
print(0)
print()
else:
print(maxi)
print(s[x:y+1])
|
246_D. Colorful Graph_10558
|
You've got an undirected graph, consisting of n vertices and m edges. We will consider the graph's vertices numbered with integers from 1 to n. Each vertex of the graph has a color. The color of the i-th vertex is an integer ci.
Let's consider all vertices of the graph, that are painted some color k. Let's denote a set of such as V(k). Let's denote the value of the neighbouring color diversity for color k as the cardinality of the set Q(k) = {cu : cu ≠ k and there is vertex v belonging to set V(k) such that nodes v and u are connected by an edge of the graph}.
Your task is to find such color k, which makes the cardinality of set Q(k) maximum. In other words, you want to find the color that has the most diverse neighbours. Please note, that you want to find such color k, that the graph has at least one vertex with such color.
Input
The first line contains two space-separated integers n, m (1 ≤ n, m ≤ 105) — the number of vertices end edges of the graph, correspondingly. The second line contains a sequence of integers c1, c2, ..., cn (1 ≤ ci ≤ 105) — the colors of the graph vertices. The numbers on the line are separated by spaces.
Next m lines contain the description of the edges: the i-th line contains two space-separated integers ai, bi (1 ≤ ai, bi ≤ n; ai ≠ bi) — the numbers of the vertices, connected by the i-th edge.
It is guaranteed that the given graph has no self-loops or multiple edges.
Output
Print the number of the color which has the set of neighbours with the maximum cardinality. It there are multiple optimal colors, print the color with the minimum number. Please note, that you want to find such color, that the graph has at least one vertex with such color.
Examples
Input
6 6
1 1 2 3 5 8
1 2
3 2
1 4
4 3
4 5
4 6
Output
3
Input
5 6
4 2 5 2 4
1 2
2 3
3 1
5 3
5 4
3 4
Output
2
|
from collections import defaultdict
l=lambda :map(int,input().split())
n,m=l()
c=list(l())
graph=defaultdict(set)
for i in range(m):
a,b=l()
if c[a-1]==c[b-1]:
continue
graph[c[a-1]].add(c[b-1])
graph[c[b - 1]].add(c[a - 1])
d,f=min(c),0
for i in sorted(graph):
h=len(graph[i])
if h>f:
f=h
d=i
print(d)
|
{
"input": [
"5 6\n4 2 5 2 4\n1 2\n2 3\n3 1\n5 3\n5 4\n3 4\n",
"6 6\n1 1 2 3 5 8\n1 2\n3 2\n1 4\n4 3\n4 5\n4 6\n",
"10 15\n1 1 1 1 2 2 2 2 1 2\n8 5\n9 1\n8 6\n3 5\n2 7\n2 9\n10 3\n3 2\n3 6\n4 2\n5 9\n7 3\n6 7\n5 10\n4 7\n",
"10 9\n1 1 1 1 1 1 1 1 1 1\n5 8\n8 6\n1 8\n8 4\n3 7\n1 10\n1 9\n2 5\n6 9\n",
"3 1\n13 13 4\n1 2\n",
"10 27\n1 1 3 2 4 1 3 2 4 1\n9 3\n7 8\n9 7\n6 5\n7 6\n7 4\n6 9\n3 8\n6 10\n8 5\n3 1\n4 6\n8 1\n10 8\n9 5\n10 1\n5 10\n3 6\n4 3\n8 2\n10 7\n10 9\n10 3\n8 4\n3 2\n2 4\n6 1\n",
"2 1\n500 300\n1 2\n",
"7 6\n1 2 3 4 3 3 3\n5 1\n6 1\n7 1\n1 2\n2 3\n2 4\n",
"2 1\n100000 100000\n1 2\n",
"5 2\n4 4 10 3 3\n1 2\n4 5\n",
"8 8\n3 3 2 3 3 3 1 3\n8 2\n6 3\n2 3\n2 6\n5 6\n4 2\n7 5\n1 6\n",
"50 47\n21 17 47 15 50 47 47 41 28 18 27 47 29 28 32 26 16 26 8 22 27 10 45 21 17 30 31 38 14 8 9 40 29 35 41 24 22 14 40 46 44 34 40 31 48 40 8 50 1 28\n7 5\n50 2\n42 5\n36 28\n8 44\n36 3\n40 15\n33 18\n5 50\n1 6\n25 20\n39 24\n45 35\n14 27\n14 39\n17 47\n19 49\n28 7\n7 13\n34 3\n22 26\n5 6\n8 17\n32 18\n40 31\n4 40\n17 21\n37 18\n30 41\n2 47\n4 48\n36 32\n45 20\n39 28\n39 43\n7 33\n44 48\n21 47\n14 26\n15 47\n16 14\n23 18\n50 12\n28 8\n10 6\n12 46\n41 5\n",
"6 1\n10 1 1 2 3 4\n2 3\n",
"6 5\n2 2 2 1 2 2\n4 5\n4 2\n5 2\n4 1\n2 3\n",
"5 4\n300 300 300 300 300\n1 2\n2 3\n3 4\n4 5\n",
"10 9\n1 1 1 1 1 1 1 1 1 1\n5 8\n8 6\n1 8\n8 4\n3 7\n2 10\n1 9\n2 5\n6 9\n",
"7 6\n1 2 3 4 3 3 3\n5 2\n6 1\n7 1\n1 2\n2 3\n2 4\n",
"8 8\n3 3 2 3 3 3 1 3\n8 2\n6 3\n2 3\n2 6\n4 6\n4 2\n7 5\n1 6\n",
"50 47\n21 17 47 15 50 47 47 41 28 18 27 47 29 28 32 26 16 26 8 22 27 10 45 21 17 30 31 38 14 8 9 40 29 35 41 24 22 14 40 46 44 34 40 31 48 40 8 50 1 28\n7 5\n50 2\n42 5\n36 28\n8 44\n36 3\n40 15\n33 18\n5 50\n1 6\n25 20\n39 24\n45 35\n14 27\n14 39\n17 47\n19 49\n28 7\n7 13\n34 3\n22 26\n5 6\n8 17\n32 18\n40 31\n7 40\n17 21\n37 18\n30 41\n2 47\n4 48\n36 32\n45 20\n39 28\n39 43\n7 33\n44 48\n21 47\n14 26\n15 47\n16 14\n23 18\n50 12\n28 8\n10 6\n12 46\n41 5\n",
"6 5\n2 2 2 1 2 2\n4 5\n4 2\n5 1\n4 1\n2 3\n",
"5 6\n4 2 5 2 4\n1 2\n2 3\n1 1\n5 3\n5 4\n3 4\n",
"6 6\n1 1 2 3 5 8\n1 2\n3 2\n2 4\n4 3\n4 5\n4 6\n",
"10 9\n1 1 1 1 1 1 1 1 1 1\n5 8\n8 3\n1 8\n8 4\n3 7\n2 10\n1 9\n2 5\n6 9\n",
"7 6\n1 2 3 4 3 5 3\n5 2\n6 1\n7 1\n1 2\n2 3\n2 4\n",
"8 8\n3 3 2 1 3 3 1 3\n8 2\n6 3\n2 3\n2 6\n4 6\n4 2\n7 5\n1 6\n",
"50 47\n21 17 47 15 50 47 47 41 28 18 27 47 29 28 32 26 16 26 8 22 27 10 45 21 17 30 31 38 14 8 9 40 29 35 41 24 22 14 40 46 44 34 40 31 48 40 8 50 1 28\n7 5\n34 2\n42 5\n36 28\n8 44\n36 3\n40 15\n33 18\n5 50\n1 6\n25 20\n39 24\n45 35\n14 27\n14 39\n17 47\n19 49\n28 7\n7 13\n34 3\n22 26\n5 6\n8 17\n32 18\n40 31\n7 40\n17 21\n37 18\n30 41\n2 47\n4 48\n36 32\n45 20\n39 28\n39 43\n7 33\n44 48\n21 47\n14 26\n15 47\n16 14\n23 18\n50 12\n28 8\n10 6\n12 46\n41 5\n",
"6 6\n1 1 2 3 5 4\n1 2\n3 2\n2 4\n4 3\n4 5\n4 6\n",
"10 9\n1 1 1 1 1 1 1 1 1 1\n5 4\n8 3\n1 8\n8 4\n3 7\n2 10\n1 9\n2 5\n6 9\n",
"8 8\n3 3 2 1 3 3 1 3\n8 2\n6 3\n2 3\n2 6\n4 6\n4 3\n7 5\n1 6\n",
"50 47\n21 17 47 15 50 47 47 41 28 18 27 47 29 28 32 26 16 26 8 22 27 10 45 21 17 30 31 38 14 8 9 40 29 35 41 24 22 14 40 46 44 34 40 31 48 40 8 50 1 28\n7 5\n34 2\n42 5\n36 28\n8 44\n36 3\n40 15\n33 18\n5 50\n1 6\n25 20\n39 24\n45 35\n14 27\n14 39\n17 47\n19 49\n28 10\n7 13\n34 3\n22 26\n5 6\n8 17\n32 18\n40 31\n7 40\n17 21\n37 18\n30 41\n2 47\n4 48\n36 32\n45 20\n39 28\n39 43\n7 33\n44 48\n21 47\n14 26\n15 47\n16 14\n23 18\n50 12\n28 8\n10 6\n12 46\n41 5\n",
"8 8\n1 3 2 1 3 3 1 3\n8 2\n6 3\n2 3\n2 6\n4 6\n4 3\n7 5\n1 6\n",
"50 47\n21 17 47 15 50 47 47 41 30 18 27 47 29 28 32 26 16 26 8 22 27 10 45 21 17 30 31 38 14 8 9 40 29 35 41 24 22 14 40 46 44 34 40 31 48 40 8 50 1 28\n7 5\n34 2\n42 5\n36 28\n8 44\n36 3\n40 15\n33 18\n5 50\n1 6\n25 20\n39 24\n45 35\n14 27\n14 39\n17 47\n19 49\n28 10\n7 13\n34 3\n22 26\n5 6\n8 17\n32 18\n40 31\n7 40\n17 21\n37 18\n30 41\n2 47\n4 48\n36 32\n45 20\n39 28\n39 43\n7 33\n44 48\n21 47\n14 26\n15 47\n16 14\n23 18\n50 12\n28 8\n10 6\n12 46\n41 5\n",
"8 8\n1 3 2 1 3 3 1 3\n8 2\n6 3\n2 3\n2 6\n4 6\n4 3\n3 5\n1 6\n",
"50 47\n21 17 47 15 50 47 47 41 30 18 27 47 29 28 32 26 16 26 8 22 27 10 45 21 17 30 31 38 14 8 9 40 10 35 41 24 22 14 40 46 44 34 40 31 48 40 8 50 1 28\n7 5\n34 2\n42 5\n36 28\n8 44\n36 3\n40 15\n33 18\n5 50\n1 6\n25 20\n39 24\n45 35\n14 27\n14 39\n17 47\n19 49\n28 10\n7 13\n34 3\n22 26\n5 6\n8 17\n32 18\n40 31\n7 40\n17 21\n37 18\n30 41\n2 47\n4 48\n36 32\n45 20\n39 28\n39 43\n7 33\n44 48\n21 47\n14 26\n15 47\n16 14\n23 18\n50 12\n28 8\n10 6\n12 46\n41 5\n",
"8 8\n1 3 2 1 3 3 1 3\n8 2\n6 3\n4 3\n2 6\n4 6\n4 3\n3 5\n1 6\n",
"50 47\n21 17 47 15 50 47 47 41 30 18 27 47 29 28 32 26 16 26 8 22 27 10 45 21 17 30 31 38 14 8 9 40 10 35 41 24 22 14 40 46 44 34 40 31 48 40 8 50 1 28\n7 5\n34 2\n42 5\n36 28\n8 44\n36 3\n40 15\n33 18\n5 50\n1 6\n25 20\n39 24\n45 35\n14 27\n21 39\n17 47\n19 49\n28 10\n7 13\n34 3\n22 26\n5 6\n8 17\n32 18\n40 31\n7 40\n17 21\n37 18\n30 41\n2 47\n4 48\n36 32\n45 20\n39 28\n39 43\n7 33\n44 48\n21 47\n14 26\n15 47\n16 14\n23 18\n50 12\n28 8\n10 6\n12 46\n41 5\n",
"8 8\n1 3 2 1 3 3 1 3\n8 2\n6 3\n4 3\n2 6\n5 6\n4 3\n3 5\n1 6\n",
"50 47\n21 17 47 15 50 47 47 41 30 18 27 47 29 28 32 26 16 26 8 22 27 10 45 21 17 30 31 38 14 8 9 40 10 35 41 24 22 14 40 46 44 34 40 31 48 40 8 50 1 28\n7 5\n34 2\n42 5\n36 28\n8 44\n36 3\n40 15\n33 18\n5 50\n1 6\n25 20\n39 24\n45 35\n14 27\n21 39\n17 47\n19 49\n28 10\n7 13\n34 3\n22 26\n5 6\n8 17\n32 18\n40 31\n7 40\n17 21\n37 18\n30 41\n2 47\n4 48\n36 32\n45 20\n39 28\n39 43\n7 33\n44 48\n21 47\n14 26\n15 6\n16 14\n23 18\n50 12\n28 8\n10 6\n12 46\n41 5\n",
"8 8\n1 3 2 2 3 3 1 3\n8 2\n6 3\n4 3\n2 6\n5 6\n4 3\n3 5\n1 6\n",
"50 47\n21 17 47 15 50 47 47 41 30 18 27 47 29 28 32 26 16 26 8 22 27 10 45 21 17 30 31 38 14 8 9 40 10 35 41 24 22 14 40 46 44 34 40 31 48 40 8 50 1 28\n7 5\n34 2\n42 5\n36 28\n8 44\n36 3\n40 15\n33 18\n5 50\n1 6\n25 20\n39 24\n45 47\n14 27\n21 39\n17 47\n19 49\n28 10\n7 13\n34 3\n22 26\n5 6\n8 17\n32 18\n40 31\n7 40\n17 21\n37 18\n30 41\n2 47\n4 48\n36 32\n45 20\n39 28\n39 43\n7 33\n44 48\n21 47\n14 26\n15 6\n16 14\n23 18\n50 12\n28 8\n10 6\n12 46\n41 5\n",
"8 8\n1 3 2 2 3 3 1 3\n8 2\n6 6\n4 3\n2 6\n5 6\n4 3\n3 5\n1 6\n",
"10 15\n1 1 1 1 2 2 2 2 1 2\n8 5\n6 1\n8 6\n3 5\n2 7\n2 9\n10 3\n3 2\n3 6\n4 2\n5 9\n7 3\n6 7\n5 10\n4 7\n",
"3 1\n2 13 4\n1 2\n",
"10 27\n1 1 3 2 4 1 3 2 4 1\n9 3\n7 8\n9 7\n6 5\n7 6\n7 4\n6 9\n3 8\n6 10\n8 5\n3 1\n4 6\n8 1\n10 8\n9 5\n10 1\n5 10\n3 6\n4 5\n8 2\n10 7\n10 9\n10 3\n8 4\n3 2\n2 4\n6 1\n",
"7 6\n1 2 3 4 3 3 3\n5 1\n6 1\n7 1\n1 2\n2 3\n3 4\n",
"5 2\n4 4 4 3 3\n1 2\n4 5\n",
"8 8\n3 3 2 3 3 3 1 3\n8 2\n6 3\n2 3\n2 6\n5 6\n4 1\n7 5\n1 6\n",
"50 47\n21 17 47 15 50 47 47 41 28 18 27 47 29 28 32 26 16 26 8 22 27 10 45 21 17 30 31 38 14 8 9 40 29 35 41 24 22 14 40 46 44 34 40 31 48 40 8 50 1 28\n7 5\n50 2\n42 5\n36 28\n8 44\n36 4\n40 15\n33 18\n5 50\n1 6\n25 20\n39 24\n45 35\n14 27\n14 39\n17 47\n19 49\n28 7\n7 13\n34 3\n22 26\n5 6\n8 17\n32 18\n40 31\n4 40\n17 21\n37 18\n30 41\n2 47\n4 48\n36 32\n45 20\n39 28\n39 43\n7 33\n44 48\n21 47\n14 26\n15 47\n16 14\n23 18\n50 12\n28 8\n10 6\n12 46\n41 5\n",
"6 1\n10 1 2 2 3 4\n2 3\n",
"5 6\n4 2 5 2 4\n1 2\n2 3\n3 1\n3 3\n5 4\n3 4\n",
"8 8\n3 3 2 3 3 3 1 3\n8 2\n6 3\n2 3\n2 6\n4 5\n4 2\n7 5\n1 6\n",
"6 5\n2 2 2 1 2 2\n4 5\n4 2\n5 1\n4 1\n2 2\n",
"5 6\n4 2 5 2 7\n1 2\n2 3\n1 1\n5 3\n5 4\n3 4\n",
"10 9\n1 1 1 1 1 1 1 1 1 1\n5 8\n8 3\n1 9\n8 4\n3 7\n2 10\n1 9\n2 5\n6 9\n",
"8 8\n3 6 2 1 3 3 1 3\n8 2\n6 3\n2 3\n2 6\n4 6\n4 2\n7 5\n1 6\n",
"50 47\n21 17 47 15 50 47 47 41 28 18 27 47 29 28 32 26 16 26 8 22 27 10 45 21 17 30 31 38 14 8 9 40 29 35 41 24 22 14 40 46 44 34 40 31 48 40 8 50 1 28\n7 5\n34 2\n42 5\n36 28\n8 44\n36 3\n40 15\n33 18\n5 50\n1 6\n25 20\n39 24\n45 35\n14 27\n14 39\n17 47\n19 49\n28 7\n7 13\n34 3\n22 26\n5 6\n8 17\n32 18\n40 31\n7 40\n17 3\n37 18\n30 41\n2 47\n4 48\n36 32\n45 20\n39 28\n39 43\n7 33\n44 48\n21 47\n14 26\n15 47\n16 14\n23 18\n50 12\n28 8\n10 6\n12 46\n41 5\n",
"6 6\n1 1 2 3 5 4\n1 2\n3 2\n2 6\n4 3\n4 5\n4 6\n",
"10 9\n1 1 1 1 1 1 1 1 1 1\n5 4\n8 3\n1 8\n8 5\n3 7\n2 10\n1 9\n2 5\n6 9\n",
"8 8\n3 3 4 1 3 3 1 3\n8 2\n6 3\n2 3\n2 6\n4 6\n4 3\n7 5\n1 6\n",
"50 47\n21 17 47 15 50 47 47 41 28 18 27 47 29 28 32 26 16 26 8 22 27 10 45 21 17 30 31 38 14 8 9 40 29 35 41 24 22 14 40 46 44 34 40 31 48 40 8 50 1 28\n10 5\n34 2\n42 5\n36 28\n8 44\n36 3\n40 15\n33 18\n5 50\n1 6\n25 20\n39 24\n45 35\n14 27\n14 39\n17 47\n19 49\n28 10\n7 13\n34 3\n22 26\n5 6\n8 17\n32 18\n40 31\n7 40\n17 21\n37 18\n30 41\n2 47\n4 48\n36 32\n45 20\n39 28\n39 43\n7 33\n44 48\n21 47\n14 26\n15 47\n16 14\n23 18\n50 12\n28 8\n10 6\n12 46\n41 5\n",
"8 8\n1 3 2 1 3 3 1 3\n8 2\n6 3\n2 3\n4 6\n4 6\n4 3\n7 5\n1 6\n",
"50 47\n21 17 47 15 50 47 47 41 30 18 27 47 29 28 32 26 16 26 8 22 27 10 45 21 17 30 31 38 14 8 9 40 29 35 41 24 22 14 40 46 44 34 40 31 48 40 8 50 1 28\n7 5\n34 2\n42 5\n36 28\n8 44\n36 3\n40 15\n33 18\n5 50\n1 6\n25 20\n39 24\n45 35\n14 27\n14 39\n17 47\n19 49\n9 10\n7 13\n34 3\n22 26\n5 6\n8 17\n32 18\n40 31\n7 40\n17 21\n37 18\n30 41\n2 47\n4 48\n36 32\n45 20\n39 28\n39 43\n7 33\n44 48\n21 47\n14 26\n15 47\n16 14\n23 18\n50 12\n28 8\n10 6\n12 46\n41 5\n",
"8 8\n1 3 2 1 3 3 1 3\n8 2\n6 4\n2 3\n2 6\n4 6\n4 3\n3 5\n1 6\n",
"50 47\n21 17 47 15 50 47 47 41 30 18 27 47 29 28 32 26 16 26 8 22 27 10 45 21 17 30 31 38 14 8 9 40 10 35 41 24 22 14 40 46 44 34 40 31 48 40 8 50 1 28\n7 5\n34 2\n42 5\n36 28\n8 44\n36 3\n40 15\n33 18\n5 50\n1 6\n25 20\n39 24\n45 35\n14 27\n14 39\n17 47\n19 49\n28 10\n7 13\n34 3\n22 26\n5 6\n8 17\n32 18\n40 31\n7 40\n17 21\n37 18\n30 41\n2 47\n4 48\n36 32\n45 20\n39 28\n39 43\n7 33\n44 48\n21 47\n14 26\n15 47\n16 14\n23 18\n50 12\n31 8\n10 6\n12 46\n41 5\n",
"8 8\n1 3 2 1 3 3 1 3\n8 2\n6 3\n4 3\n2 6\n4 6\n4 3\n4 5\n1 6\n",
"50 47\n21 17 47 15 50 47 47 41 30 18 27 47 29 28 32 26 16 26 8 22 27 10 45 21 17 30 31 38 14 8 9 40 10 35 41 24 22 14 40 46 44 34 40 31 48 40 8 50 1 28\n7 5\n34 2\n42 5\n36 28\n8 44\n36 3\n40 15\n33 18\n5 50\n1 6\n25 20\n39 24\n45 35\n14 27\n21 39\n17 47\n19 49\n28 10\n7 13\n34 3\n22 26\n5 6\n8 17\n32 18\n40 31\n7 40\n17 21\n37 18\n30 41\n2 47\n4 48\n36 32\n45 5\n39 28\n39 43\n7 33\n44 48\n21 47\n14 26\n15 47\n16 14\n23 18\n50 12\n28 8\n10 6\n12 46\n41 5\n",
"8 8\n1 3 2 1 3 3 1 4\n8 2\n6 3\n4 3\n2 6\n5 6\n4 3\n3 5\n1 6\n",
"50 47\n21 17 47 15 50 47 47 41 30 18 27 47 29 28 32 26 16 26 8 22 27 10 45 21 17 30 31 38 14 8 9 40 10 35 41 24 22 14 40 46 44 34 40 31 48 40 8 50 1 28\n7 5\n34 2\n42 5\n36 28\n8 44\n36 3\n40 15\n33 18\n5 50\n1 6\n25 20\n39 24\n45 35\n14 27\n21 39\n17 47\n19 49\n28 10\n7 13\n34 3\n22 26\n5 6\n8 17\n32 18\n40 31\n2 40\n17 21\n37 18\n30 41\n2 47\n4 48\n36 32\n45 20\n39 28\n39 43\n7 33\n44 48\n21 47\n14 26\n15 6\n16 14\n23 18\n50 12\n28 8\n10 6\n12 46\n41 5\n",
"8 8\n1 3 2 2 3 3 1 3\n8 2\n6 3\n4 3\n2 6\n8 6\n4 3\n3 5\n1 6\n",
"50 47\n21 17 47 15 50 47 47 41 30 18 27 47 46 28 32 26 16 26 8 22 27 10 45 21 17 30 31 38 14 8 9 40 10 35 41 24 22 14 40 46 44 34 40 31 48 40 8 50 1 28\n7 5\n34 2\n42 5\n36 28\n8 44\n36 3\n40 15\n33 18\n5 50\n1 6\n25 20\n39 24\n45 47\n14 27\n21 39\n17 47\n19 49\n28 10\n7 13\n34 3\n22 26\n5 6\n8 17\n32 18\n40 31\n7 40\n17 21\n37 18\n30 41\n2 47\n4 48\n36 32\n45 20\n39 28\n39 43\n7 33\n44 48\n21 47\n14 26\n15 6\n16 14\n23 18\n50 12\n28 8\n10 6\n12 46\n41 5\n",
"8 8\n1 3 2 2 3 3 1 3\n8 2\n6 6\n4 5\n2 6\n5 6\n4 3\n3 5\n1 6\n",
"10 15\n1 1 1 1 2 2 2 2 1 2\n8 5\n6 1\n8 6\n3 5\n2 7\n2 9\n10 3\n3 2\n3 6\n4 2\n5 9\n7 3\n9 7\n5 10\n4 7\n",
"10 27\n1 1 3 2 4 1 3 2 4 1\n9 3\n7 8\n9 7\n6 9\n7 6\n7 4\n6 9\n3 8\n6 10\n8 5\n3 1\n4 6\n8 1\n10 8\n9 5\n10 1\n5 10\n3 6\n4 5\n8 2\n10 7\n10 9\n10 3\n8 4\n3 2\n2 4\n6 1\n",
"7 6\n1 2 3 4 3 3 3\n5 2\n6 1\n7 1\n1 2\n2 3\n3 4\n",
"5 2\n2 4 4 3 3\n1 2\n4 5\n",
"50 47\n21 17 47 15 50 47 47 41 28 18 27 47 29 28 32 26 16 26 8 22 27 10 45 21 17 30 31 38 14 8 9 40 29 35 41 24 22 14 40 46 44 34 40 31 48 44 8 50 1 28\n7 5\n50 2\n42 5\n36 28\n8 44\n36 4\n40 15\n33 18\n5 50\n1 6\n25 20\n39 24\n45 35\n14 27\n14 39\n17 47\n19 49\n28 7\n7 13\n34 3\n22 26\n5 6\n8 17\n32 18\n40 31\n4 40\n17 21\n37 18\n30 41\n2 47\n4 48\n36 32\n45 20\n39 28\n39 43\n7 33\n44 48\n21 47\n14 26\n15 47\n16 14\n23 18\n50 12\n28 8\n10 6\n12 46\n41 5\n",
"5 6\n4 2 5 2 4\n1 2\n2 3\n3 1\n3 3\n5 4\n5 4\n",
"5 6\n4 2 4 2 7\n1 2\n2 3\n1 1\n5 3\n5 4\n3 4\n",
"10 9\n1 1 1 1 1 1 1 1 1 1\n5 8\n8 3\n1 9\n8 4\n3 7\n2 10\n1 9\n4 5\n6 9\n",
"8 8\n4 6 2 1 3 3 1 3\n8 2\n6 3\n2 3\n2 6\n4 6\n4 2\n7 5\n1 6\n",
"50 47\n21 17 47 15 50 47 47 41 28 18 27 47 29 28 32 26 16 26 8 22 27 10 45 21 17 30 31 38 14 8 9 40 29 35 41 24 22 14 40 46 44 34 40 31 48 40 8 50 1 28\n7 5\n34 2\n42 5\n36 28\n8 44\n36 3\n40 15\n33 18\n5 50\n1 6\n25 20\n39 24\n45 35\n14 27\n14 39\n17 47\n19 49\n28 7\n7 13\n34 3\n22 26\n5 6\n8 17\n32 18\n40 31\n7 40\n17 3\n37 18\n30 41\n2 47\n4 48\n36 32\n45 20\n39 28\n39 43\n7 33\n44 48\n21 47\n14 26\n15 47\n16 24\n23 18\n50 12\n28 8\n10 6\n12 46\n41 5\n",
"10 9\n1 1 1 1 1 1 1 1 1 1\n5 1\n8 3\n1 8\n8 5\n3 7\n2 10\n1 9\n2 5\n6 9\n",
"8 8\n3 3 4 1 3 3 1 3\n8 2\n6 3\n2 3\n2 6\n7 6\n4 3\n7 5\n1 6\n",
"50 47\n21 17 47 15 50 47 47 41 30 18 27 47 29 28 32 26 23 26 8 22 27 10 45 21 17 30 31 38 14 8 9 40 29 35 41 24 22 14 40 46 44 34 40 31 48 40 8 50 1 28\n7 5\n34 2\n42 5\n36 28\n8 44\n36 3\n40 15\n33 18\n5 50\n1 6\n25 20\n39 24\n45 35\n14 27\n14 39\n17 47\n19 49\n9 10\n7 13\n34 3\n22 26\n5 6\n8 17\n32 18\n40 31\n7 40\n17 21\n37 18\n30 41\n2 47\n4 48\n36 32\n45 20\n39 28\n39 43\n7 33\n44 48\n21 47\n14 26\n15 47\n16 14\n23 18\n50 12\n28 8\n10 6\n12 46\n41 5\n",
"8 8\n1 5 2 1 3 3 1 3\n8 2\n6 4\n2 3\n2 6\n4 6\n4 3\n3 5\n1 6\n",
"50 47\n21 17 47 15 50 47 47 41 30 18 27 47 29 28 32 26 16 26 8 22 27 10 45 21 17 30 31 38 14 8 9 40 10 35 41 24 22 14 40 46 44 34 40 31 48 40 8 50 1 28\n7 5\n34 2\n42 5\n36 28\n8 44\n36 3\n40 15\n33 18\n5 50\n1 6\n25 20\n39 24\n45 35\n14 27\n14 19\n17 47\n19 49\n28 10\n7 13\n34 3\n22 26\n5 6\n8 17\n32 18\n40 31\n7 40\n17 21\n37 18\n30 41\n2 47\n4 48\n36 32\n45 20\n39 28\n39 43\n7 33\n44 48\n21 47\n14 26\n15 47\n16 14\n23 18\n50 12\n31 8\n10 6\n12 46\n41 5\n",
"50 47\n21 17 47 15 50 47 47 41 30 18 27 47 29 28 32 26 16 26 8 22 27 10 45 21 17 30 31 38 14 8 9 40 10 35 41 24 22 14 40 46 44 34 40 31 48 40 8 50 1 28\n7 5\n34 2\n42 5\n36 28\n8 44\n36 3\n40 15\n33 18\n5 50\n1 6\n25 20\n39 24\n45 35\n14 27\n21 39\n17 47\n19 49\n28 10\n7 13\n34 3\n22 26\n5 6\n8 17\n32 18\n40 31\n7 40\n17 21\n37 18\n15 41\n2 47\n4 48\n36 32\n45 5\n39 28\n39 43\n7 33\n44 48\n21 47\n14 26\n15 47\n16 14\n23 18\n50 12\n28 8\n10 6\n12 46\n41 5\n",
"8 8\n1 3 2 1 3 3 1 4\n8 2\n6 4\n4 3\n2 6\n5 6\n4 3\n3 5\n1 6\n",
"50 47\n21 17 47 15 50 47 47 41 30 18 27 47 29 28 32 26 16 26 8 22 27 10 45 21 17 30 31 38 14 8 9 40 10 35 41 24 22 14 40 46 44 34 40 31 48 40 8 50 1 28\n7 5\n34 2\n42 5\n36 28\n8 44\n36 3\n40 15\n33 18\n5 50\n1 6\n25 20\n39 24\n45 35\n14 27\n21 39\n17 47\n19 49\n28 10\n7 13\n34 3\n22 26\n5 6\n8 17\n10 18\n40 31\n2 40\n17 21\n37 18\n30 41\n2 47\n4 48\n36 32\n45 20\n39 28\n39 43\n7 33\n44 48\n21 47\n14 26\n15 6\n16 14\n23 18\n50 12\n28 8\n10 6\n12 46\n41 5\n",
"8 8\n1 3 2 2 3 3 1 3\n8 2\n6 3\n4 3\n2 6\n8 6\n4 3\n3 3\n1 6\n",
"50 47\n21 17 47 15 50 47 47 41 30 18 27 47 46 28 32 26 16 26 8 22 27 10 45 21 17 30 31 38 14 8 9 40 10 35 41 24 22 14 40 76 44 34 40 31 48 40 8 50 1 28\n7 5\n34 2\n42 5\n36 28\n8 44\n36 3\n40 15\n33 18\n5 50\n1 6\n25 20\n39 24\n45 47\n14 27\n21 39\n17 47\n19 49\n28 10\n7 13\n34 3\n22 26\n5 6\n8 17\n32 18\n40 31\n7 40\n17 21\n37 18\n30 41\n2 47\n4 48\n36 32\n45 20\n39 28\n39 43\n7 33\n44 48\n21 47\n14 26\n15 6\n16 14\n23 18\n50 12\n28 8\n10 6\n12 46\n41 5\n",
"10 15\n1 1 1 1 2 2 2 2 1 2\n8 5\n6 1\n8 6\n3 5\n2 7\n2 9\n10 3\n6 2\n3 6\n4 2\n5 9\n7 3\n9 7\n5 10\n4 7\n",
"10 27\n1 1 3 2 4 1 3 2 4 1\n9 3\n7 8\n9 7\n6 9\n7 6\n7 4\n6 9\n3 8\n6 10\n8 5\n3 1\n4 6\n8 1\n10 8\n9 5\n10 1\n5 10\n3 6\n4 5\n8 2\n10 7\n10 2\n10 3\n8 4\n3 2\n2 4\n6 1\n",
"50 47\n21 17 47 15 50 47 47 41 28 18 27 47 29 28 32 26 16 26 8 22 27 10 45 21 17 30 31 38 14 8 9 40 29 35 41 24 22 14 40 46 44 34 40 31 48 44 8 50 1 28\n7 5\n50 2\n42 5\n36 28\n8 44\n36 4\n40 15\n33 18\n5 50\n1 6\n25 20\n39 24\n45 35\n14 27\n14 39\n17 47\n19 49\n28 7\n7 13\n34 3\n22 26\n5 6\n8 17\n32 18\n40 31\n4 40\n17 21\n37 18\n30 41\n2 47\n4 48\n36 32\n45 20\n39 28\n39 43\n7 33\n44 48\n21 47\n14 26\n15 47\n11 14\n23 18\n50 12\n28 8\n10 6\n12 46\n41 5\n",
"5 6\n4 2 5 2 4\n1 2\n2 3\n3 1\n3 3\n5 2\n5 4\n",
"10 9\n1 1 1 1 1 1 1 1 1 1\n5 8\n8 3\n1 9\n8 4\n3 7\n2 10\n1 9\n4 5\n6 8\n",
"8 8\n4 6 2 1 3 3 1 3\n8 2\n6 3\n2 3\n2 6\n5 6\n4 2\n7 5\n1 6\n",
"10 9\n1 1 1 1 1 1 1 1 1 1\n5 1\n8 3\n1 8\n8 5\n3 7\n2 10\n2 9\n2 5\n6 9\n",
"50 47\n21 17 47 15 50 47 47 41 30 18 27 47 29 28 32 26 23 26 8 22 27 10 45 21 17 30 31 38 14 8 9 40 29 35 41 24 22 14 40 46 44 34 40 31 48 40 8 50 1 28\n7 5\n34 3\n42 5\n36 28\n8 44\n36 3\n40 15\n33 18\n5 50\n1 6\n25 20\n39 24\n45 35\n14 27\n14 39\n17 47\n19 49\n9 10\n7 13\n34 3\n22 26\n5 6\n8 17\n32 18\n40 31\n7 40\n17 21\n37 18\n30 41\n2 47\n4 48\n36 32\n45 20\n39 28\n39 43\n7 33\n44 48\n21 47\n14 26\n15 47\n16 14\n23 18\n50 12\n28 8\n10 6\n12 46\n41 5\n",
"50 47\n21 17 47 15 50 47 47 41 30 18 27 47 29 28 32 26 16 26 8 22 27 10 45 21 17 30 31 38 14 8 9 40 10 35 41 24 22 14 40 46 44 34 40 31 48 40 8 50 1 28\n7 5\n34 2\n42 5\n36 28\n8 44\n36 3\n40 15\n33 2\n5 50\n1 6\n25 20\n39 24\n45 35\n14 27\n14 19\n17 47\n19 49\n28 10\n7 13\n34 3\n22 26\n5 6\n8 17\n32 18\n40 31\n7 40\n17 21\n37 18\n30 41\n2 47\n4 48\n36 32\n45 20\n39 28\n39 43\n7 33\n44 48\n21 47\n14 26\n15 47\n16 14\n23 18\n50 12\n31 8\n10 6\n12 46\n41 5\n",
"50 47\n21 17 47 15 50 47 47 41 30 18 27 47 29 28 32 26 16 26 8 22 27 10 45 21 17 30 31 38 14 8 9 40 10 35 41 25 22 14 40 46 44 34 40 31 48 40 8 50 1 28\n7 5\n34 2\n42 5\n36 28\n8 44\n36 3\n40 15\n33 18\n5 50\n1 6\n25 20\n39 24\n45 35\n14 27\n21 39\n17 47\n19 49\n28 10\n7 13\n34 3\n22 26\n5 6\n8 17\n32 18\n40 31\n7 40\n17 21\n37 18\n15 41\n2 47\n4 48\n36 32\n45 5\n39 28\n39 43\n7 33\n44 48\n21 47\n14 26\n15 47\n16 14\n23 18\n50 12\n28 8\n10 6\n12 46\n41 5\n",
"8 8\n1 3 2 1 3 3 1 4\n3 2\n6 4\n4 3\n2 6\n5 6\n4 3\n3 5\n1 6\n",
"50 47\n21 17 47 15 50 47 47 41 30 18 27 47 29 28 32 26 16 26 8 22 27 10 45 21 17 30 31 38 14 8 9 40 10 35 41 24 22 14 40 46 44 34 40 31 48 40 8 50 1 28\n7 5\n34 2\n42 5\n36 28\n8 44\n36 3\n40 15\n33 18\n5 50\n1 6\n25 20\n39 24\n45 35\n14 27\n21 39\n17 47\n19 49\n28 10\n7 13\n34 3\n22 26\n5 6\n8 17\n10 18\n40 31\n2 40\n17 21\n37 18\n30 41\n2 47\n4 48\n36 32\n45 20\n39 28\n39 43\n7 33\n44 48\n21 50\n14 26\n15 6\n16 14\n23 18\n50 12\n28 8\n10 6\n12 46\n41 5\n",
"8 8\n1 3 2 2 3 3 1 3\n8 2\n6 3\n4 3\n2 6\n8 6\n4 2\n3 3\n1 6\n",
"10 15\n1 1 1 1 2 2 2 2 1 2\n8 5\n6 1\n8 6\n3 5\n2 7\n2 9\n10 3\n6 4\n3 6\n4 2\n5 9\n7 3\n9 7\n5 10\n4 7\n",
"10 27\n1 1 3 2 4 1 3 2 4 1\n9 3\n7 8\n9 7\n6 9\n7 6\n7 4\n6 9\n3 8\n6 10\n8 5\n3 1\n4 6\n8 1\n10 8\n9 5\n9 1\n5 10\n3 6\n4 5\n8 2\n10 7\n10 2\n10 3\n8 4\n3 2\n2 4\n6 1\n",
"10 9\n1 1 1 1 1 1 1 1 1 1\n5 8\n8 3\n1 9\n8 4\n3 7\n2 10\n1 9\n4 5\n6 6\n",
"10 9\n1 1 1 1 1 1 1 1 1 1\n3 1\n8 3\n1 8\n8 5\n3 7\n2 10\n2 9\n2 5\n6 9\n",
"50 47\n21 17 47 15 50 47 47 41 30 18 27 47 29 28 32 26 23 26 8 22 27 10 45 21 17 30 31 38 14 8 9 40 29 35 41 24 22 14 40 46 44 34 40 31 48 40 8 50 1 28\n7 5\n34 3\n42 5\n36 28\n8 44\n36 3\n40 15\n33 18\n5 50\n1 6\n25 20\n39 24\n45 35\n14 27\n14 39\n17 47\n19 49\n9 10\n13 13\n34 3\n22 26\n5 6\n8 17\n32 18\n40 31\n7 40\n17 21\n37 18\n30 41\n2 47\n4 48\n36 32\n45 20\n39 28\n39 43\n7 33\n44 48\n21 47\n14 26\n15 47\n16 14\n23 18\n50 12\n28 8\n10 6\n12 46\n41 5\n"
],
"output": [
"2",
"3",
"1",
"1",
"4",
"1",
"300",
"2",
"100000",
"3",
"3",
"47",
"1",
"1",
"300",
"1\n",
"2\n",
"3\n",
"47\n",
"1\n",
"2\n",
"3\n",
"1\n",
"1\n",
"3\n",
"47\n",
"3\n",
"1\n",
"1\n",
"47\n",
"1\n",
"47\n",
"1\n",
"47\n",
"1\n",
"47\n",
"1\n",
"47\n",
"3\n",
"47\n",
"3\n",
"1\n",
"2\n",
"1\n",
"3\n",
"3\n",
"3\n",
"47\n",
"1\n",
"2\n",
"3\n",
"1\n",
"2\n",
"1\n",
"3\n",
"47\n",
"3\n",
"1\n",
"1\n",
"47\n",
"1\n",
"47\n",
"1\n",
"47\n",
"1\n",
"47\n",
"3\n",
"47\n",
"3\n",
"47\n",
"3\n",
"1\n",
"1\n",
"3\n",
"2\n",
"47\n",
"2\n",
"2\n",
"1\n",
"3\n",
"47\n",
"1\n",
"1\n",
"47\n",
"2\n",
"47\n",
"47\n",
"3\n",
"47\n",
"3\n",
"47\n",
"1\n",
"1\n",
"47\n",
"2\n",
"1\n",
"3\n",
"1\n",
"47\n",
"47\n",
"47\n",
"1\n",
"47\n",
"3\n",
"1\n",
"1\n",
"1\n",
"1\n",
"47\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You've got an undirected graph, consisting of n vertices and m edges. We will consider the graph's vertices numbered with integers from 1 to n. Each vertex of the graph has a color. The color of the i-th vertex is an integer ci.
Let's consider all vertices of the graph, that are painted some color k. Let's denote a set of such as V(k). Let's denote the value of the neighbouring color diversity for color k as the cardinality of the set Q(k) = {cu : cu ≠ k and there is vertex v belonging to set V(k) such that nodes v and u are connected by an edge of the graph}.
Your task is to find such color k, which makes the cardinality of set Q(k) maximum. In other words, you want to find the color that has the most diverse neighbours. Please note, that you want to find such color k, that the graph has at least one vertex with such color.
Input
The first line contains two space-separated integers n, m (1 ≤ n, m ≤ 105) — the number of vertices end edges of the graph, correspondingly. The second line contains a sequence of integers c1, c2, ..., cn (1 ≤ ci ≤ 105) — the colors of the graph vertices. The numbers on the line are separated by spaces.
Next m lines contain the description of the edges: the i-th line contains two space-separated integers ai, bi (1 ≤ ai, bi ≤ n; ai ≠ bi) — the numbers of the vertices, connected by the i-th edge.
It is guaranteed that the given graph has no self-loops or multiple edges.
Output
Print the number of the color which has the set of neighbours with the maximum cardinality. It there are multiple optimal colors, print the color with the minimum number. Please note, that you want to find such color, that the graph has at least one vertex with such color.
Examples
Input
6 6
1 1 2 3 5 8
1 2
3 2
1 4
4 3
4 5
4 6
Output
3
Input
5 6
4 2 5 2 4
1 2
2 3
3 1
5 3
5 4
3 4
Output
2
### Input:
5 6
4 2 5 2 4
1 2
2 3
3 1
5 3
5 4
3 4
### Output:
2
### Input:
6 6
1 1 2 3 5 8
1 2
3 2
1 4
4 3
4 5
4 6
### Output:
3
### Code:
from collections import defaultdict
l=lambda :map(int,input().split())
n,m=l()
c=list(l())
graph=defaultdict(set)
for i in range(m):
a,b=l()
if c[a-1]==c[b-1]:
continue
graph[c[a-1]].add(c[b-1])
graph[c[b - 1]].add(c[a - 1])
d,f=min(c),0
for i in sorted(graph):
h=len(graph[i])
if h>f:
f=h
d=i
print(d)
|
271_E. Three Horses_10562
|
There are three horses living in a horse land: one gray, one white and one gray-and-white. The horses are really amusing animals, which is why they adore special cards. Each of those cards must contain two integers, the first one on top, the second one in the bottom of the card. Let's denote a card with a on the top and b in the bottom as (a, b).
Each of the three horses can paint the special cards. If you show an (a, b) card to the gray horse, then the horse can paint a new (a + 1, b + 1) card. If you show an (a, b) card, such that a and b are even integers, to the white horse, then the horse can paint a new <image> card. If you show two cards (a, b) and (b, c) to the gray-and-white horse, then he can paint a new (a, c) card.
Polycarpus really wants to get n special cards (1, a1), (1, a2), ..., (1, an). For that he is going to the horse land. He can take exactly one (x, y) card to the horse land, such that 1 ≤ x < y ≤ m. How many ways are there to choose the card so that he can perform some actions in the horse land and get the required cards?
Polycarpus can get cards from the horses only as a result of the actions that are described above. Polycarpus is allowed to get additional cards besides the cards that he requires.
Input
The first line contains two integers n, m (1 ≤ n ≤ 105, 2 ≤ m ≤ 109). The second line contains the sequence of integers a1, a2, ..., an (2 ≤ ai ≤ 109). Note, that the numbers in the sequence can coincide.
The numbers in the lines are separated by single spaces.
Output
Print a single integer — the answer to the problem.
Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specifier.
Examples
Input
1 6
2
Output
11
Input
1 6
7
Output
14
Input
2 10
13 7
Output
36
|
# written with help of editorial
n, m = map(int, input().split())
a = list(map(int, input().split()))
def gcd(x, y):
while y:
x, y = y, x % y
return x
g = 0
for x in a:
g = gcd(g, x - 1)
answer = 0
def process(x):
global answer
if x % 2 == 0:
return 0
for i in range(30):
v = 2 ** i * x
if v > m:
break
answer += m - v
for i in range(1, g + 1):
if i * i > g:
break
if g % i:
continue
process(i)
if i * i != g:
process(g // i)
print(answer)
|
{
"input": [
"1 6\n2\n",
"2 10\n13 7\n",
"1 6\n7\n",
"5 1000000000\n812747000 266266300 444091950 694572960 414735290\n",
"10 10\n4 8 4 10 2 10 8 10 4 6\n",
"5 22\n14 7 14 21 14\n",
"1 1000000000\n12\n",
"1 1000000000\n1000000000\n",
"5 20\n11 11 11 11 11\n",
"6 23\n16 16 16 8 8 8\n",
"1 922296375\n922296375\n",
"1 24\n10\n",
"2 20\n9 9\n",
"2 1000000000\n2 1000000000\n",
"5 21\n12 12 12 12 12\n",
"10 10\n9 3 6 6 3 3 6 3 6 9\n",
"5 1000000000\n812747000 266266300 444091950 694572960 275914385\n",
"10 10\n4 11 4 10 2 10 8 10 4 6\n",
"1 1000010000\n12\n",
"5 20\n11 11 6 11 11\n",
"1 24\n16\n",
"5 22\n12 12 12 12 12\n",
"1 6\n3\n",
"1 1000010000\n16\n",
"5 20\n15 11 6 11 11\n",
"5 22\n19 12 12 12 12\n",
"1 6\n4\n",
"10 14\n4 11 4 10 2 10 8 10 4 5\n",
"1 1000000000\n16\n",
"1 1010000000\n16\n",
"10 26\n6 11 4 10 2 10 8 10 4 5\n",
"5 32\n25 11 2 11 11\n",
"6 19\n16 16 16 8 8 8\n",
"1 922296375\n216617768\n",
"2 33\n9 9\n",
"10 1\n4 11 4 10 2 10 8 10 4 5\n",
"5 36\n25 11 6 11 11\n",
"1 1010000000\n8\n",
"5 9\n25 11 2 11 11\n",
"2 57\n9 9\n",
"1 1010000000\n5\n",
"10 10\n4 11 4 10 2 10 8 10 4 5\n",
"5 20\n25 11 6 11 11\n",
"10 14\n6 11 4 10 2 10 8 10 4 5\n",
"5 20\n25 11 2 11 11\n",
"10 26\n6 11 4 10 4 10 8 10 4 5\n",
"5 32\n25 11 2 11 5\n",
"10 26\n6 10 4 10 4 10 8 10 4 5\n",
"5 32\n25 15 2 11 5\n",
"10 26\n6 10 4 10 4 10 8 10 4 4\n",
"5 1000000000\n812747000 266266300 444091950 694572960 293081217\n",
"5 20\n11 11 11 11 8\n",
"10 10\n5 3 6 6 3 3 6 3 6 9\n",
"1 7\n2\n",
"5 22\n12 12 24 12 12\n",
"10 6\n4 11 4 10 2 10 8 10 4 5\n",
"5 20\n28 11 6 11 11\n",
"5 22\n19 12 12 2 12\n",
"1 1000000000\n31\n",
"10 14\n6 11 4 17 2 10 8 10 4 5\n",
"5 32\n25 11 2 11 21\n",
"5 32\n36 11 2 11 5\n",
"5 32\n25 15 2 21 5\n",
"5 1000000000\n812747000 266266300 444091950 1102981225 293081217\n",
"10 10\n5 3 6 6 3 3 6 5 6 9\n",
"5 22\n12 11 24 12 12\n",
"10 9\n4 11 4 10 2 10 8 10 4 5\n",
"5 20\n28 11 6 11 8\n",
"10 1\n4 9 4 10 2 10 8 10 4 5\n",
"5 36\n25 13 6 11 11\n",
"10 14\n6 11 5 17 2 10 8 10 4 5\n"
],
"output": [
" 11\n",
" 36\n",
" 14\n",
"28926258177\n",
" 25\n",
" 79\n",
"54449863180\n",
"281663002102\n",
" 94\n",
" 84\n",
"27056297616\n",
" 161\n",
" 69\n",
"28926258177\n",
" 84\n",
" 25\n",
"28926258177\n",
"25\n",
"54450433180\n",
"94\n",
"186\n",
"90\n",
"11\n",
"107967965224\n",
"69\n",
"79\n",
"14\n",
"41\n",
"107966835224\n",
"109100202264\n",
"99\n",
"129\n",
"64\n",
"110920093076\n",
"135\n",
"0\n",
"153\n",
"55627209992\n",
"21\n",
"279\n",
"29226258177\n",
"25\n",
"69\n",
"41\n",
"69\n",
"99\n",
"129\n",
"99\n",
"129\n",
"99\n",
"28926258177\n",
"69\n",
"25\n",
"14\n",
"79\n",
"11\n",
"69\n",
"79\n",
"107966835224\n",
"41\n",
"129\n",
"129\n",
"129\n",
"28926258177\n",
"25\n",
"79\n",
"21\n",
"69\n",
"0\n",
"153\n",
"41\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
There are three horses living in a horse land: one gray, one white and one gray-and-white. The horses are really amusing animals, which is why they adore special cards. Each of those cards must contain two integers, the first one on top, the second one in the bottom of the card. Let's denote a card with a on the top and b in the bottom as (a, b).
Each of the three horses can paint the special cards. If you show an (a, b) card to the gray horse, then the horse can paint a new (a + 1, b + 1) card. If you show an (a, b) card, such that a and b are even integers, to the white horse, then the horse can paint a new <image> card. If you show two cards (a, b) and (b, c) to the gray-and-white horse, then he can paint a new (a, c) card.
Polycarpus really wants to get n special cards (1, a1), (1, a2), ..., (1, an). For that he is going to the horse land. He can take exactly one (x, y) card to the horse land, such that 1 ≤ x < y ≤ m. How many ways are there to choose the card so that he can perform some actions in the horse land and get the required cards?
Polycarpus can get cards from the horses only as a result of the actions that are described above. Polycarpus is allowed to get additional cards besides the cards that he requires.
Input
The first line contains two integers n, m (1 ≤ n ≤ 105, 2 ≤ m ≤ 109). The second line contains the sequence of integers a1, a2, ..., an (2 ≤ ai ≤ 109). Note, that the numbers in the sequence can coincide.
The numbers in the lines are separated by single spaces.
Output
Print a single integer — the answer to the problem.
Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specifier.
Examples
Input
1 6
2
Output
11
Input
1 6
7
Output
14
Input
2 10
13 7
Output
36
### Input:
1 6
2
### Output:
11
### Input:
2 10
13 7
### Output:
36
### Code:
# written with help of editorial
n, m = map(int, input().split())
a = list(map(int, input().split()))
def gcd(x, y):
while y:
x, y = y, x % y
return x
g = 0
for x in a:
g = gcd(g, x - 1)
answer = 0
def process(x):
global answer
if x % 2 == 0:
return 0
for i in range(30):
v = 2 ** i * x
if v > m:
break
answer += m - v
for i in range(1, g + 1):
if i * i > g:
break
if g % i:
continue
process(i)
if i * i != g:
process(g // i)
print(answer)
|
295_B. Greg and Graph_10565
|
Greg has a weighed directed graph, consisting of n vertices. In this graph any pair of distinct vertices has an edge between them in both directions. Greg loves playing with the graph and now he has invented a new game:
* The game consists of n steps.
* On the i-th step Greg removes vertex number xi from the graph. As Greg removes a vertex, he also removes all the edges that go in and out of this vertex.
* Before executing each step, Greg wants to know the sum of lengths of the shortest paths between all pairs of the remaining vertices. The shortest path can go through any remaining vertex. In other words, if we assume that d(i, v, u) is the shortest path between vertices v and u in the graph that formed before deleting vertex xi, then Greg wants to know the value of the following sum: <image>.
Help Greg, print the value of the required sum before each step.
Input
The first line contains integer n (1 ≤ n ≤ 500) — the number of vertices in the graph.
Next n lines contain n integers each — the graph adjacency matrix: the j-th number in the i-th line aij (1 ≤ aij ≤ 105, aii = 0) represents the weight of the edge that goes from vertex i to vertex j.
The next line contains n distinct integers: x1, x2, ..., xn (1 ≤ xi ≤ n) — the vertices that Greg deletes.
Output
Print n integers — the i-th number equals the required sum before the i-th step.
Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams of the %I64d specifier.
Examples
Input
1
0
1
Output
0
Input
2
0 5
4 0
1 2
Output
9 0
Input
4
0 3 1 1
6 0 400 1
2 4 0 1
1 1 1 0
4 1 2 3
Output
17 23 404 0
|
#!/usr/bin/env python3
# from typing import *
import sys
import io
import math
import collections
import decimal
import itertools
import bisect
import heapq
from array import array
def input():
return sys.stdin.readline()[:-1]
# sys.setrecursionlimit(1000000)
# _INPUT = """4
# 0 57148 51001 13357
# 71125 0 98369 67226
# 49388 90852 0 66291
# 39573 38165 97007 0
# 2 3 1 4
# """
# sys.stdin = io.StringIO(_INPUT)
INF = 10**10
N = int(input())
A = [array('i', list(map(int, input().split()))) for _ in range(N)]
X = list(map(lambda x: int(x)-1, input().split()))
result = []
for k in reversed(range(N)):
x = X[k]
for i in range(N):
for j in range(N):
d = A[i][x] + A[x][j]
if d < A[i][j]:
A[i][j] = d
v = 0
upper = 0
for i in X[k:]:
for j in X[k:]:
v += A[i][j]
if v > 10**9:
v -= 10**9
upper += 1
result.append(str((10**9) * upper + v))
print(' '.join(reversed(result)))
|
{
"input": [
"4\n0 3 1 1\n6 0 400 1\n2 4 0 1\n1 1 1 0\n4 1 2 3\n",
"2\n0 5\n4 0\n1 2\n",
"1\n0\n1\n",
"6\n0 72137 71041 29217 96749 46417\n40199 0 55907 57677 68590 78796\n83463 50721 0 30963 31779 28646\n94529 47831 98222 0 61665 73941\n24397 66286 2971 81613 0 52501\n26285 3381 51438 45360 20160 0\n6 3 2 4 5 1\n",
"5\n0 27799 15529 16434 44291\n47134 0 90227 26873 52252\n41605 21269 0 9135 55784\n70744 17563 79061 0 73981\n70529 35681 91073 52031 0\n5 2 3 1 4\n",
"4\n0 57148 51001 13357\n71125 0 98369 67226\n49388 90852 0 66291\n39573 38165 97007 0\n2 3 1 4\n",
"8\n0 74961 47889 4733 72876 21399 63105 48239\n15623 0 9680 89133 57989 63401 26001 29608\n42369 82390 0 32866 46171 11871 67489 54070\n23425 80027 18270 0 28105 42657 40876 29267\n78793 18701 7655 94798 0 88885 71424 86914\n44835 76636 11553 46031 13617 0 16971 51915\n33037 53719 43116 52806 56897 71241 0 11629\n2119 62373 93265 69513 5770 90751 36619 0\n3 7 6 5 8 1 2 4\n",
"7\n0 34385 31901 51111 10191 14089 95685\n11396 0 8701 33277 1481 517 46253\n51313 2255 0 5948 66085 37201 65310\n21105 60985 10748 0 89271 42883 77345\n34686 29401 73565 47795 0 13793 66997\n70279 49576 62900 40002 70943 0 89601\n65045 1681 28239 12023 40414 89585 0\n3 5 7 6 1 2 4\n",
"9\n0 85236 27579 82251 69479 24737 87917 15149 52311\n59640 0 74687 34711 3685 30121 4961 7552 83399\n33376 68733 0 81357 18042 74297 15466 29476 5865\n7493 5601 3321 0 20263 55901 45756 55361 87633\n26751 17161 76681 40376 0 39745 50717 56887 90055\n18885 76353 47089 43601 21561 0 60571 33551 53753\n74595 877 71853 93156 97499 70876 0 22713 63961\n67725 25309 56358 92376 40641 35433 39781 0 97482\n81818 12561 85961 81445 3941 76799 31701 43725 0\n6 2 9 3 5 7 1 4 8\n",
"6\n0 72137 71041 29217 96749 46417\n40199 0 55907 57677 68590 78796\n83463 50721 0 30963 31779 28646\n94529 47831 98222 0 61665 143301\n24397 66286 2971 81613 0 52501\n26285 3381 51438 45360 20160 0\n6 3 2 4 5 1\n",
"5\n0 27799 15529 16434 44291\n47134 0 90227 26873 52252\n41605 21269 0 9135 55784\n70744 17563 79061 0 73981\n70529 35681 120985 52031 0\n5 2 3 1 4\n",
"8\n0 74961 47889 4733 72876 21399 63105 48239\n15623 0 9680 89133 57989 63401 26001 29608\n42369 82390 0 32866 46171 11871 67489 54070\n23425 80027 18270 0 28105 42657 40876 29267\n78793 18701 7655 94798 0 88885 71424 86914\n44835 76636 11553 46031 13617 0 16971 51915\n33037 53719 43116 52806 56897 71241 0 11629\n2119 62373 32481 69513 5770 90751 36619 0\n3 7 6 5 8 1 2 4\n",
"9\n0 85236 27579 82251 69479 24737 87917 15149 52311\n59640 0 74687 34711 3685 30121 4961 7552 83399\n33376 68733 0 81357 18042 74297 15466 29476 5865\n7493 5601 3321 0 20263 55901 45756 55361 87633\n26751 17161 76681 40376 0 39745 50717 56887 90055\n18885 76353 47089 43601 21561 0 60571 33551 53753\n74595 877 71853 141251 97499 70876 0 22713 63961\n67725 25309 56358 92376 40641 35433 39781 0 97482\n81818 12561 85961 81445 3941 76799 31701 43725 0\n6 2 9 3 5 7 1 4 8\n",
"2\n0 5\n7 0\n1 2\n",
"8\n0 74961 47889 4733 72876 21399 63105 8963\n15623 0 9680 89133 57989 63401 26001 29608\n42369 82390 0 32866 46171 11871 67489 54070\n23425 80027 18270 0 28105 42657 40876 29267\n78793 18701 7655 94798 0 88885 71424 86914\n44835 76636 11553 46031 13617 0 16971 51915\n33037 53719 43116 52806 56897 71241 0 11629\n2119 62373 32481 69513 5770 90751 36619 0\n3 7 6 5 8 1 2 4\n",
"9\n0 85236 27579 82251 69479 24737 87917 15149 52311\n59640 0 74687 34711 3685 30121 4961 7552 83399\n33376 68733 0 81357 18042 74297 15466 29476 5865\n7493 5601 3321 0 20263 55901 45756 55361 87633\n26751 17161 76681 58775 0 39745 50717 56887 90055\n18885 76353 47089 43601 21561 0 60571 33551 53753\n74595 877 71853 141251 97499 70876 0 22713 63961\n67725 25309 56358 92376 40641 35433 39781 0 97482\n81818 12561 85961 81445 3941 76799 31701 43725 0\n6 2 9 3 5 7 1 4 8\n",
"2\n0 4\n7 0\n1 2\n",
"9\n0 85236 27579 82251 69479 24737 87917 15149 52311\n59640 0 74687 34711 3685 30121 4961 7552 83399\n33376 68733 0 81357 18042 74297 15466 29476 5865\n7493 5601 3321 0 20263 55901 58229 55361 87633\n26751 17161 76681 58775 0 39745 50717 56887 90055\n18885 76353 47089 43601 21561 0 60571 33551 53753\n74595 877 71853 141251 97499 70876 0 22713 63961\n67725 25309 56358 92376 40641 35433 39781 0 97482\n81818 12561 85961 81445 3941 76799 31701 43725 0\n6 2 9 3 5 7 1 4 8\n",
"2\n0 9\n7 0\n1 2\n",
"8\n0 74961 47889 4733 72876 21399 63105 8963\n15623 0 10052 89133 57989 63401 26001 29608\n42369 82390 0 32866 46171 11871 67489 54070\n23425 80027 18270 0 28105 42657 40876 29267\n78793 18701 7655 94798 0 87054 71424 86914\n44835 76636 11553 46031 13617 0 16971 51915\n33037 53719 43116 52806 56897 71241 0 11629\n2119 62373 32481 69513 5770 90751 36619 0\n3 7 6 5 8 1 2 4\n",
"9\n0 85236 27579 82251 69479 24737 87917 15149 52311\n59640 0 74687 34711 3685 30121 4961 7552 83399\n33376 68733 0 81357 18042 74297 15466 29476 5865\n7493 5601 3321 0 20263 55901 58229 55361 87633\n26751 17161 76681 58775 0 39745 50717 56887 90055\n18885 76353 47089 43601 21561 0 60571 33551 53753\n74595 877 71853 141251 97499 70876 0 22713 63961\n67725 25309 56358 92376 40641 35433 39781 0 97482\n81818 10112 85961 81445 3941 76799 31701 43725 0\n6 2 9 3 5 7 1 4 8\n",
"8\n0 74961 47889 4733 72876 21399 63105 8963\n15623 0 10052 89133 12762 63401 26001 29608\n42369 82390 0 32866 46171 11871 67489 54070\n23425 80027 18270 0 28105 42657 40876 29267\n78793 18701 7655 94798 0 87054 71424 86914\n44835 76636 11553 46031 13617 0 16971 51915\n33037 53719 43116 52806 56897 71241 0 11629\n2119 62373 32481 69513 5770 90751 36619 0\n3 7 6 5 8 1 2 4\n",
"8\n0 74961 47889 4733 72876 21399 63105 8963\n15623 0 5883 89133 12762 63401 26001 29608\n42369 82390 0 32866 46171 11871 67489 54070\n23425 80027 18270 0 28105 42657 40876 29267\n78793 18701 7655 94798 0 87054 71424 86914\n44835 76636 11553 46031 13617 0 16971 51915\n33037 53719 43116 52806 56897 71241 0 11629\n2119 62373 32481 69513 5770 90751 36619 0\n3 7 6 5 8 1 2 4\n",
"8\n0 74961 47889 4733 72876 21399 63105 8963\n15623 0 5883 89133 12762 63401 26001 29608\n42369 82390 0 32866 46171 11871 67489 54070\n23425 80027 18270 0 55173 42657 40876 29267\n78793 18701 7655 94798 0 87054 71424 86914\n44835 76636 11553 46031 13617 0 16971 51915\n33037 53719 43116 52806 56897 71241 0 11629\n2119 62373 32481 69513 5770 90751 36619 0\n3 7 6 5 8 1 2 4\n",
"5\n0 27799 15529 16434 44291\n47134 0 90227 26873 52252\n41605 23663 0 9135 55784\n70744 17563 79061 0 73981\n70529 35681 91073 52031 0\n5 2 3 1 4\n",
"4\n0 57148 51001 13357\n71125 0 98369 67226\n49388 162774 0 66291\n39573 38165 97007 0\n2 3 1 4\n",
"8\n0 74961 47889 4733 72876 21399 63105 48239\n15623 0 9680 89133 57989 63401 26001 29608\n42369 82390 0 32866 46171 11871 67489 54070\n23425 80027 18270 0 28105 42657 40876 29267\n78793 18701 7655 94798 0 88885 71424 86914\n44835 76636 11553 5530 13617 0 16971 51915\n33037 53719 43116 52806 56897 71241 0 11629\n2119 62373 93265 69513 5770 90751 36619 0\n3 7 6 5 8 1 2 4\n",
"7\n0 34385 31901 51111 10191 14089 95685\n11396 0 9257 33277 1481 517 46253\n51313 2255 0 5948 66085 37201 65310\n21105 60985 10748 0 89271 42883 77345\n34686 29401 73565 47795 0 13793 66997\n70279 49576 62900 40002 70943 0 89601\n65045 1681 28239 12023 40414 89585 0\n3 5 7 6 1 2 4\n",
"9\n0 85236 27579 82251 69479 24737 87917 15149 52311\n59640 0 74687 34711 3685 30121 4961 7552 83399\n3024 68733 0 81357 18042 74297 15466 29476 5865\n7493 5601 3321 0 20263 55901 45756 55361 87633\n26751 17161 76681 40376 0 39745 50717 56887 90055\n18885 76353 47089 43601 21561 0 60571 33551 53753\n74595 877 71853 93156 97499 70876 0 22713 63961\n67725 25309 56358 92376 40641 35433 39781 0 97482\n81818 12561 85961 81445 3941 76799 31701 43725 0\n6 2 9 3 5 7 1 4 8\n",
"4\n0 3 1 1\n11 0 400 1\n2 4 0 1\n1 1 1 0\n4 1 2 3\n",
"6\n0 72137 71041 29217 96749 46417\n40199 0 17734 57677 68590 78796\n83463 50721 0 30963 31779 28646\n94529 47831 98222 0 61665 143301\n24397 66286 2971 81613 0 52501\n26285 3381 51438 45360 20160 0\n6 3 2 4 5 1\n",
"5\n0 34536 15529 16434 44291\n47134 0 90227 26873 52252\n41605 21269 0 9135 55784\n70744 17563 79061 0 73981\n70529 35681 120985 52031 0\n5 2 3 1 4\n",
"8\n0 74961 47889 4733 72876 21399 63105 48239\n15623 0 9680 89133 57989 63401 26001 29608\n42369 82390 0 32866 46171 11871 67489 54070\n23425 80027 18270 0 28105 42657 40876 29267\n78793 18701 7655 94798 0 88885 71424 86914\n44835 76636 11553 46031 13617 0 16971 51915\n33037 53719 43116 52806 56897 71241 0 11629\n2119 62373 32481 69513 10784 90751 36619 0\n3 7 6 5 8 1 2 4\n",
"2\n0 5\n14 0\n1 2\n",
"8\n0 74961 47889 4733 72876 21399 63105 8963\n15623 0 9680 89133 57989 63401 26001 29608\n42369 82390 0 32866 46171 11871 67489 54070\n23425 80027 18270 0 28105 42657 40876 29267\n78793 18701 7655 94798 0 88885 71424 86914\n44835 76636 11553 46031 13617 0 16971 51915\n33037 53719 43116 52806 56897 71241 0 11629\n3896 62373 32481 69513 5770 90751 36619 0\n3 7 6 5 8 1 2 4\n",
"9\n0 85236 27579 16105 69479 24737 87917 15149 52311\n59640 0 74687 34711 3685 30121 4961 7552 83399\n33376 68733 0 81357 18042 74297 15466 29476 5865\n7493 5601 3321 0 20263 55901 45756 55361 87633\n26751 17161 76681 58775 0 39745 50717 56887 90055\n18885 76353 47089 43601 21561 0 60571 33551 53753\n74595 877 71853 141251 97499 70876 0 22713 63961\n67725 25309 56358 92376 40641 35433 39781 0 97482\n81818 12561 85961 81445 3941 76799 31701 43725 0\n6 2 9 3 5 7 1 4 8\n",
"2\n0 1\n7 0\n1 2\n",
"8\n0 74961 47889 4733 72876 21399 63105 8963\n15623 0 9680 89133 57989 63401 26001 29608\n42369 82390 0 32866 46171 11871 67489 54070\n23425 80027 18270 0 28105 42657 40876 29267\n78793 18701 7655 94798 0 87054 71424 86914\n78814 76636 11553 46031 13617 0 16971 51915\n33037 53719 43116 52806 56897 71241 0 11629\n2119 62373 32481 69513 5770 90751 36619 0\n3 7 6 5 8 1 2 4\n",
"9\n0 85236 27579 82251 69479 24737 87917 15149 52311\n59640 0 74687 34711 3685 30121 4961 7552 83399\n33376 68733 0 81357 18042 74297 15466 29476 5865\n7493 5601 3321 0 20263 55901 58229 55361 87633\n26751 17161 76681 58775 0 39745 50717 56887 90055\n18885 76353 47089 43601 21561 0 60571 33551 53753\n103347 877 71853 141251 97499 70876 0 22713 63961\n67725 25309 56358 92376 40641 35433 39781 0 97482\n81818 12561 85961 81445 3941 76799 31701 43725 0\n6 2 9 3 5 7 1 4 8\n",
"8\n0 74961 47889 4733 72876 21399 63105 8963\n15623 0 10052 89133 57989 63401 26001 29608\n42369 82390 0 32866 46171 11871 67489 54070\n23425 80027 18270 0 28105 42657 40876 29267\n78793 18701 7655 94798 0 87054 71424 86914\n44835 76636 22241 46031 13617 0 16971 51915\n33037 53719 43116 52806 56897 71241 0 11629\n2119 62373 32481 69513 5770 90751 36619 0\n3 7 6 5 8 1 2 4\n",
"8\n0 74961 47889 4733 72876 21399 63105 8963\n15623 0 5883 89133 12762 63401 26001 29608\n42369 82390 0 32866 46171 11871 67489 54070\n23425 80027 18270 0 28105 42657 40876 29267\n78793 18701 7655 94798 0 87054 71424 86914\n44835 76636 11553 46031 13617 0 16971 51915\n33037 53719 43116 52806 56897 71241 0 6063\n2119 62373 32481 69513 5770 90751 36619 0\n3 7 6 5 8 1 2 4\n",
"8\n0 74961 47889 4733 72876 21399 63105 8963\n15623 0 5883 89133 12762 63401 26001 29608\n42369 82390 0 32866 46171 11871 67489 54070\n23425 80027 18270 0 55173 42657 40876 29267\n78793 18701 7655 94798 0 87054 71424 86914\n44835 76636 11553 46031 13617 0 16971 51915\n33037 53719 43116 52806 56897 71241 0 11629\n2119 62373 32481 69513 5770 90751 18300 0\n3 7 6 5 8 1 2 4\n",
"6\n0 72137 71041 29217 96749 46417\n40199 0 55907 57677 68590 78796\n83463 2353 0 30963 31779 28646\n94529 47831 98222 0 61665 100737\n24397 66286 2971 81613 0 52501\n26285 3381 51438 45360 20160 0\n6 3 2 4 5 1\n",
"5\n0 27799 18371 16434 44291\n47134 0 90227 26873 52252\n41605 23663 0 9135 55784\n70744 17563 79061 0 73981\n70529 35681 91073 52031 0\n5 2 3 1 4\n",
"4\n0 57148 51001 13357\n71125 0 98369 1237\n49388 162774 0 66291\n39573 38165 97007 0\n2 3 1 4\n",
"8\n0 74961 47889 4733 72876 21399 63105 48239\n15623 0 9680 89133 57989 63401 26001 29608\n42369 82390 0 32866 46171 11871 67489 54070\n23425 80027 18270 0 28105 42657 40876 29267\n78793 18701 7655 94798 0 88885 71424 86914\n44835 76636 11553 5530 13617 0 16971 51915\n33037 53719 43116 52806 56897 71241 0 11629\n2119 62373 93265 69513 5770 90751 34618 0\n3 7 6 5 8 1 2 4\n",
"7\n0 34385 31901 51111 10191 14089 95685\n11396 0 9257 33277 1481 517 46253\n51313 2255 0 5948 66085 37201 65310\n21105 60985 20101 0 89271 42883 77345\n34686 29401 73565 47795 0 13793 66997\n70279 49576 62900 40002 70943 0 89601\n65045 1681 28239 12023 40414 89585 0\n3 5 7 6 1 2 4\n",
"6\n0 72137 71041 29217 96749 52586\n40199 0 17734 57677 68590 78796\n83463 50721 0 30963 31779 28646\n94529 47831 98222 0 61665 143301\n24397 66286 2971 81613 0 52501\n26285 3381 51438 45360 20160 0\n6 3 2 4 5 1\n",
"5\n0 34536 15529 16434 44291\n47134 0 90227 26873 52252\n5796 21269 0 9135 55784\n70744 17563 79061 0 73981\n70529 35681 120985 52031 0\n5 2 3 1 4\n",
"2\n0 5\n27 0\n1 2\n",
"9\n0 85236 27579 16105 69479 24737 87917 15149 52311\n59640 0 74687 34711 3685 30121 4961 7552 83399\n33376 68733 0 81357 18042 74297 15466 29476 3984\n7493 5601 3321 0 20263 55901 45756 55361 87633\n26751 17161 76681 58775 0 39745 50717 56887 90055\n18885 76353 47089 43601 21561 0 60571 33551 53753\n74595 877 71853 141251 97499 70876 0 22713 63961\n67725 25309 56358 92376 40641 35433 39781 0 97482\n81818 12561 85961 81445 3941 76799 31701 43725 0\n6 2 9 3 5 7 1 4 8\n",
"2\n0 1\n13 0\n1 2\n",
"8\n0 74961 47889 4733 72876 21399 63105 8963\n15623 0 9680 89133 57989 63401 26001 29608\n42369 82390 0 32866 46171 11871 67489 54070\n23425 80027 18270 0 28105 42657 40876 29267\n78793 18701 7655 94798 0 87054 71424 86914\n78814 76636 11553 46031 13617 0 16971 27076\n33037 53719 43116 52806 56897 71241 0 11629\n2119 62373 32481 69513 5770 90751 36619 0\n3 7 6 5 8 1 2 4\n",
"9\n0 85236 27579 82251 69479 24737 87917 15149 52311\n59640 0 74687 34711 3685 30121 4961 7552 83399\n33376 68733 0 81357 18042 74297 15466 29476 5865\n7493 5601 3321 0 20263 55901 58229 55361 87633\n26751 17161 76681 63912 0 39745 50717 56887 90055\n18885 76353 47089 43601 21561 0 60571 33551 53753\n103347 877 71853 141251 97499 70876 0 22713 63961\n67725 25309 56358 92376 40641 35433 39781 0 97482\n81818 12561 85961 81445 3941 76799 31701 43725 0\n6 2 9 3 5 7 1 4 8\n",
"8\n0 74961 47889 4733 72876 21399 63105 8963\n15623 0 10052 89133 57989 63401 26001 29608\n42369 82390 0 32866 46171 11871 67489 54070\n23425 80027 18270 0 28105 84135 40876 29267\n78793 18701 7655 94798 0 87054 71424 86914\n44835 76636 22241 46031 13617 0 16971 51915\n33037 53719 43116 52806 56897 71241 0 11629\n2119 62373 32481 69513 5770 90751 36619 0\n3 7 6 5 8 1 2 4\n",
"5\n0 27799 18371 16434 67708\n47134 0 90227 26873 52252\n41605 23663 0 9135 55784\n70744 17563 79061 0 73981\n70529 35681 91073 52031 0\n5 2 3 1 4\n",
"4\n0 57148 51001 13357\n71125 0 79531 1237\n49388 162774 0 66291\n39573 38165 97007 0\n2 3 1 4\n",
"8\n0 74961 47889 53 72876 21399 63105 48239\n15623 0 9680 89133 57989 63401 26001 29608\n42369 82390 0 32866 46171 11871 67489 54070\n23425 80027 18270 0 28105 42657 40876 29267\n78793 18701 7655 94798 0 88885 71424 86914\n44835 76636 11553 5530 13617 0 16971 51915\n33037 53719 43116 52806 56897 71241 0 11629\n2119 62373 93265 69513 5770 90751 34618 0\n3 7 6 5 8 1 2 4\n",
"5\n0 34536 15491 16434 44291\n47134 0 90227 26873 52252\n5796 21269 0 9135 55784\n70744 17563 79061 0 73981\n70529 35681 120985 52031 0\n5 2 3 1 4\n",
"2\n0 9\n27 0\n1 2\n",
"8\n0 74961 47889 4733 72876 21399 63105 8963\n15623 0 9680 89133 57989 63401 26001 29608\n42369 82390 0 32866 46171 11871 67489 54070\n23425 80027 18270 0 28105 42657 40876 29267\n78793 18701 7655 94798 0 88885 71424 86914\n44835 76636 11553 83783 13617 0 16971 51915\n26533 53719 43116 52806 56897 71241 0 11629\n3896 62373 32481 69513 5770 90751 36619 0\n3 7 6 5 8 1 2 4\n",
"9\n0 85236 27579 16105 69479 24737 87917 15149 52311\n59640 0 74687 34711 3685 39125 4961 7552 83399\n33376 68733 0 81357 18042 74297 15466 29476 3984\n7493 5601 3321 0 20263 55901 45756 55361 87633\n26751 17161 76681 58775 0 39745 50717 56887 90055\n18885 76353 47089 43601 21561 0 60571 33551 53753\n74595 877 71853 141251 97499 70876 0 22713 63961\n67725 25309 56358 92376 40641 35433 39781 0 97482\n81818 12561 85961 81445 3941 76799 31701 43725 0\n6 2 9 3 5 7 1 4 8\n",
"2\n0 0\n13 0\n1 2\n",
"9\n0 85236 27579 82251 69479 24737 87917 15149 52311\n59640 0 74687 34711 3685 30121 4961 7552 83399\n33376 68733 0 81357 18042 74297 15466 29476 5865\n7493 5601 3321 0 20263 55901 58229 55361 87633\n26751 17161 76681 63912 0 39745 41472 56887 90055\n18885 76353 47089 43601 21561 0 60571 33551 53753\n103347 877 71853 141251 97499 70876 0 22713 63961\n67725 25309 56358 92376 40641 35433 39781 0 97482\n81818 12561 85961 81445 3941 76799 31701 43725 0\n6 2 9 3 5 7 1 4 8\n",
"8\n0 74961 47889 4733 72876 21399 63105 8963\n15623 0 10052 89133 57989 63401 26001 29608\n42369 82390 0 32866 46171 11871 67489 54070\n23425 80027 18270 0 28105 36954 40876 29267\n78793 18701 7655 94798 0 87054 71424 86914\n44835 76636 22241 46031 13617 0 16971 51915\n33037 53719 43116 52806 56897 71241 0 11629\n2119 62373 32481 69513 5770 90751 36619 0\n3 7 6 5 8 1 2 4\n",
"8\n0 74961 47889 4733 72876 21399 63105 8963\n15623 0 9680 89133 57989 63401 26001 29608\n42369 82390 0 32866 46171 11871 67489 54070\n23425 80027 18270 0 28105 42657 40876 29267\n78793 18701 7655 94798 0 87054 71424 86914\n44835 76636 11553 46031 13617 0 16971 51915\n33037 53719 43116 52806 56897 71241 0 11629\n2119 62373 32481 69513 5770 90751 36619 0\n3 7 6 5 8 1 2 4\n",
"6\n0 72137 71041 29217 96749 46417\n40199 0 55907 57677 68590 78796\n83463 50721 0 30963 31779 28646\n94529 47831 98222 0 61665 100737\n24397 66286 2971 81613 0 52501\n26285 3381 51438 45360 20160 0\n6 3 2 4 5 1\n",
"8\n0 74961 47889 4733 72876 21399 63105 8963\n15623 0 9680 89133 57989 63401 26001 29608\n42369 82390 0 32866 46171 11871 67489 54070\n23425 80027 18270 0 28105 42657 40876 29267\n78793 18701 7655 94798 0 88885 71424 86914\n44835 76636 11553 46031 13617 0 16971 51915\n26533 53719 43116 52806 56897 71241 0 11629\n3896 62373 32481 69513 5770 90751 36619 0\n3 7 6 5 8 1 2 4\n",
"8\n0 74961 47889 4733 72876 21399 63105 8963\n15623 0 5883 89133 12762 63401 26001 29608\n42369 82390 0 32866 46171 11871 67489 90944\n23425 80027 18270 0 28105 42657 40876 29267\n78793 18701 7655 94798 0 87054 71424 86914\n44835 76636 11553 46031 13617 0 16971 51915\n33037 53719 43116 52806 56897 71241 0 6063\n2119 62373 32481 69513 5770 90751 36619 0\n3 7 6 5 8 1 2 4\n",
"8\n0 74961 47889 4733 72876 21399 63105 8963\n15623 0 5883 89133 12762 63401 26001 29608\n42369 82390 0 32866 46171 11871 67489 54070\n23425 80027 18270 0 55173 42657 40876 29267\n78793 18701 7655 94798 0 87054 71424 86914\n44835 76636 11553 46031 13617 0 16971 51915\n33037 53719 43116 52806 44720 71241 0 11629\n2119 62373 32481 69513 5770 90751 18300 0\n3 7 6 5 8 1 2 4\n",
"7\n0 34385 31901 51111 10191 14089 95685\n11396 0 9257 33277 1481 517 46253\n51313 2255 0 5948 66085 37201 65310\n21105 60985 20101 0 89271 42883 77345\n34686 29401 73565 47795 0 13793 66997\n70279 49576 62900 40002 70943 0 89601\n78233 1681 28239 12023 40414 89585 0\n3 5 7 6 1 2 4\n",
"6\n0 72137 71041 29217 96749 52586\n40199 0 17734 57677 68590 78796\n83463 50721 0 30963 31779 28646\n185361 47831 98222 0 61665 143301\n24397 66286 2971 81613 0 52501\n26285 3381 51438 45360 20160 0\n6 3 2 4 5 1\n",
"8\n0 74961 47889 4733 72876 21399 63105 8963\n15623 0 9680 89133 57989 63401 26001 29608\n42369 82390 0 32866 46171 11871 67489 54070\n23425 80027 18270 0 28105 42657 40876 29267\n101383 18701 7655 94798 0 87054 71424 86914\n78814 76636 11553 46031 13617 0 16971 27076\n33037 53719 43116 52806 56897 71241 0 11629\n2119 62373 32481 69513 5770 90751 36619 0\n3 7 6 5 8 1 2 4\n"
],
"output": [
"17 23 404 0 \n",
"9 0 \n",
"0 \n",
"1321441 1030477 698557 345837 121146 0 \n",
"896203 429762 232508 87178 0 \n",
"723897 306638 52930 0 \n",
"1450303 1188349 900316 531281 383344 219125 169160 0 \n",
"1108867 1016339 729930 407114 206764 94262 0 \n",
"2106523 1533575 1645151 1255230 946667 618567 287636 147737 0 \n",
"1340782 1030477 698557 345837 121146 0",
"896203 429762 232508 87178 0",
"1450303 1188349 900316 531281 383344 219125 169160 0",
"2106523 1533575 1655725 1265804 957241 640500 287636 147737 0",
"12 0",
"1373768 1112036 824003 454968 349660 219125 169160 0",
"2146067 1573119 1770029 1335953 998358 640500 287636 147737 0",
"11 0",
"2146067 1573119 1770029 1335953 1010831 652973 287636 147737 0",
"16 0",
"1374512 1112036 824003 454968 349660 219125 169160 0",
"2129909 1559776 1770029 1335953 1010831 652973 287636 147737 0",
"1356918 1094442 806409 437374 349660 219125 169160 0",
"1348580 1094442 806409 437374 349660 219125 169160 0",
"1362444 1108306 820273 451238 349660 219125 169160 0",
"898597 432156 232508 87178 0",
"733955 306638 52930 0",
"1387608 1156663 826817 531281 383344 219125 169160 0",
"1111647 1016339 729930 407114 206764 94262 0",
"2049450 1496353 1593190 1203269 946667 618567 287636 147737 0",
"17 33 404 0",
"1238104 964247 698557 345837 121146 0",
"902401 435960 232508 87178 0",
"1480387 1213419 915358 546323 383344 219125 169160 0",
"19 0",
"1387984 1126252 829334 458522 353214 219125 169160 0",
"1977642 1422780 1562606 1159572 863603 541419 212944 147737 0",
"8 0",
"1373768 1112036 827109 454968 349660 219125 169160 0",
"2146067 1573119 1785539 1351463 1026341 668816 287636 147737 0",
"1384231 1112036 824003 454968 349660 219125 169160 0",
"1281282 1044348 806409 437374 349660 219125 169160 0",
"1333018 1078880 820273 451238 349660 219125 169160 0",
"1269055 920117 698557 345837 121146 0",
"907123 437840 235350 87178 0",
"631093 306638 52930 0",
"1385607 1154662 826817 531281 383344 219125 169160 0",
"1166495 1016339 729930 407114 206764 94262 0",
"1260120 964247 698557 345837 121146 0",
"860895 400151 196699 87178 0",
"32 0",
"1960713 1407732 1547558 1159572 863603 541419 212944 147737 0",
"14 0",
"1366369 1107464 771421 454968 349660 219125 169160 0",
"2146067 1573119 1800950 1361140 1031478 668816 287636 147737 0",
"1384231 1114203 826170 454968 349660 219125 169160 0",
"930540 437840 235350 87178 0",
"618813 306638 52930 0",
"1348167 1117222 794057 498521 364624 209765 169160 0",
"860781 400075 196661 87178 0",
"36 0",
"1387984 1126252 832871 458522 353214 219125 169160 0",
"1980931 1407732 1547558 1159572 863603 541419 212944 147737 0",
"13 0",
"2146067 1573119 1791705 1351895 1022233 668816 287636 147737 0",
"1384231 1106333 818300 454968 349660 219125 169160 0",
"1373768 1112036 824003 454968 349660 219125 169160 0",
"1340782 1030477 698557 345837 121146 0",
"1387984 1126252 829334 458522 353214 219125 169160 0",
"1281282 1044348 806409 437374 349660 219125 169160 0",
"1333018 1078880 820273 451238 349660 219125 169160 0",
"1166495 1016339 729930 407114 206764 94262 0",
"1260120 964247 698557 345837 121146 0",
"1366369 1107464 771421 454968 349660 219125 169160 0"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Greg has a weighed directed graph, consisting of n vertices. In this graph any pair of distinct vertices has an edge between them in both directions. Greg loves playing with the graph and now he has invented a new game:
* The game consists of n steps.
* On the i-th step Greg removes vertex number xi from the graph. As Greg removes a vertex, he also removes all the edges that go in and out of this vertex.
* Before executing each step, Greg wants to know the sum of lengths of the shortest paths between all pairs of the remaining vertices. The shortest path can go through any remaining vertex. In other words, if we assume that d(i, v, u) is the shortest path between vertices v and u in the graph that formed before deleting vertex xi, then Greg wants to know the value of the following sum: <image>.
Help Greg, print the value of the required sum before each step.
Input
The first line contains integer n (1 ≤ n ≤ 500) — the number of vertices in the graph.
Next n lines contain n integers each — the graph adjacency matrix: the j-th number in the i-th line aij (1 ≤ aij ≤ 105, aii = 0) represents the weight of the edge that goes from vertex i to vertex j.
The next line contains n distinct integers: x1, x2, ..., xn (1 ≤ xi ≤ n) — the vertices that Greg deletes.
Output
Print n integers — the i-th number equals the required sum before the i-th step.
Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams of the %I64d specifier.
Examples
Input
1
0
1
Output
0
Input
2
0 5
4 0
1 2
Output
9 0
Input
4
0 3 1 1
6 0 400 1
2 4 0 1
1 1 1 0
4 1 2 3
Output
17 23 404 0
### Input:
4
0 3 1 1
6 0 400 1
2 4 0 1
1 1 1 0
4 1 2 3
### Output:
17 23 404 0
### Input:
2
0 5
4 0
1 2
### Output:
9 0
### Code:
#!/usr/bin/env python3
# from typing import *
import sys
import io
import math
import collections
import decimal
import itertools
import bisect
import heapq
from array import array
def input():
return sys.stdin.readline()[:-1]
# sys.setrecursionlimit(1000000)
# _INPUT = """4
# 0 57148 51001 13357
# 71125 0 98369 67226
# 49388 90852 0 66291
# 39573 38165 97007 0
# 2 3 1 4
# """
# sys.stdin = io.StringIO(_INPUT)
INF = 10**10
N = int(input())
A = [array('i', list(map(int, input().split()))) for _ in range(N)]
X = list(map(lambda x: int(x)-1, input().split()))
result = []
for k in reversed(range(N)):
x = X[k]
for i in range(N):
for j in range(N):
d = A[i][x] + A[x][j]
if d < A[i][j]:
A[i][j] = d
v = 0
upper = 0
for i in X[k:]:
for j in X[k:]:
v += A[i][j]
if v > 10**9:
v -= 10**9
upper += 1
result.append(str((10**9) * upper + v))
print(' '.join(reversed(result)))
|
342_E. Xenia and Tree_10570
|
Xenia the programmer has a tree consisting of n nodes. We will consider the tree nodes indexed from 1 to n. We will also consider the first node to be initially painted red, and the other nodes — to be painted blue.
The distance between two tree nodes v and u is the number of edges in the shortest path between v and u.
Xenia needs to learn how to quickly execute queries of two types:
1. paint a specified blue node in red;
2. calculate which red node is the closest to the given one and print the shortest distance to the closest red node.
Your task is to write a program which will execute the described queries.
Input
The first line contains two integers n and m (2 ≤ n ≤ 105, 1 ≤ m ≤ 105) — the number of nodes in the tree and the number of queries. Next n - 1 lines contain the tree edges, the i-th line contains a pair of integers ai, bi (1 ≤ ai, bi ≤ n, ai ≠ bi) — an edge of the tree.
Next m lines contain queries. Each query is specified as a pair of integers ti, vi (1 ≤ ti ≤ 2, 1 ≤ vi ≤ n). If ti = 1, then as a reply to the query we need to paint a blue node vi in red. If ti = 2, then we should reply to the query by printing the shortest distance from some red node to node vi.
It is guaranteed that the given graph is a tree and that all queries are correct.
Output
For each second type query print the reply in a single line.
Examples
Input
5 4
1 2
2 3
2 4
4 5
2 1
2 5
1 2
2 5
Output
0
3
2
|
class CentroidDecomposition():
def __init__(self, g):
self.g = g
self.n = len(g)
self.parent = [-1]*self.n
self.size = [1]*self.n
self.cdparent = [-1]*self.n
self.cddepth = [0]*self.n
self.cdorder = [-1]*self.n
self.cdused = [0]*self.n
cnt = 0
stack = [0]
while stack:
v = stack.pop()
p = self.cdparent[v]
c = self.get_centroid(v)
self.cdused[c] = True
self.cdparent[c] = p
self.cddepth[c] = self.cddepth[v]
self.cdorder[c] = cnt
cnt += 1
for u in self.g[c]:
if self.cdused[u]:
continue
self.cdparent[u] = c
self.cddepth[u] = self.cddepth[c]+1
stack.append(u)
def get_centroid(self, root):
self.parent[root] = -1
self.size[root] = 1
stack = [root]
order = []
while stack:
v = stack.pop()
order.append(v)
for u in g[v]:
if self.parent[v] == u or self.cdused[u]:
continue
self.size[u] = 1
self.parent[u] = v
stack.append(u)
if len(order) <= 2:
return root
for v in reversed(order):
if self.parent[v] == -1:
continue
self.size[self.parent[v]] += self.size[v]
total = self.size[root]
v = root
while True:
for u in self.g[v]:
if self.parent[v] == u or self.cdused[u]:
continue
if self.size[u] > total//2:
v = u
break
else:
return v
class HLD:
def __init__(self, g):
self.g = g
self.n = len(g)
self.parent = [-1]*self.n
self.size = [1]*self.n
self.head = [0]*self.n
self.preorder = [0]*self.n
self.k = 0
self.depth = [0]*self.n
for v in range(self.n):
if self.parent[v] == -1:
self.dfs_pre(v)
self.dfs_hld(v)
def dfs_pre(self, v):
g = self.g
stack = [v]
order = [v]
while stack:
v = stack.pop()
for u in g[v]:
if self.parent[v] == u:
continue
self.parent[u] = v
self.depth[u] = self.depth[v]+1
stack.append(u)
order.append(u)
# 隣接リストの左端: heavyな頂点への辺
# 隣接リストの右端: 親への辺
while order:
v = order.pop()
child_v = g[v]
if len(child_v) and child_v[0] == self.parent[v]:
child_v[0], child_v[-1] = child_v[-1], child_v[0]
for i, u in enumerate(child_v):
if u == self.parent[v]:
continue
self.size[v] += self.size[u]
if self.size[u] > self.size[child_v[0]]:
child_v[i], child_v[0] = child_v[0], child_v[i]
def dfs_hld(self, v):
stack = [v]
while stack:
v = stack.pop()
self.preorder[v] = self.k
self.k += 1
top = self.g[v][0]
# 隣接リストを逆順に見ていく（親 > lightな頂点への辺 > heavyな頂点 (top)）
# 連結成分が連続するようにならべる
for u in reversed(self.g[v]):
if u == self.parent[v]:
continue
if u == top:
self.head[u] = self.head[v]
else:
self.head[u] = u
stack.append(u)
def for_each(self, u, v):
# [u, v]上の頂点集合の区間を列挙
while True:
if self.preorder[u] > self.preorder[v]:
u, v = v, u
l = max(self.preorder[self.head[v]], self.preorder[u])
r = self.preorder[v]
yield l, r # [l, r]
if self.head[u] != self.head[v]:
v = self.parent[self.head[v]]
else:
return
def for_each_edge(self, u, v):
# [u, v]上の辺集合の区間列挙
# 辺の情報は子の頂点に
while True:
if self.preorder[u] > self.preorder[v]:
u, v = v, u
if self.head[u] != self.head[v]:
yield self.preorder[self.head[v]], self.preorder[v]
v = self.parent[self.head[v]]
else:
if u != v:
yield self.preorder[u]+1, self.preorder[v]
break
def subtree(self, v):
# 頂点vの部分木の頂点集合の区間 [l, r)
l = self.preorder[v]
r = self.preorder[v]+self.size[v]
return l, r
def lca(self, u, v):
# 頂点u, vのLCA
while True:
if self.preorder[u] > self.preorder[v]:
u, v = v, u
if self.head[u] == self.head[v]:
return u
v = self.parent[self.head[v]]
import sys
import io, os
input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
n, m = map(int, input().split())
g = [[] for i in range(n)]
for i in range(n-1):
a, b = map(int, input().split())
a, b = a-1, b-1
g[a].append(b)
g[b].append(a)
cd = CentroidDecomposition(g)
hld = HLD(g)
#print(cd.cdparent)
min_dist = [0]*n
for i in range(n):
min_dist[i] = hld.depth[i]
#print(min_dist)
for i in range(m):
t, v = map(int, input().split())
v -= 1
if t == 1:
cur = v
while cur != -1:
l = hld.lca(cur, v)
d = hld.depth[cur]+hld.depth[v]-2*hld.depth[l]
min_dist[cur] = min(min_dist[cur], d)
cur = cd.cdparent[cur]
else:
ans = n
cur = v
while cur != -1:
l = hld.lca(cur, v)
d = hld.depth[cur]+hld.depth[v]-2*hld.depth[l]
ans = min(ans, d+min_dist[cur])
cur = cd.cdparent[cur]
print(ans)
|
{
"input": [
"5 4\n1 2\n2 3\n2 4\n4 5\n2 1\n2 5\n1 2\n2 5\n",
"5 4\n1 2\n2 3\n2 4\n4 5\n2 1\n2 5\n1 2\n2 1\n",
"5 4\n1 2\n2 3\n2 4\n4 5\n2 1\n2 1\n1 2\n2 1\n",
"5 4\n1 2\n2 3\n2 4\n1 5\n2 1\n2 5\n1 2\n2 5\n",
"5 4\n1 2\n2 3\n2 4\n4 5\n2 1\n1 5\n1 2\n2 1\n",
"5 4\n1 2\n2 3\n2 4\n1 5\n2 2\n2 5\n1 2\n2 5\n",
"5 4\n1 2\n2 3\n1 4\n4 5\n2 1\n2 5\n1 2\n2 1\n",
"5 4\n1 2\n2 3\n2 4\n1 5\n1 2\n2 5\n1 2\n2 5\n",
"5 4\n1 2\n2 3\n2 4\n4 5\n2 1\n2 3\n1 2\n2 5\n",
"5 4\n1 2\n2 3\n2 4\n4 5\n2 1\n2 5\n2 2\n2 1\n",
"5 4\n1 2\n2 3\n2 4\n4 5\n2 1\n2 3\n1 3\n2 5\n",
"5 4\n1 2\n2 3\n2 4\n1 5\n1 2\n2 5\n1 2\n1 5\n",
"5 3\n1 2\n2 3\n2 4\n1 5\n2 1\n2 5\n1 2\n2 5\n",
"5 4\n1 2\n2 3\n2 4\n4 5\n2 1\n2 5\n2 2\n2 5\n",
"5 4\n1 2\n2 3\n2 4\n1 5\n2 2\n2 5\n2 2\n2 5\n",
"5 4\n1 2\n2 3\n2 4\n4 5\n2 1\n1 5\n2 2\n2 1\n",
"5 4\n1 2\n2 3\n2 4\n1 5\n2 3\n2 2\n1 2\n2 5\n",
"5 4\n1 2\n2 3\n2 4\n4 5\n2 2\n1 5\n1 2\n2 5\n",
"5 4\n1 2\n1 3\n2 4\n4 5\n2 2\n2 1\n1 2\n2 1\n",
"5 4\n1 2\n2 3\n2 4\n1 5\n2 4\n2 5\n2 2\n2 5\n",
"5 4\n1 2\n2 3\n3 4\n4 5\n2 1\n2 5\n1 2\n2 5\n",
"5 4\n1 2\n2 3\n2 4\n4 5\n2 1\n2 5\n1 4\n2 1\n",
"5 4\n1 2\n2 3\n2 4\n1 5\n2 2\n2 2\n1 2\n2 5\n",
"5 4\n1 2\n2 3\n2 4\n4 5\n2 1\n1 5\n1 2\n2 5\n",
"5 4\n1 2\n1 3\n2 4\n4 5\n2 1\n2 1\n1 2\n2 1\n",
"5 4\n1 2\n2 3\n2 4\n1 5\n2 1\n2 1\n1 2\n2 1\n",
"5 4\n1 2\n2 3\n1 4\n4 5\n2 1\n1 5\n1 2\n2 1\n",
"5 4\n1 2\n2 3\n1 4\n4 5\n2 1\n2 3\n1 3\n2 5\n",
"5 4\n1 2\n1 3\n2 4\n1 5\n2 1\n2 5\n1 2\n2 5\n",
"5 4\n1 2\n2 3\n2 4\n1 5\n2 1\n2 1\n1 4\n2 1\n",
"5 4\n1 2\n2 3\n2 4\n4 5\n2 1\n2 1\n1 4\n2 1\n",
"5 4\n1 2\n4 3\n2 4\n1 5\n1 2\n2 5\n1 2\n1 5\n",
"5 4\n1 3\n2 3\n2 4\n4 5\n2 1\n1 5\n2 2\n2 1\n",
"5 4\n1 2\n2 3\n1 4\n4 5\n2 1\n2 5\n1 3\n2 1\n",
"5 4\n1 2\n2 3\n2 4\n1 5\n2 3\n2 2\n1 3\n2 5\n",
"5 4\n1 2\n1 3\n2 4\n4 5\n2 2\n1 5\n1 2\n2 5\n",
"5 4\n1 2\n1 3\n2 4\n1 5\n2 2\n2 1\n1 2\n2 1\n",
"5 4\n1 2\n4 3\n2 4\n1 5\n1 2\n2 5\n1 3\n1 5\n",
"5 4\n1 2\n1 3\n3 4\n1 5\n2 2\n2 1\n1 2\n2 1\n",
"5 4\n1 2\n1 3\n1 4\n1 5\n2 2\n2 1\n1 2\n2 1\n",
"5 4\n1 2\n1 3\n1 4\n1 5\n2 2\n2 1\n1 4\n2 1\n",
"5 4\n1 2\n2 3\n2 4\n1 5\n1 2\n2 5\n1 3\n2 5\n",
"5 4\n1 2\n2 3\n1 4\n4 5\n2 1\n1 5\n1 2\n2 5\n",
"5 4\n1 2\n2 3\n2 4\n1 5\n1 2\n2 5\n1 2\n1 4\n"
],
"output": [
"0\n3\n2\n",
"0\n3\n0\n",
"0\n0\n0\n",
"0\n1\n1\n",
"0\n0\n",
"1\n1\n1\n",
"0\n2\n0\n",
"1\n1\n",
"0\n2\n2\n",
"0\n3\n1\n0\n",
"0\n2\n3\n",
"1\n",
"0\n1\n",
"0\n3\n1\n3\n",
"1\n1\n1\n1\n",
"0\n1\n0\n",
"2\n1\n1\n",
"1\n0\n",
"1\n0\n0\n",
"2\n1\n1\n1\n",
"0\n4\n3\n",
"0\n3\n0\n",
"1\n1\n1\n",
"0\n0\n",
"0\n0\n0\n",
"0\n0\n0\n",
"0\n0\n",
"0\n2\n2\n",
"0\n1\n1\n",
"0\n0\n0\n",
"0\n0\n0\n",
"1\n",
"0\n2\n0\n",
"0\n2\n0\n",
"2\n1\n1\n",
"1\n0\n",
"1\n0\n0\n",
"1\n",
"1\n0\n0\n",
"1\n0\n0\n",
"1\n0\n0\n",
"1\n1\n",
"0\n0\n",
"1\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Xenia the programmer has a tree consisting of n nodes. We will consider the tree nodes indexed from 1 to n. We will also consider the first node to be initially painted red, and the other nodes — to be painted blue.
The distance between two tree nodes v and u is the number of edges in the shortest path between v and u.
Xenia needs to learn how to quickly execute queries of two types:
1. paint a specified blue node in red;
2. calculate which red node is the closest to the given one and print the shortest distance to the closest red node.
Your task is to write a program which will execute the described queries.
Input
The first line contains two integers n and m (2 ≤ n ≤ 105, 1 ≤ m ≤ 105) — the number of nodes in the tree and the number of queries. Next n - 1 lines contain the tree edges, the i-th line contains a pair of integers ai, bi (1 ≤ ai, bi ≤ n, ai ≠ bi) — an edge of the tree.
Next m lines contain queries. Each query is specified as a pair of integers ti, vi (1 ≤ ti ≤ 2, 1 ≤ vi ≤ n). If ti = 1, then as a reply to the query we need to paint a blue node vi in red. If ti = 2, then we should reply to the query by printing the shortest distance from some red node to node vi.
It is guaranteed that the given graph is a tree and that all queries are correct.
Output
For each second type query print the reply in a single line.
Examples
Input
5 4
1 2
2 3
2 4
4 5
2 1
2 5
1 2
2 5
Output
0
3
2
### Input:
5 4
1 2
2 3
2 4
4 5
2 1
2 5
1 2
2 5
### Output:
0
3
2
### Input:
5 4
1 2
2 3
2 4
4 5
2 1
2 5
1 2
2 1
### Output:
0
3
0
### Code:
class CentroidDecomposition():
def __init__(self, g):
self.g = g
self.n = len(g)
self.parent = [-1]*self.n
self.size = [1]*self.n
self.cdparent = [-1]*self.n
self.cddepth = [0]*self.n
self.cdorder = [-1]*self.n
self.cdused = [0]*self.n
cnt = 0
stack = [0]
while stack:
v = stack.pop()
p = self.cdparent[v]
c = self.get_centroid(v)
self.cdused[c] = True
self.cdparent[c] = p
self.cddepth[c] = self.cddepth[v]
self.cdorder[c] = cnt
cnt += 1
for u in self.g[c]:
if self.cdused[u]:
continue
self.cdparent[u] = c
self.cddepth[u] = self.cddepth[c]+1
stack.append(u)
def get_centroid(self, root):
self.parent[root] = -1
self.size[root] = 1
stack = [root]
order = []
while stack:
v = stack.pop()
order.append(v)
for u in g[v]:
if self.parent[v] == u or self.cdused[u]:
continue
self.size[u] = 1
self.parent[u] = v
stack.append(u)
if len(order) <= 2:
return root
for v in reversed(order):
if self.parent[v] == -1:
continue
self.size[self.parent[v]] += self.size[v]
total = self.size[root]
v = root
while True:
for u in self.g[v]:
if self.parent[v] == u or self.cdused[u]:
continue
if self.size[u] > total//2:
v = u
break
else:
return v
class HLD:
def __init__(self, g):
self.g = g
self.n = len(g)
self.parent = [-1]*self.n
self.size = [1]*self.n
self.head = [0]*self.n
self.preorder = [0]*self.n
self.k = 0
self.depth = [0]*self.n
for v in range(self.n):
if self.parent[v] == -1:
self.dfs_pre(v)
self.dfs_hld(v)
def dfs_pre(self, v):
g = self.g
stack = [v]
order = [v]
while stack:
v = stack.pop()
for u in g[v]:
if self.parent[v] == u:
continue
self.parent[u] = v
self.depth[u] = self.depth[v]+1
stack.append(u)
order.append(u)
# 隣接リストの左端: heavyな頂点への辺
# 隣接リストの右端: 親への辺
while order:
v = order.pop()
child_v = g[v]
if len(child_v) and child_v[0] == self.parent[v]:
child_v[0], child_v[-1] = child_v[-1], child_v[0]
for i, u in enumerate(child_v):
if u == self.parent[v]:
continue
self.size[v] += self.size[u]
if self.size[u] > self.size[child_v[0]]:
child_v[i], child_v[0] = child_v[0], child_v[i]
def dfs_hld(self, v):
stack = [v]
while stack:
v = stack.pop()
self.preorder[v] = self.k
self.k += 1
top = self.g[v][0]
# 隣接リストを逆順に見ていく（親 > lightな頂点への辺 > heavyな頂点 (top)）
# 連結成分が連続するようにならべる
for u in reversed(self.g[v]):
if u == self.parent[v]:
continue
if u == top:
self.head[u] = self.head[v]
else:
self.head[u] = u
stack.append(u)
def for_each(self, u, v):
# [u, v]上の頂点集合の区間を列挙
while True:
if self.preorder[u] > self.preorder[v]:
u, v = v, u
l = max(self.preorder[self.head[v]], self.preorder[u])
r = self.preorder[v]
yield l, r # [l, r]
if self.head[u] != self.head[v]:
v = self.parent[self.head[v]]
else:
return
def for_each_edge(self, u, v):
# [u, v]上の辺集合の区間列挙
# 辺の情報は子の頂点に
while True:
if self.preorder[u] > self.preorder[v]:
u, v = v, u
if self.head[u] != self.head[v]:
yield self.preorder[self.head[v]], self.preorder[v]
v = self.parent[self.head[v]]
else:
if u != v:
yield self.preorder[u]+1, self.preorder[v]
break
def subtree(self, v):
# 頂点vの部分木の頂点集合の区間 [l, r)
l = self.preorder[v]
r = self.preorder[v]+self.size[v]
return l, r
def lca(self, u, v):
# 頂点u, vのLCA
while True:
if self.preorder[u] > self.preorder[v]:
u, v = v, u
if self.head[u] == self.head[v]:
return u
v = self.parent[self.head[v]]
import sys
import io, os
input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
n, m = map(int, input().split())
g = [[] for i in range(n)]
for i in range(n-1):
a, b = map(int, input().split())
a, b = a-1, b-1
g[a].append(b)
g[b].append(a)
cd = CentroidDecomposition(g)
hld = HLD(g)
#print(cd.cdparent)
min_dist = [0]*n
for i in range(n):
min_dist[i] = hld.depth[i]
#print(min_dist)
for i in range(m):
t, v = map(int, input().split())
v -= 1
if t == 1:
cur = v
while cur != -1:
l = hld.lca(cur, v)
d = hld.depth[cur]+hld.depth[v]-2*hld.depth[l]
min_dist[cur] = min(min_dist[cur], d)
cur = cd.cdparent[cur]
else:
ans = n
cur = v
while cur != -1:
l = hld.lca(cur, v)
d = hld.depth[cur]+hld.depth[v]-2*hld.depth[l]
ans = min(ans, d+min_dist[cur])
cur = cd.cdparent[cur]
print(ans)
|
366_B. Dima and To-do List_10574
|
You helped Dima to have a great weekend, but it's time to work. Naturally, Dima, as all other men who have girlfriends, does everything wrong.
Inna and Dima are now in one room. Inna tells Dima off for everything he does in her presence. After Inna tells him off for something, she goes to another room, walks there in circles muttering about how useless her sweetheart is. During that time Dima has time to peacefully complete k - 1 tasks. Then Inna returns and tells Dima off for the next task he does in her presence and goes to another room again. It continues until Dima is through with his tasks.
Overall, Dima has n tasks to do, each task has a unique number from 1 to n. Dima loves order, so he does tasks consecutively, starting from some task. For example, if Dima has 6 tasks to do in total, then, if he starts from the 5-th task, the order is like that: first Dima does the 5-th task, then the 6-th one, then the 1-st one, then the 2-nd one, then the 3-rd one, then the 4-th one.
Inna tells Dima off (only lovingly and appropriately!) so often and systematically that he's very well learned the power with which she tells him off for each task. Help Dima choose the first task so that in total he gets told off with as little power as possible.
Input
The first line of the input contains two integers n, k (1 ≤ k ≤ n ≤ 105). The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 103), where ai is the power Inna tells Dima off with if she is present in the room while he is doing the i-th task.
It is guaranteed that n is divisible by k.
Output
In a single line print the number of the task Dima should start with to get told off with as little power as possible. If there are multiple solutions, print the one with the minimum number of the first task to do.
Examples
Input
6 2
3 2 1 6 5 4
Output
1
Input
10 5
1 3 5 7 9 9 4 1 8 5
Output
3
Note
Explanation of the first example.
If Dima starts from the first task, Inna tells him off with power 3, then Dima can do one more task (as k = 2), then Inna tells him off for the third task with power 1, then she tells him off for the fifth task with power 5. Thus, Dima gets told off with total power 3 + 1 + 5 = 9. If Dima started from the second task, for example, then Inna would tell him off for tasks 2, 4 and 6 with power 2 + 6 + 4 = 12.
Explanation of the second example.
In the second example k = 5, thus, Dima manages to complete 4 tasks in-between the telling off sessions. Thus, Inna tells Dima off for tasks number 1 and 6 (if he starts from 1 or 6), 2 and 7 (if he starts from 2 or 7) and so on. The optimal answer is to start from task 3 or 8, 3 has a smaller number, so the answer is 3.
|
n,k = map(int, input().split())
t = list(map(int, input().split()))
current_sum = None
flag = 1
for i in range(k):
if current_sum == None or sum(t[i :: k]) < current_sum:
current_sum = sum(t[i :: k])
flag = i+1
print(flag)
#print(min((sum(t[i :: k]), i) for i in range(k))[1] + 1)
|
{
"input": [
"10 5\n1 3 5 7 9 9 4 1 8 5\n",
"6 2\n3 2 1 6 5 4\n",
"20 4\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
"4 2\n2 1 1 3\n",
"50 10\n1 2 3 4 5 6 7 8 9 10 10 1 1 1 1 1 1 1 1 1 10 1 1 1 1 1 1 1 1 1 10 1 1 1 1 1 1 1 1 1 10 1 1 1 1 1 1 1 1 1\n",
"10 10\n8 4 5 7 6 9 2 2 3 5\n",
"2 1\n1 1\n",
"1 1\n1\n",
"15 5\n5 5 5 5 5 1 2 3 4 5 1 2 3 4 5\n",
"20 10\n3 3 3 3 3 3 3 3 2 3 3 3 3 3 3 3 3 3 6 4\n",
"20 4\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2\n",
"50 10\n1 2 3 4 5 4 7 8 9 10 10 1 1 1 1 1 1 1 1 1 10 1 1 1 1 1 1 1 1 1 10 1 1 1 1 1 1 1 1 1 10 1 1 1 1 1 1 1 1 1\n",
"50 10\n1 2 3 4 5 1 7 8 9 10 10 1 1 1 1 1 1 1 1 1 10 1 1 1 1 1 1 1 1 1 10 1 1 1 1 1 1 1 1 1 10 1 1 1 1 1 1 1 1 1\n",
"10 5\n1 3 5 2 9 9 4 1 8 5\n",
"50 10\n1 2 3 4 5 1 7 8 9 0 10 1 1 1 1 1 1 1 1 1 10 1 1 1 1 1 1 1 1 1 10 1 1 1 1 1 1 1 1 1 10 1 1 1 1 1 0 1 1 1\n",
"4 2\n2 1 1 6\n",
"2 1\n0 1\n",
"1 1\n2\n",
"15 5\n5 5 5 5 5 0 2 3 4 5 1 2 3 4 5\n",
"10 5\n1 0 5 7 9 9 4 1 8 5\n",
"6 2\n3 2 1 1 5 4\n",
"20 4\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2\n",
"4 2\n2 1 1 5\n",
"1 1\n4\n",
"15 1\n5 5 5 5 5 0 2 3 4 5 1 2 3 4 5\n",
"10 5\n1 0 5 7 9 9 4 1 8 6\n",
"6 2\n3 2 1 1 5 5\n",
"20 4\n1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 2 2\n",
"4 2\n2 1 1 7\n",
"50 10\n1 2 3 4 5 1 7 8 9 10 10 1 1 1 1 1 1 1 1 1 10 1 1 1 1 1 1 1 1 1 10 1 1 1 1 1 1 1 1 1 10 1 1 1 1 1 0 1 1 1\n",
"15 1\n5 5 5 5 5 0 2 3 4 5 1 2 0 4 5\n",
"10 5\n1 0 5 7 9 9 1 1 8 6\n",
"20 4\n2 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 2 2\n",
"4 2\n2 1 2 7\n",
"50 10\n1 2 3 4 5 1 7 8 9 10 10 2 1 1 1 1 1 1 1 1 10 1 1 1 1 1 1 1 1 1 10 1 1 1 1 1 1 1 1 1 10 1 1 1 1 1 0 1 1 1\n",
"15 1\n5 5 5 5 5 0 2 5 4 5 1 2 0 4 5\n",
"10 5\n1 0 5 8 9 9 1 1 8 6\n",
"4 2\n2 1 0 7\n",
"50 10\n1 2 3 4 5 1 7 8 9 10 10 2 1 1 1 1 1 1 1 1 10 1 1 1 1 1 1 1 1 1 10 1 1 1 1 1 1 1 1 1 10 2 1 1 1 1 0 1 1 1\n",
"15 1\n5 5 5 5 5 0 2 5 2 5 1 2 0 4 5\n",
"4 2\n4 1 0 7\n",
"50 10\n1 2 3 4 5 1 7 8 9 10 10 2 1 1 1 1 1 1 1 1 10 1 1 1 1 1 1 1 1 1 10 1 1 1 1 1 1 1 1 1 10 2 1 1 1 1 0 1 2 1\n",
"15 1\n5 5 5 5 5 0 2 5 2 5 1 2 0 2 5\n",
"15 1\n5 5 5 5 5 0 2 5 2 5 0 2 0 2 5\n",
"15 1\n5 5 5 5 5 0 2 5 2 5 0 4 0 2 5\n",
"15 1\n5 5 6 5 5 0 2 5 2 5 0 4 0 2 5\n",
"15 1\n5 5 6 6 5 0 2 5 2 5 0 4 0 2 5\n",
"15 1\n5 5 6 6 5 0 2 5 2 5 0 4 -1 2 5\n",
"15 1\n5 5 6 3 5 0 2 5 2 5 0 4 -1 2 5\n",
"15 1\n5 5 6 4 5 0 2 5 2 5 0 4 -1 2 5\n",
"15 1\n5 5 6 4 5 0 2 5 2 5 0 4 -1 2 4\n",
"15 1\n5 5 6 4 5 0 2 5 1 5 0 4 -1 2 4\n",
"20 4\n1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
"4 1\n2 1 1 3\n",
"50 10\n1 2 3 4 5 6 7 8 9 10 10 1 1 1 1 1 1 1 1 1 10 1 1 1 1 1 1 1 1 1 10 1 1 0 1 1 1 1 1 1 10 1 1 1 1 1 1 1 1 1\n",
"20 10\n3 1 3 3 3 3 3 3 2 3 3 3 3 3 3 3 3 3 6 4\n",
"6 2\n3 2 2 6 5 4\n",
"20 4\n1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2\n",
"4 2\n2 1 0 6\n",
"50 10\n1 2 3 4 5 4 7 8 9 10 10 1 1 1 1 1 1 0 1 1 10 1 1 1 1 1 1 1 1 1 10 1 1 1 1 1 1 1 1 1 10 1 1 1 1 1 1 1 1 1\n",
"2 1\n0 2\n",
"10 5\n1 0 5 7 9 9 4 2 8 5\n",
"6 2\n3 2 1 0 5 4\n",
"50 10\n1 2 3 4 5 1 7 8 9 10 10 1 1 1 1 1 1 1 1 1 10 1 1 1 1 1 1 1 1 2 10 1 1 1 1 1 1 1 1 1 10 1 1 1 1 1 1 1 1 1\n",
"15 1\n5 5 5 5 5 0 2 3 4 5 1 4 3 4 5\n",
"10 5\n1 0 5 6 9 9 4 1 8 5\n",
"6 2\n3 2 1 0 5 5\n",
"20 4\n1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 2 2\n",
"4 4\n2 1 1 7\n",
"15 1\n5 5 5 5 5 0 2 3 1 5 1 2 0 4 5\n",
"10 5\n1 0 5 7 3 9 1 1 8 6\n",
"20 4\n2 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 2 2\n",
"4 2\n0 1 2 7\n",
"50 10\n1 2 3 4 5 1 7 8 9 10 10 2 1 1 1 1 1 1 1 1 10 1 1 1 1 1 1 1 1 1 10 1 1 1 1 1 1 1 1 1 10 1 2 1 1 1 0 1 1 1\n",
"15 1\n5 5 5 5 5 0 2 5 4 5 1 2 1 4 5\n",
"50 10\n1 2 3 4 5 1 7 8 9 10 10 2 1 1 1 1 1 1 1 1 10 1 1 1 1 1 1 0 1 1 10 1 1 1 1 1 1 1 1 1 10 2 1 1 1 1 0 1 1 1\n",
"15 1\n5 5 5 5 5 0 2 5 2 3 1 2 0 4 5\n",
"4 2\n4 2 0 7\n",
"50 10\n2 2 3 4 5 1 7 8 9 10 10 2 1 1 1 1 1 1 1 1 10 1 1 1 1 1 1 1 1 1 10 1 1 1 1 1 1 1 1 1 10 2 1 1 1 1 0 1 2 1\n",
"15 1\n5 5 5 5 5 0 2 5 3 5 1 2 0 2 5\n",
"15 1\n5 5 5 5 5 -1 2 5 2 5 0 2 0 2 5\n",
"15 1\n8 5 5 5 5 0 2 5 2 5 0 4 0 2 5\n",
"15 1\n5 5 6 5 2 0 2 5 2 5 0 4 0 2 5\n",
"15 1\n5 5 1 6 5 0 2 5 2 5 0 4 0 2 5\n",
"15 1\n5 5 6 6 5 0 2 5 2 5 0 4 -1 2 9\n",
"15 1\n5 0 6 3 5 0 2 5 2 5 0 4 -1 2 5\n",
"15 1\n5 5 6 4 5 0 2 5 1 5 0 4 -1 2 5\n",
"15 1\n5 5 6 1 5 0 2 5 2 5 0 4 -1 2 4\n",
"15 1\n5 5 6 4 5 0 2 5 1 8 0 4 -1 2 4\n",
"20 4\n1 1 1 1 1 0 1 1 1 2 1 1 1 1 1 1 1 1 1 1\n",
"4 1\n2 1 1 5\n",
"50 10\n1 2 3 7 5 6 7 8 9 10 10 1 1 1 1 1 1 1 1 1 10 1 1 1 1 1 1 1 1 1 10 1 1 0 1 1 1 1 1 1 10 1 1 1 1 1 1 1 1 1\n",
"20 10\n0 1 3 3 3 3 3 3 2 3 3 3 3 3 3 3 3 3 6 4\n",
"10 5\n1 3 5 2 3 9 4 1 8 5\n",
"6 2\n3 2 2 1 5 4\n",
"20 4\n1 2 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 2\n",
"10 5\n1 0 5 7 9 5 4 2 8 5\n",
"6 2\n3 2 1 0 0 4\n",
"50 10\n1 2 3 4 5 1 7 8 5 10 10 1 1 1 1 1 1 1 1 1 10 1 1 1 1 1 1 1 1 2 10 1 1 1 1 1 1 1 1 1 10 1 1 1 1 1 1 1 1 1\n",
"15 1\n5 5 5 5 5 0 1 3 4 5 1 4 3 4 5\n",
"10 5\n1 0 5 1 9 9 4 1 8 5\n",
"6 2\n3 2 1 0 8 5\n",
"20 4\n1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 2 1 2 2\n",
"50 10\n1 2 3 4 8 1 7 8 9 0 10 1 1 1 1 1 1 1 1 1 10 1 1 1 1 1 1 1 1 1 10 1 1 1 1 1 1 1 1 1 10 1 1 1 1 1 0 1 1 1\n",
"15 1\n7 5 5 5 5 0 2 3 1 5 1 2 0 4 5\n",
"10 5\n1 0 8 7 3 9 1 1 8 6\n",
"20 4\n2 1 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 2 2\n",
"4 2\n0 2 2 7\n",
"50 10\n1 2 3 4 5 1 7 8 9 10 10 2 1 1 1 1 1 1 0 1 10 1 1 1 1 1 1 1 1 1 10 1 1 1 1 1 1 1 1 1 10 1 2 1 1 1 0 1 1 1\n",
"15 1\n5 3 5 5 5 0 2 5 4 5 1 2 1 4 5\n"
],
"output": [
"3",
"1",
"1",
"1",
"2",
"7",
"1",
"1",
"1",
"1",
"1\n",
"2\n",
"6\n",
"3\n",
"10\n",
"1\n",
"1\n",
"1\n",
"1\n",
"2\n",
"2\n",
"1\n",
"1\n",
"1\n",
"1\n",
"2\n",
"2\n",
"1\n",
"1\n",
"6\n",
"1\n",
"2\n",
"1\n",
"1\n",
"6\n",
"1\n",
"2\n",
"1\n",
"6\n",
"1\n",
"1\n",
"6\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"2\n",
"1\n",
"2\n",
"2\n",
"1\n",
"1\n",
"1\n",
"2\n",
"1\n",
"2\n",
"2\n",
"6\n",
"1\n",
"2\n",
"2\n",
"1\n",
"2\n",
"1\n",
"2\n",
"1\n",
"1\n",
"6\n",
"1\n",
"6\n",
"1\n",
"1\n",
"6\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"2\n",
"1\n",
"3\n",
"2\n",
"1\n",
"2\n",
"1\n",
"6\n",
"1\n",
"2\n",
"2\n",
"1\n",
"10\n",
"1\n",
"2\n",
"1\n",
"1\n",
"6\n",
"1\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You helped Dima to have a great weekend, but it's time to work. Naturally, Dima, as all other men who have girlfriends, does everything wrong.
Inna and Dima are now in one room. Inna tells Dima off for everything he does in her presence. After Inna tells him off for something, she goes to another room, walks there in circles muttering about how useless her sweetheart is. During that time Dima has time to peacefully complete k - 1 tasks. Then Inna returns and tells Dima off for the next task he does in her presence and goes to another room again. It continues until Dima is through with his tasks.
Overall, Dima has n tasks to do, each task has a unique number from 1 to n. Dima loves order, so he does tasks consecutively, starting from some task. For example, if Dima has 6 tasks to do in total, then, if he starts from the 5-th task, the order is like that: first Dima does the 5-th task, then the 6-th one, then the 1-st one, then the 2-nd one, then the 3-rd one, then the 4-th one.
Inna tells Dima off (only lovingly and appropriately!) so often and systematically that he's very well learned the power with which she tells him off for each task. Help Dima choose the first task so that in total he gets told off with as little power as possible.
Input
The first line of the input contains two integers n, k (1 ≤ k ≤ n ≤ 105). The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 103), where ai is the power Inna tells Dima off with if she is present in the room while he is doing the i-th task.
It is guaranteed that n is divisible by k.
Output
In a single line print the number of the task Dima should start with to get told off with as little power as possible. If there are multiple solutions, print the one with the minimum number of the first task to do.
Examples
Input
6 2
3 2 1 6 5 4
Output
1
Input
10 5
1 3 5 7 9 9 4 1 8 5
Output
3
Note
Explanation of the first example.
If Dima starts from the first task, Inna tells him off with power 3, then Dima can do one more task (as k = 2), then Inna tells him off for the third task with power 1, then she tells him off for the fifth task with power 5. Thus, Dima gets told off with total power 3 + 1 + 5 = 9. If Dima started from the second task, for example, then Inna would tell him off for tasks 2, 4 and 6 with power 2 + 6 + 4 = 12.
Explanation of the second example.
In the second example k = 5, thus, Dima manages to complete 4 tasks in-between the telling off sessions. Thus, Inna tells Dima off for tasks number 1 and 6 (if he starts from 1 or 6), 2 and 7 (if he starts from 2 or 7) and so on. The optimal answer is to start from task 3 or 8, 3 has a smaller number, so the answer is 3.
### Input:
10 5
1 3 5 7 9 9 4 1 8 5
### Output:
3
### Input:
6 2
3 2 1 6 5 4
### Output:
1
### Code:
n,k = map(int, input().split())
t = list(map(int, input().split()))
current_sum = None
flag = 1
for i in range(k):
if current_sum == None or sum(t[i :: k]) < current_sum:
current_sum = sum(t[i :: k])
flag = i+1
print(flag)
#print(min((sum(t[i :: k]), i) for i in range(k))[1] + 1)
|
38_A. Army_10578
|
The Berland Armed Forces System consists of n ranks that are numbered using natural numbers from 1 to n, where 1 is the lowest rank and n is the highest rank.
One needs exactly di years to rise from rank i to rank i + 1. Reaching a certain rank i having not reached all the previous i - 1 ranks is impossible.
Vasya has just reached a new rank of a, but he dreams of holding the rank of b. Find for how many more years Vasya should serve in the army until he can finally realize his dream.
Input
The first input line contains an integer n (2 ≤ n ≤ 100). The second line contains n - 1 integers di (1 ≤ di ≤ 100). The third input line contains two integers a and b (1 ≤ a < b ≤ n). The numbers on the lines are space-separated.
Output
Print the single number which is the number of years that Vasya needs to rise from rank a to rank b.
Examples
Input
3
5 6
1 2
Output
5
Input
3
5 6
1 3
Output
11
|
#!/usr/bin/python3
def readln(): return tuple(map(int, input().split()))
n, = readln()
d = readln()
a, b = readln()
print(sum(d[a - 1:b - 1]))
|
{
"input": [
"3\n5 6\n1 2\n",
"3\n5 6\n1 3\n",
"80\n65 15 43 6 43 98 100 16 69 98 4 54 25 40 2 35 12 23 38 29 10 89 30 6 4 8 7 96 64 43 11 49 89 38 20 59 54 85 46 16 16 89 60 54 28 37 32 34 67 9 78 30 50 87 58 53 99 48 77 3 5 6 19 99 16 20 31 10 80 76 82 56 56 83 72 81 84 60 28\n18 24\n",
"51\n85 38 22 38 42 36 55 24 36 80 49 15 66 91 88 61 46 82 1 61 89 92 6 56 28 8 46 80 56 90 91 38 38 17 69 64 57 68 13 44 45 38 8 72 61 39 87 2 73 88\n15 27\n",
"3\n85 78\n1 3\n",
"30\n35 69 50 44 19 56 86 56 98 24 21 2 61 24 85 30 2 22 57 35 59 84 12 77 92 53 50 92 9\n1 16\n",
"96\n1 1 2 3 3 5 8 9 9 10 10 10 11 11 11 11 11 12 13 13 13 14 15 15 16 16 17 17 17 17 18 18 20 20 20 21 21 21 23 24 24 25 25 26 27 27 27 27 29 29 29 30 30 30 32 32 32 32 32 32 33 33 34 34 34 35 35 35 36 36 37 37 37 38 39 40 41 41 41 41 42 42 43 43 45 45 45 46 46 47 47 49 50 52 52\n76 96\n",
"100\n1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 3 3 3 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 8 8 8 8 9 9 9 9 10 10 10 10 11 11 11 11 12 12 12 13 13 13 13 13 13 13 13 13 13 14 14 14 14 14 14 15 15 15 15 15 15 16 16 16 17 17\n39 52\n",
"70\n1 2 3 3 4 5 5 7 7 7 8 8 8 8 9 9 10 12 12 12 12 13 16 16 16 16 16 16 17 17 18 18 20 20 21 23 24 25 25 26 29 29 29 29 31 32 32 34 35 36 36 37 37 38 39 39 40 40 40 40 41 41 42 43 44 44 44 45 45\n62 65\n",
"90\n61 35 100 99 67 87 42 90 44 4 81 65 29 63 66 56 53 22 55 87 39 30 34 42 27 80 29 97 85 28 81 22 50 22 24 75 67 86 78 79 94 35 13 97 48 76 68 66 94 13 82 1 22 85 5 36 86 73 65 97 43 56 35 26 87 25 74 47 81 67 73 75 99 75 53 38 70 21 66 78 38 17 57 40 93 57 68 55 1\n12 44\n",
"60\n24 28 25 21 43 71 64 73 71 90 51 83 69 43 75 43 78 72 56 61 99 7 23 86 9 16 16 94 23 74 18 56 20 72 13 31 75 34 35 86 61 49 4 72 84 7 65 70 66 52 21 38 6 43 69 40 73 46 5\n28 60\n",
"2\n55\n1 2\n",
"35\n2 34 47 15 27 61 6 88 67 20 53 65 29 68 77 5 78 86 44 98 32 81 91 79 54 84 95 23 65 97 22 33 42 87\n8 35\n",
"8\n82 14 24 5 91 49 94\n3 8\n",
"98\n2 3 4 4 5 7 8 10 10 10 11 11 12 12 12 12 13 14 15 15 16 16 18 19 19 20 21 21 21 21 22 23 24 25 26 26 27 27 27 27 29 29 30 30 31 31 37 40 40 40 41 41 41 42 43 44 44 44 46 46 47 49 49 50 50 50 51 53 55 55 56 56 56 56 56 57 57 58 59 60 60 60 62 62 63 64 64 64 65 66 66 67 68 70 70 71 71\n8 90\n",
"95\n37 74 53 96 65 84 65 72 95 45 6 77 91 35 58 50 51 51 97 30 51 20 79 81 92 10 89 34 40 76 71 54 26 34 73 72 72 28 53 19 95 64 97 10 44 15 12 38 5 63 96 95 86 8 36 96 45 53 81 5 18 18 47 97 65 9 33 53 41 86 37 53 5 40 15 76 83 45 33 18 26 5 19 90 46 40 100 42 10 90 13 81 40 53\n6 15\n",
"20\n1 1 1 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 3\n5 17\n",
"4\n63 4 49\n2 3\n",
"60\n1 2 4 4 4 6 6 8 9 10 10 13 14 18 20 20 21 22 23 23 26 29 30 32 33 34 35 38 40 42 44 44 46 48 52 54 56 56 60 60 66 67 68 68 69 73 73 74 80 80 81 81 82 84 86 86 87 89 89\n56 58\n",
"10\n95 81 32 59 71 30 50 61 100\n1 6\n",
"80\n1 1 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 4 4 4 4 5 5 5 5 5 5 5 6 7 7 7 7 7 7 8 8 8 8 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12\n17 65\n",
"99\n46 5 16 66 53 12 84 89 26 27 35 68 41 44 63 17 88 43 80 15 59 1 42 50 53 34 75 16 16 55 92 30 28 11 12 71 27 65 11 28 86 47 24 10 60 47 7 53 16 75 6 49 56 66 70 3 20 78 75 41 38 57 89 23 16 74 30 39 1 32 49 84 9 33 25 95 75 45 54 59 17 17 29 40 79 96 47 11 69 86 73 56 91 4 87 47 31 24\n23 36\n",
"100\n63 65 21 41 95 23 3 4 12 23 95 50 75 63 58 34 71 27 75 31 23 94 96 74 69 34 43 25 25 55 44 19 43 86 68 17 52 65 36 29 72 96 84 25 84 23 71 54 6 7 71 7 21 100 99 58 93 35 62 47 36 70 68 9 75 13 35 70 76 36 62 22 52 51 2 87 66 41 54 35 78 62 30 35 65 44 74 93 78 37 96 70 26 32 71 27 85 85 63\n43 92\n",
"95\n2 2 3 3 4 6 6 7 7 7 9 10 12 12 12 12 13 14 15 16 17 18 20 20 20 20 21 21 21 21 22 22 22 22 22 23 23 23 25 26 26 27 27 27 28 29 29 30 30 31 32 33 34 36 37 37 38 39 39 39 42 43 43 43 45 47 48 50 50 51 52 53 54 54 54 55 55 55 58 59 60 61 61 61 61 62 62 63 64 65 66 67 67 67\n64 93\n",
"6\n22 9 87 89 57\n1 6\n",
"50\n1 8 8 13 14 15 15 16 19 21 22 24 26 31 32 37 45 47 47 47 50 50 51 54 55 56 58 61 61 61 63 63 64 66 66 67 67 70 71 80 83 84 85 92 92 94 95 95 100\n4 17\n",
"20\n91 1 41 51 95 67 92 35 23 70 44 91 57 50 21 8 9 71 40\n8 17\n",
"40\n32 88 59 36 95 45 28 78 73 30 97 13 13 47 48 100 43 21 22 45 88 25 15 13 63 25 72 92 29 5 25 11 50 5 54 51 48 84 23\n7 26\n",
"6\n3 12 27 28 28\n3 4\n",
"25\n1 1 1 4 5 6 8 11 11 11 11 12 13 14 14 14 15 16 16 17 17 17 19 19\n4 8\n",
"9\n12 40 69 39 59 21 59 5\n4 6\n",
"2\n3\n1 2\n",
"51\n5 7 9 16 19 25 26 29 29 30 31 32 32 41 43 44 47 49 50 50 51 52 54 55 56 63 64 66 67 70 74 74 77 78 79 80 80 85 86 87 89 89 90 92 93 94 94 95 95 97\n3 44\n",
"25\n70 95 21 84 97 39 12 98 53 24 78 29 84 65 70 22 100 17 69 27 62 48 35 80\n8 23\n",
"70\n69 95 34 14 67 61 6 95 94 44 28 94 73 66 39 13 19 71 73 71 28 48 26 22 32 88 38 95 43 59 88 77 80 55 17 95 40 83 67 1 38 95 58 63 56 98 49 2 41 4 73 8 78 41 64 71 60 71 41 61 67 4 4 19 97 14 39 20 27\n9 41\n",
"35\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n30 31\n",
"7\n52 36 31 23 74 78\n2 7\n",
"99\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n66 95\n",
"45\n1 1 1 1 2 2 2 2 2 2 2 3 3 3 3 3 3 4 5 5 5 5 6 6 6 6 6 6 6 7 7 7 7 8 8 8 9 9 9 9 9 10 10 10\n42 45\n",
"5\n6 8 22 22\n2 3\n",
"5\n93 83 42 56\n2 5\n",
"9\n1 2 2 2 2 3 3 5\n3 7\n",
"96\n51 32 95 75 23 54 70 89 67 3 1 51 4 100 97 30 9 35 56 38 54 77 56 98 43 17 60 43 72 46 87 61 100 65 81 22 74 38 16 96 5 10 54 22 23 22 10 91 9 54 49 82 29 73 33 98 75 8 4 26 24 90 71 42 90 24 94 74 94 10 41 98 56 63 18 43 56 21 26 64 74 33 22 38 67 66 38 60 64 76 53 10 4 65 76\n21 26\n",
"97\n18 90 84 7 33 24 75 55 86 10 96 72 16 64 37 9 19 71 62 97 5 34 85 15 46 72 82 51 52 16 55 68 27 97 42 72 76 97 32 73 14 56 11 86 2 81 59 95 60 93 1 22 71 37 77 100 6 16 78 47 78 62 94 86 16 91 56 46 47 35 93 44 7 86 70 10 29 45 67 62 71 61 74 39 36 92 24 26 65 14 93 92 15 28 79 59\n6 68\n",
"50\n28 8 16 29 19 82 70 51 96 84 74 72 17 69 12 21 37 21 39 3 18 66 19 49 86 96 94 93 2 90 96 84 59 88 58 15 61 33 55 22 35 54 51 29 64 68 29 38 40\n23 28\n",
"90\n1 1 3 5 8 9 10 11 11 11 11 12 13 14 15 15 15 16 16 19 19 20 22 23 24 25 25 28 29 29 30 31 33 34 35 37 37 38 41 43 43 44 45 47 51 54 55 56 58 58 59 59 60 62 66 67 67 67 68 68 69 70 71 72 73 73 76 77 77 78 78 78 79 79 79 82 83 84 85 85 87 87 89 93 93 93 95 99 99\n28 48\n",
"15\n89 55 94 4 15 69 19 60 91 77 3 94 91 62\n3 14\n",
"45\n83 74 73 95 10 31 100 26 29 15 80 100 22 70 31 88 9 56 19 70 2 62 48 30 27 47 52 50 94 44 21 94 23 85 15 3 95 72 43 62 94 89 68 88\n17 40\n",
"98\n32 47 26 86 43 42 79 72 6 68 40 46 29 80 24 89 29 7 21 56 8 92 13 33 50 79 5 7 84 85 24 23 1 80 51 21 26 55 96 51 24 2 68 98 81 88 57 100 64 84 54 10 14 2 74 1 89 71 1 20 84 85 17 31 42 58 69 67 48 60 97 90 58 10 21 29 2 21 60 61 68 89 77 39 57 18 61 44 67 100 33 74 27 40 83 29 6\n8 77\n",
"10\n1 1 1 1 1 1 1 1 1\n6 8\n",
"80\n65 15 43 6 43 98 100 16 69 98 4 54 25 40 2 35 12 23 38 29 10 89 30 6 4 8 7 96 64 43 11 49 89 38 20 59 54 85 46 16 16 89 60 54 28 37 32 34 67 9 78 30 50 87 58 53 99 48 77 3 5 6 19 99 16 20 31 10 80 76 82 56 56 83 72 81 84 60 39\n18 24\n",
"51\n85 38 22 38 42 36 55 24 36 80 51 15 66 91 88 61 46 82 1 61 89 92 6 56 28 8 46 80 56 90 91 38 38 17 69 64 57 68 13 44 45 38 8 72 61 39 87 2 73 88\n15 27\n",
"30\n35 69 50 44 19 56 86 56 98 24 21 2 61 24 85 30 1 22 57 35 59 84 12 77 92 53 50 92 9\n1 16\n",
"96\n1 1 2 3 3 5 8 9 9 10 10 10 11 11 11 11 11 12 13 13 13 14 5 15 16 16 17 17 17 17 18 18 20 20 20 21 21 21 23 24 24 25 25 26 27 27 27 27 29 29 29 30 30 30 32 32 32 32 32 32 33 33 34 34 34 35 35 35 36 36 37 37 37 38 39 40 41 41 41 41 42 42 43 43 45 45 45 46 46 47 47 49 50 52 52\n76 96\n",
"100\n1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 3 3 3 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 4 6 7 7 7 7 7 7 8 8 8 8 9 9 9 9 10 10 10 10 11 11 11 11 12 12 12 13 13 13 13 13 13 13 13 13 13 14 14 14 14 14 14 15 15 15 15 15 15 16 16 16 17 17\n39 52\n",
"70\n1 2 3 3 4 5 5 7 7 7 8 8 8 8 9 9 10 12 12 12 12 13 16 16 16 16 16 16 17 17 18 18 20 20 21 23 24 25 25 26 29 29 29 29 31 32 32 34 35 36 36 37 37 38 39 39 40 40 40 40 41 41 42 43 44 44 44 45 45\n38 65\n",
"90\n61 35 100 99 67 87 42 90 43 4 81 65 29 63 66 56 53 22 55 87 39 30 34 42 27 80 29 97 85 28 81 22 50 22 24 75 67 86 78 79 94 35 13 97 48 76 68 66 94 13 82 1 22 85 5 36 86 73 65 97 43 56 35 26 87 25 74 47 81 67 73 75 99 75 53 38 70 21 66 78 38 17 57 40 93 57 68 55 1\n12 44\n",
"60\n24 28 25 21 43 71 64 73 71 90 51 83 69 43 75 43 78 72 56 61 99 7 23 86 9 16 16 94 14 74 18 56 20 72 13 31 75 34 35 86 61 49 4 72 84 7 65 70 66 52 21 38 6 43 69 40 73 46 5\n28 60\n",
"35\n2 34 47 15 27 61 6 88 67 20 53 65 29 68 77 10 78 86 44 98 32 81 91 79 54 84 95 23 65 97 22 33 42 87\n8 35\n",
"98\n2 3 4 4 5 7 8 10 10 10 11 11 12 12 12 12 13 14 15 15 16 16 18 19 19 20 21 21 21 21 22 23 24 25 26 26 27 27 27 27 29 29 30 30 31 31 37 40 40 40 41 41 41 42 43 44 44 44 46 46 47 49 34 50 50 50 51 53 55 55 56 56 56 56 56 57 57 58 59 60 60 60 62 62 63 64 64 64 65 66 66 67 68 70 70 71 71\n8 90\n",
"20\n1 1 1 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 1\n5 17\n",
"60\n1 2 4 4 4 6 6 8 9 10 10 13 14 18 20 20 21 22 23 23 26 29 30 32 33 34 35 38 40 42 44 44 46 48 52 54 56 56 60 60 66 67 68 16 69 73 73 74 80 80 81 81 82 84 86 86 87 89 89\n56 58\n",
"10\n95 81 32 59 71 30 19 61 100\n1 6\n",
"80\n1 1 2 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 4 4 4 4 5 5 5 5 5 5 5 6 7 7 7 7 7 7 8 8 8 8 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12\n17 65\n",
"99\n46 5 19 66 53 12 84 89 26 27 35 68 41 44 63 17 88 43 80 15 59 1 42 50 53 34 75 16 16 55 92 30 28 11 12 71 27 65 11 28 86 47 24 10 60 47 7 53 16 75 6 49 56 66 70 3 20 78 75 41 38 57 89 23 16 74 30 39 1 32 49 84 9 33 25 95 75 45 54 59 17 17 29 40 79 96 47 11 69 86 73 56 91 4 87 47 31 24\n23 36\n",
"100\n63 65 21 41 95 23 3 4 12 23 95 50 75 63 58 34 71 27 75 31 23 94 96 74 69 34 43 25 25 55 44 19 43 86 68 17 52 65 36 29 72 96 84 25 84 23 71 54 6 7 71 7 21 100 99 58 93 35 62 47 36 70 68 9 75 13 35 70 76 36 62 22 52 51 2 87 66 41 54 35 78 62 30 56 65 44 74 93 78 37 96 70 26 32 71 27 85 85 63\n43 92\n",
"95\n2 2 3 3 4 6 6 7 7 7 9 10 12 12 12 12 13 14 15 16 17 33 20 20 20 20 21 21 21 21 22 22 22 22 22 23 23 23 25 26 26 27 27 27 28 29 29 30 30 31 32 33 34 36 37 37 38 39 39 39 42 43 43 43 45 47 48 50 50 51 52 53 54 54 54 55 55 55 58 59 60 61 61 61 61 62 62 63 64 65 66 67 67 67\n64 93\n",
"6\n22 9 87 89 3\n1 6\n",
"50\n1 8 8 13 14 15 15 16 19 21 22 24 26 31 32 37 45 47 47 47 50 50 51 54 55 56 58 61 61 61 63 63 64 66 66 67 67 70 71 21 83 84 85 92 92 94 95 95 100\n4 17\n",
"20\n70 1 41 51 95 67 92 35 23 70 44 91 57 50 21 8 9 71 40\n8 17\n",
"6\n3 12 27 18 28\n3 4\n",
"9\n12 65 69 39 59 21 59 5\n4 6\n",
"2\n4\n1 2\n",
"51\n5 7 9 16 19 34 26 29 29 30 31 32 32 41 43 44 47 49 50 50 51 52 54 55 56 63 64 66 67 70 74 74 77 78 79 80 80 85 86 87 89 89 90 92 93 94 94 95 95 97\n3 44\n",
"25\n70 95 21 84 97 39 12 98 53 24 78 29 84 65 70 22 100 17 69 43 62 48 35 80\n8 23\n",
"35\n1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n30 31\n",
"9\n1 2 2 2 2 3 2 5\n3 7\n",
"96\n51 32 95 75 23 54 70 89 67 3 1 51 4 100 97 30 9 35 56 38 54 77 56 98 43 17 60 43 72 46 87 61 100 65 81 22 74 38 16 96 5 10 54 22 23 22 10 91 9 54 49 82 29 73 33 98 75 4 4 26 24 90 71 42 90 24 94 74 94 10 41 98 56 63 18 43 56 21 26 64 74 33 22 38 67 66 38 60 64 76 53 10 4 65 76\n21 26\n",
"97\n18 90 84 7 33 24 75 55 86 10 96 72 16 64 37 9 19 71 62 97 5 34 85 15 46 72 82 51 52 16 55 68 27 97 42 72 76 97 32 73 14 56 11 86 2 81 59 95 60 93 1 43 71 37 77 100 6 16 78 47 78 62 94 86 16 91 56 46 47 35 93 44 7 86 70 10 29 45 67 62 71 61 74 39 36 92 24 26 65 14 93 92 15 28 79 59\n6 68\n",
"50\n28 8 16 29 19 82 70 51 96 84 73 72 17 69 12 21 37 21 39 3 18 66 19 49 86 96 94 93 2 90 96 84 59 88 58 15 61 33 55 22 35 54 51 29 64 68 29 38 40\n23 28\n",
"90\n1 1 3 5 8 9 10 11 11 11 11 12 13 14 15 15 15 16 16 19 19 20 22 23 24 25 25 28 29 29 30 31 33 34 35 37 37 38 41 43 43 44 45 47 51 54 55 56 58 58 59 46 60 62 66 67 67 67 68 68 69 70 71 72 73 73 76 77 77 78 78 78 79 79 79 82 83 84 85 85 87 87 89 93 93 93 95 99 99\n28 48\n",
"45\n83 74 73 95 10 31 100 26 29 15 80 100 22 70 31 88 9 56 19 70 1 62 48 30 27 47 52 50 94 44 21 94 23 85 15 3 95 72 43 62 94 89 68 88\n17 40\n",
"3\n9 6\n1 3\n",
"30\n35 69 50 19 19 56 86 56 98 24 21 2 61 24 85 30 1 22 57 35 59 84 12 77 92 53 50 92 9\n1 16\n",
"96\n1 1 2 3 3 5 8 9 9 10 10 10 11 11 11 11 11 12 13 13 13 14 5 15 16 16 17 17 17 17 18 18 20 20 20 21 21 21 23 24 24 25 25 26 27 27 27 27 29 29 29 30 30 30 32 32 32 32 32 32 33 33 34 34 34 35 35 35 36 36 37 37 37 38 39 40 41 41 41 41 42 42 43 43 45 45 45 46 46 47 8 49 50 52 52\n76 96\n",
"100\n1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 3 3 3 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 4 2 7 7 7 7 7 7 8 8 8 8 9 9 9 9 10 10 10 10 11 11 11 11 12 12 12 13 13 13 13 13 13 13 13 13 13 14 14 14 14 14 14 15 15 15 15 15 15 16 16 16 17 17\n39 52\n",
"90\n61 35 100 99 67 87 42 90 43 4 81 65 29 63 66 56 53 22 55 87 39 30 34 42 27 80 29 97 85 28 81 22 50 22 24 75 39 86 78 79 94 35 13 97 48 76 68 66 94 13 82 1 22 85 5 36 86 73 65 97 43 56 35 26 87 25 74 47 81 67 73 75 99 75 53 38 70 21 66 78 38 17 57 40 93 57 68 55 1\n12 44\n",
"35\n2 34 47 15 27 61 6 88 67 20 53 65 29 68 77 10 78 86 44 98 32 81 30 79 54 84 95 23 65 97 22 33 42 87\n8 35\n",
"98\n2 3 4 4 5 7 8 10 10 10 11 11 12 12 12 12 13 14 15 15 16 16 18 19 19 20 21 21 21 21 22 23 24 25 26 35 27 27 27 27 29 29 30 30 31 31 37 40 40 40 41 41 41 42 43 44 44 44 46 46 47 49 34 50 50 50 51 53 55 55 56 56 56 56 56 57 57 58 59 60 60 60 62 62 63 64 64 64 65 66 66 67 68 70 70 71 71\n8 90\n",
"20\n1 1 1 1 1 1 1 1 4 2 2 2 2 3 3 3 3 3 1\n5 17\n",
"80\n1 1 2 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 4 4 4 4 5 5 5 5 1 5 5 6 7 7 7 7 7 7 8 8 8 8 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12\n17 65\n",
"99\n46 5 19 66 53 12 84 89 26 27 35 68 41 44 63 17 88 43 80 15 59 1 42 50 53 52 75 16 16 55 92 30 28 11 12 71 27 65 11 28 86 47 24 10 60 47 7 53 16 75 6 49 56 66 70 3 20 78 75 41 38 57 89 23 16 74 30 39 1 32 49 84 9 33 25 95 75 45 54 59 17 17 29 40 79 96 47 11 69 86 73 56 91 4 87 47 31 24\n23 36\n",
"6\n7 9 87 89 3\n1 6\n",
"20\n70 1 41 51 95 67 92 35 23 70 44 91 57 50 21 8 9 71 40\n8 16\n",
"2\n8\n1 2\n",
"51\n5 7 9 16 19 34 26 29 5 30 31 32 32 41 43 44 47 49 50 50 51 52 54 55 56 63 64 66 67 70 74 74 77 78 79 80 80 85 86 87 89 89 90 92 93 94 94 95 95 97\n3 44\n",
"60\n24 28 25 21 43 71 64 73 71 90 51 83 69 43 75 43 78 72 56 61 99 7 23 22 9 16 16 94 14 74 18 56 20 72 13 31 75 34 35 86 61 49 4 72 84 7 65 70 66 52 21 38 6 43 1 40 73 46 5\n28 60\n",
"35\n2 34 47 15 27 61 6 88 67 20 53 65 29 68 77 10 78 86 44 98 32 81 30 79 54 84 95 23 65 97 22 49 42 87\n8 35\n",
"98\n2 3 4 4 5 7 8 10 10 10 11 11 12 12 12 12 13 14 15 15 16 16 18 19 19 20 21 21 21 21 22 23 24 25 26 35 27 27 27 27 29 29 30 30 31 31 37 40 40 40 41 41 41 42 43 44 44 44 46 49 47 49 34 50 50 50 51 53 55 55 56 56 56 56 56 57 57 58 59 60 60 60 62 62 63 64 64 64 65 66 66 67 68 70 70 71 71\n8 90\n",
"20\n1 1 1 1 2 1 1 1 4 2 2 2 2 3 3 3 3 3 1\n5 17\n",
"80\n1 1 2 1 1 1 1 1 2 2 2 2 2 2 3 3 3 4 3 3 3 3 3 3 4 4 4 4 5 5 5 5 1 5 5 6 7 7 7 7 7 7 8 8 8 8 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12\n17 65\n",
"6\n7 9 87 76 3\n1 6\n",
"9\n12 65 97 39 59 21 59 5\n2 6\n",
"2\n1\n1 2\n",
"97\n18 90 84 2 33 24 75 55 86 10 96 72 16 64 37 9 19 71 62 97 5 34 85 15 46 72 82 51 52 9 55 68 27 97 42 72 76 97 32 73 14 56 11 86 2 81 59 95 60 93 1 43 71 37 77 100 6 16 78 47 78 62 94 86 16 91 56 46 47 35 93 44 7 86 70 10 29 45 67 62 71 61 74 39 36 92 24 26 65 14 93 92 15 28 79 59\n6 68\n",
"45\n83 74 73 95 10 31 100 12 29 15 80 100 22 70 31 88 9 56 19 70 1 62 48 30 27 47 52 50 94 44 21 94 23 85 12 3 95 72 43 62 94 89 68 88\n17 40\n",
"51\n85 17 22 38 42 36 55 24 36 80 51 15 66 91 88 61 30 82 1 61 89 92 6 56 28 8 46 80 56 90 91 38 38 17 69 38 57 68 13 44 45 38 8 72 61 39 87 2 73 88\n15 27\n",
"30\n35 69 50 19 3 56 86 56 98 24 21 2 61 24 85 30 1 22 57 35 59 84 12 77 92 53 50 92 11\n1 16\n",
"70\n1 2 3 3 4 5 5 7 7 7 8 8 8 8 9 9 10 12 12 7 12 13 16 16 16 16 16 16 17 17 18 18 20 20 18 23 24 25 25 26 29 29 29 29 31 11 32 34 35 36 36 37 37 38 39 39 40 40 40 40 41 41 42 43 44 44 44 45 45\n38 65\n",
"98\n2 3 4 4 5 7 8 10 10 2 11 11 12 12 12 12 13 14 15 15 16 16 18 19 19 20 21 21 21 21 22 23 24 25 26 35 27 27 27 27 29 29 30 30 31 31 37 40 40 40 41 41 41 42 43 44 44 44 46 49 47 49 34 50 50 50 51 53 55 55 56 56 56 56 56 57 57 58 59 60 60 60 62 62 63 64 64 64 65 66 66 67 68 70 70 71 71\n8 90\n",
"25\n1 1 1 4 5 6 8 11 3 11 11 12 13 14 14 14 15 16 16 17 17 17 19 19\n4 8\n",
"45\n1 1 1 1 2 2 2 2 2 2 2 3 3 3 3 3 3 4 5 5 5 5 6 6 6 6 6 6 6 7 7 7 7 8 8 8 9 9 9 9 9 10 10 3\n42 45\n",
"80\n65 15 43 6 43 98 100 16 69 98 4 54 25 40 2 35 12 23 38 29 10 89 30 6 4 8 7 96 64 43 11 49 89 38 20 59 54 85 46 16 16 89 60 54 28 37 32 34 67 9 78 30 50 87 58 53 99 48 77 3 5 6 19 99 16 20 8 10 80 76 82 56 56 83 72 81 84 60 39\n18 24\n",
"51\n85 17 22 38 42 36 55 24 36 80 51 15 66 91 88 61 46 82 1 61 89 92 6 56 28 8 46 80 56 90 91 38 38 17 69 64 57 68 13 44 45 38 8 72 61 39 87 2 73 88\n15 27\n",
"70\n1 2 3 3 4 5 5 7 7 7 8 8 8 8 9 9 10 12 12 7 12 13 16 16 16 16 16 16 17 17 18 18 20 20 21 23 24 25 25 26 29 29 29 29 31 32 32 34 35 36 36 37 37 38 39 39 40 40 40 40 41 41 42 43 44 44 44 45 45\n38 65\n",
"60\n24 28 25 21 43 71 64 73 71 90 51 83 69 43 75 43 78 72 56 61 99 7 23 22 9 16 16 94 14 74 18 56 20 72 13 31 75 34 35 86 61 49 4 72 84 7 65 70 66 52 21 38 6 43 69 40 73 46 5\n28 60\n",
"60\n1 2 4 4 4 6 6 8 9 10 10 13 14 18 20 20 21 22 23 23 26 29 30 32 33 34 35 38 40 42 44 7 46 48 52 54 56 56 60 60 66 67 68 16 69 73 73 74 80 80 81 81 82 84 86 86 87 89 89\n56 58\n",
"95\n2 2 3 3 4 6 6 7 7 7 9 10 12 12 12 12 13 14 15 16 17 33 20 20 20 20 21 21 21 21 22 22 22 22 22 23 23 23 25 26 26 27 27 27 28 29 29 30 30 31 32 33 34 36 37 37 63 39 39 39 42 43 43 43 45 47 48 50 50 51 52 53 54 54 54 55 55 55 58 59 60 61 61 61 61 62 62 63 64 65 66 67 67 67\n64 93\n",
"50\n1 8 8 13 14 15 15 16 19 21 22 24 26 31 32 37 45 47 47 47 50 50 51 54 55 56 58 61 61 61 63 63 64 66 66 67 67 70 71 21 83 84 85 92 97 94 95 95 100\n4 17\n",
"6\n3 12 27 27 28\n3 4\n",
"25\n1 1 1 4 5 6 8 11 3 11 11 12 13 14 14 14 15 16 16 17 17 1 19 19\n4 8\n",
"9\n12 65 97 39 59 21 59 5\n4 6\n",
"25\n70 95 21 84 97 39 12 98 53 24 78 29 84 65 70 22 100 17 69 43 62 48 35 68\n8 23\n",
"35\n1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 4\n30 31\n",
"45\n1 1 1 1 2 2 2 2 2 2 2 3 3 3 3 3 3 4 5 5 5 5 6 6 6 6 1 6 6 7 7 7 7 8 8 8 9 9 9 9 9 10 10 3\n42 45\n",
"9\n1 2 2 2 2 3 4 5\n3 7\n",
"96\n51 32 95 75 32 54 70 89 67 3 1 51 4 100 97 30 9 35 56 38 54 77 56 98 43 17 60 43 72 46 87 61 100 65 81 22 74 38 16 96 5 10 54 22 23 22 10 91 9 54 49 82 29 73 33 98 75 4 4 26 24 90 71 42 90 24 94 74 94 10 41 98 56 63 18 43 56 21 26 64 74 33 22 38 67 66 38 60 64 76 53 10 4 65 76\n21 26\n",
"97\n18 90 84 2 33 24 75 55 86 10 96 72 16 64 37 9 19 71 62 97 5 34 85 15 46 72 82 51 52 16 55 68 27 97 42 72 76 97 32 73 14 56 11 86 2 81 59 95 60 93 1 43 71 37 77 100 6 16 78 47 78 62 94 86 16 91 56 46 47 35 93 44 7 86 70 10 29 45 67 62 71 61 74 39 36 92 24 26 65 14 93 92 15 28 79 59\n6 68\n",
"50\n28 8 16 29 19 82 70 51 96 84 73 72 17 69 12 21 37 21 39 3 18 66 19 49 86 96 94 93 2 90 96 84 59 88 58 15 61 33 55 22 35 54 5 29 64 68 29 38 40\n23 28\n",
"45\n83 74 73 95 10 31 100 12 29 15 80 100 22 70 31 88 9 56 19 70 1 62 48 30 27 47 52 50 94 44 21 94 23 85 15 3 95 72 43 62 94 89 68 88\n17 40\n",
"51\n85 17 22 38 42 36 55 24 36 80 51 15 66 91 88 61 46 82 1 61 89 92 6 56 28 8 46 80 56 90 91 38 38 17 69 38 57 68 13 44 45 38 8 72 61 39 87 2 73 88\n15 27\n",
"30\n35 69 50 19 19 56 86 56 98 24 21 2 61 24 85 30 1 22 57 35 59 84 12 77 92 53 50 92 11\n1 16\n",
"96\n1 1 2 3 3 5 8 9 9 10 10 10 11 11 11 11 11 12 13 13 13 14 5 15 16 16 17 17 17 17 18 18 20 20 20 21 21 21 23 24 24 25 25 26 27 27 27 27 29 29 29 30 30 30 32 32 32 32 32 32 33 33 34 34 34 67 35 35 36 36 37 37 37 38 39 40 41 41 41 41 42 42 43 43 45 45 45 46 46 47 8 49 50 52 52\n76 96\n",
"100\n1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 3 3 3 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 4 2 7 7 7 7 7 7 8 8 8 8 9 9 9 9 10 10 10 10 11 11 11 11 12 12 12 13 13 13 13 13 13 13 13 13 13 14 14 14 14 14 14 15 15 15 15 15 30 16 16 16 17 17\n39 52\n",
"70\n1 2 3 3 4 5 5 7 7 7 8 8 8 8 9 9 10 12 12 7 12 13 16 16 16 16 16 16 17 17 18 18 20 20 18 23 24 25 25 26 29 29 29 29 31 32 32 34 35 36 36 37 37 38 39 39 40 40 40 40 41 41 42 43 44 44 44 45 45\n38 65\n",
"90\n61 35 100 99 67 87 42 90 43 4 81 65 29 63 66 56 53 22 55 87 39 30 34 42 27 80 29 97 85 28 81 22 50 22 24 75 39 86 78 79 94 35 13 97 48 76 68 66 94 13 82 1 22 85 5 36 86 73 65 97 43 56 35 26 87 25 74 47 81 67 73 75 99 75 53 38 70 21 66 54 38 17 57 40 93 57 68 55 1\n12 44\n",
"60\n1 2 4 4 4 6 6 8 9 10 10 13 14 18 20 20 21 22 23 23 26 29 30 32 33 34 35 38 40 42 44 7 46 48 52 54 56 56 20 60 66 67 68 16 69 73 73 74 80 80 81 81 82 84 86 86 87 89 89\n56 58\n",
"99\n46 5 19 66 53 12 84 89 26 27 35 68 41 44 63 17 88 43 80 15 59 1 42 50 53 52 75 16 16 55 92 30 28 11 12 71 27 65 11 28 86 47 24 10 60 47 7 53 16 75 6 49 56 66 70 3 20 78 75 70 38 57 89 23 16 74 30 39 1 32 49 84 9 33 25 95 75 45 54 59 17 17 29 40 79 96 47 11 69 86 73 56 91 4 87 47 31 24\n23 36\n",
"95\n2 2 3 3 4 6 6 7 7 7 9 10 12 12 12 12 13 14 15 16 17 33 20 20 20 20 21 21 21 21 22 22 22 22 22 23 23 25 25 26 26 27 27 27 28 29 29 30 30 31 32 33 34 36 37 37 63 39 39 39 42 43 43 43 45 47 48 50 50 51 52 53 54 54 54 55 55 55 58 59 60 61 61 61 61 62 62 63 64 65 66 67 67 67\n64 93\n",
"50\n1 8 8 13 14 15 15 16 19 21 22 24 26 31 32 37 45 47 47 47 50 50 51 54 55 56 58 61 61 61 63 63 64 66 96 67 67 70 71 21 83 84 85 92 97 94 95 95 100\n4 17\n",
"20\n70 1 41 51 95 67 78 35 23 70 44 91 57 50 21 8 9 71 40\n8 16\n",
"6\n3 12 2 27 28\n3 4\n",
"25\n70 7 21 84 97 39 12 98 53 24 78 29 84 65 70 22 100 17 69 43 62 48 35 68\n8 23\n",
"45\n1 1 1 1 2 2 2 2 1 2 2 3 3 3 3 3 3 4 5 5 5 5 6 6 6 6 1 6 6 7 7 7 7 8 8 8 9 9 9 9 9 10 10 3\n42 45\n",
"96\n51 32 95 75 32 54 70 89 67 3 1 51 4 100 97 30 9 35 56 38 54 77 56 98 43 17 60 43 72 46 87 61 100 65 81 22 74 38 16 96 5 10 54 22 23 22 10 91 9 54 49 82 29 73 33 98 75 4 4 26 24 90 71 42 90 24 94 74 94 10 41 98 56 63 18 43 56 21 30 64 74 33 22 38 67 66 38 60 64 76 53 10 4 65 76\n21 26\n",
"96\n1 1 2 3 3 5 8 9 9 10 10 10 11 11 11 11 11 14 13 13 13 14 5 15 16 16 17 17 17 17 18 18 20 20 20 21 21 21 23 24 24 25 25 26 27 27 27 27 29 29 29 30 30 30 32 32 32 32 32 32 33 33 34 34 34 67 35 35 36 36 37 37 37 38 39 40 41 41 41 41 42 42 43 43 45 45 45 46 46 47 8 49 50 52 52\n76 96\n",
"100\n1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 3 3 3 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 4 2 7 7 7 7 7 7 8 8 8 8 9 9 4 9 10 10 10 10 11 11 11 11 12 12 12 13 13 13 13 13 13 13 13 13 13 14 14 14 14 14 14 15 15 15 15 15 30 16 16 16 17 17\n39 52\n",
"90\n91 35 100 99 67 87 42 90 43 4 81 65 29 63 66 56 53 22 55 87 39 30 34 42 27 80 29 97 85 28 81 22 50 22 24 75 39 86 78 79 94 35 13 97 48 76 68 66 94 13 82 1 22 85 5 36 86 73 65 97 43 56 35 26 87 25 74 47 81 67 73 75 99 75 53 38 70 21 66 54 38 17 57 40 93 57 68 55 1\n12 44\n",
"60\n24 28 25 21 43 71 64 73 71 90 51 83 69 43 75 43 78 72 56 61 99 10 23 22 9 16 16 94 14 74 18 56 20 72 13 31 75 34 35 86 61 49 4 72 84 7 65 70 66 52 21 38 6 43 1 40 73 46 5\n28 60\n",
"60\n1 2 4 4 4 6 6 8 9 10 10 13 14 18 20 20 21 37 23 23 26 29 30 32 33 34 35 38 40 42 44 7 46 48 52 54 56 56 20 60 66 67 68 16 69 73 73 74 80 80 81 81 82 84 86 86 87 89 89\n56 58\n"
],
"output": [
"5\n",
"11\n",
"219\n",
"618\n",
"163\n",
"730\n",
"898\n",
"82\n",
"126\n",
"1713\n",
"1502\n",
"55\n",
"1663\n",
"263\n",
"3016\n",
"570\n",
"23\n",
"4\n",
"173\n",
"338\n",
"326\n",
"514\n",
"2599\n",
"1636\n",
"264\n",
"285\n",
"399\n",
"862\n",
"27\n",
"23\n",
"98\n",
"3\n",
"2268\n",
"846\n",
"1767\n",
"2\n",
"242\n",
"29\n",
"30\n",
"8\n",
"181\n",
"9\n",
"328\n",
"3385\n",
"344\n",
"784\n",
"617\n",
"1061\n",
"3319\n",
"2\n",
"219\n",
"618\n",
"730\n",
"898\n",
"80\n",
"945\n",
"1713\n",
"1493\n",
"1668\n",
"3001\n",
"23\n",
"173\n",
"338\n",
"326\n",
"514\n",
"2620\n",
"1636\n",
"210\n",
"285\n",
"399\n",
"27\n",
"98\n",
"4\n",
"2277\n",
"862\n",
"2\n",
"9\n",
"328\n",
"3406\n",
"344\n",
"784\n",
"1060\n",
"15\n",
"705\n",
"859\n",
"76\n",
"1685\n",
"1607\n",
"3010\n",
"25\n",
"322\n",
"532\n",
"195\n",
"391\n",
"8\n",
"2253\n",
"1425\n",
"1623\n",
"3013\n",
"26\n",
"323\n",
"182\n",
"260\n",
"1\n",
"3399\n",
"1057\n",
"602\n",
"689\n",
"924\n",
"3005\n",
"23\n",
"23\n",
"219\n",
"618\n",
"945\n",
"1493\n",
"173\n",
"1636\n",
"285\n",
"27\n",
"23\n",
"98\n",
"862\n",
"2\n",
"23\n",
"9\n",
"328\n",
"3406\n",
"344\n",
"1060\n",
"618\n",
"705\n",
"859\n",
"76\n",
"945\n",
"1685\n",
"173\n",
"532\n",
"1636\n",
"285\n",
"391\n",
"2\n",
"862\n",
"23\n",
"328\n",
"859\n",
"76\n",
"1685\n",
"1425\n",
"173\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
The Berland Armed Forces System consists of n ranks that are numbered using natural numbers from 1 to n, where 1 is the lowest rank and n is the highest rank.
One needs exactly di years to rise from rank i to rank i + 1. Reaching a certain rank i having not reached all the previous i - 1 ranks is impossible.
Vasya has just reached a new rank of a, but he dreams of holding the rank of b. Find for how many more years Vasya should serve in the army until he can finally realize his dream.
Input
The first input line contains an integer n (2 ≤ n ≤ 100). The second line contains n - 1 integers di (1 ≤ di ≤ 100). The third input line contains two integers a and b (1 ≤ a < b ≤ n). The numbers on the lines are space-separated.
Output
Print the single number which is the number of years that Vasya needs to rise from rank a to rank b.
Examples
Input
3
5 6
1 2
Output
5
Input
3
5 6
1 3
Output
11
### Input:
3
5 6
1 2
### Output:
5
### Input:
3
5 6
1 3
### Output:
11
### Code:
#!/usr/bin/python3
def readln(): return tuple(map(int, input().split()))
n, = readln()
d = readln()
a, b = readln()
print(sum(d[a - 1:b - 1]))
|
409_I. Feed the Golorp_10582
|
Golorps are mysterious creatures who feed on variables. Golorp's name is a program in some programming language. Some scientists believe that this language is Befunge; golorps are tantalizingly silent.
Variables consumed by golorps can take values from 0 to 9, inclusive. For each golorp its daily diet is defined by its name. Some golorps are so picky that they can't be fed at all. Besides, all golorps are very health-conscious and try to eat as little as possible. Given a choice of several valid sequences of variable values, each golorp will choose lexicographically smallest one.
For the purposes of this problem you can assume that a golorp consists of jaws and a stomach. The number of variables necessary to feed a golorp is defined by the shape of its jaws. Variables can get to the stomach only via the jaws.
A hungry golorp is visiting you. You know its name; feed it or figure out that it's impossible.
Input
The input is a single string (between 13 and 1024 characters long) — the name of the visiting golorp. All names are similar and will resemble the ones given in the samples. The name is guaranteed to be valid.
Output
Output lexicographically smallest sequence of variable values fit for feeding this golorp. Values should be listed in the order in which they get into the jaws. If the golorp is impossible to feed, output "false".
Examples
Input
?(_-_/___*__):-___>__.
Output
0010
Input
?(__-_+_/_____):-__>__,_____<__.
Output
false
Input
?(______________________/____+_______*__-_____*______-___):-__<___,___<____,____<_____,_____<______,______<_______.
Output
0250341
Input
?(__+___+__-___):-___>__.
Output
0101
|
"""
Codeforces April Fools Contest 2014 Problem I
Author : chaotic_iak
Language: Python 3.3.4
"""
class InputHandlerObject(object):
inputs = []
def getInput(self, n = 0):
res = ""
inputs = self.inputs
if not inputs: inputs.extend(input().split(" "))
if n == 0:
res = inputs[:]
inputs[:] = []
while n > len(inputs):
inputs.extend(input().split(" "))
if n > 0:
res = inputs[:n]
inputs[:n] = []
return res
InputHandler = InputHandlerObject()
g = InputHandler.getInput
############################## SOLUTION ##############################
# ?(_/____+_______*__-_____*______-___):-__<___,___<____,____<_____,_____<______,______<_______.
golorp = input().split(":-")
golorp[0] = golorp[0][2:]
ct = 0
jaws = []
for x in range(len(golorp[0])):
if golorp[0][x] == "_":
ct += 1
else:
jaws.append(ct)
ct = 0
ct = 0
conditionsraw = []
for x in range(len(golorp[1])):
if golorp[1][x] == "_":
ct += 1
else:
conditionsraw.append(ct)
conditionsraw.append(golorp[1][x])
ct = 0
conditions = []
for x in range(0, len(conditionsraw)//4):
if conditionsraw[4*x+1] == ">":
conditions.append((conditionsraw[4*x+2], conditionsraw[4*x]))
else:
conditions.append((conditionsraw[4*x], conditionsraw[4*x+2]))
inedges = [[-1]] * (max(jaws) + 1)
outedges = [[-1]] * (max(jaws) + 1)
val = [-1] * (max(jaws) + 1)
processed = [False] * (max(jaws) + 1)
for x in jaws:
inedges[x] = []
outedges[x] = []
for x, y in conditions:
inedges[y].append(x)
outedges[x].append(y)
for i in range(10):
for x in jaws:
if not inedges[x] and not processed[x]:
val[x] += 1
processed[x] = True
for y in outedges[x]:
val[y] = max(val[y], val[x])
inedges[y].remove(x)
failure = False
for x in jaws:
if not processed[x] or val[x] > 9:
failure = True
break
if failure:
print("false")
else:
s = ""
for x in jaws:
s += str(val[x])
print(s)
|
{
"input": [
"?(__-_+_/_____):-__>__,_____<__.\n",
"?(______________________/____+_______*__-_____*______-___):-__<___,___<____,____<_____,_____<______,______<_______.\n",
"?(__+___+__-___):-___>__.\n",
"?(_-_/___*__):-___>__.\n",
"?(____________*___________*__________*_________*________*_______*______*_____*____*___*__*_):-__<___,___<____,____<_____,_____<______,______<_______,_______<________,________<_________,_________<__________,__________<___________.\n",
"?(__+__+___):-___<__.\n",
"?(__*___+_-____):-___>__,____<__.\n",
"?(_*__*___*____*_____*______*_______*________*_________*__________*___________*____________):-__<___,___<____,____<_____,_____<______,______<_______,_______<________,________<_________,_________<__________,__________<___________,___________<____________.\n",
"?(_-_/___*__):-___>__.\n",
"?(_+__-___-____*_____):-__<___,__<____,___<_____,____<_____.\n",
"?(_*____*_______*__*_____*______*___):-__<___,___<____,____<_____,_____<______,______<_______.\n",
"?(____________*___________*__________*_________*________*_______*______*_____*____*___*__*_):-__________<___________,______<_______,_______<________,________<_________,_________<__________,_____<______,____<_____,___<____,__<___.\n",
"?(______________________/____+_______*__-_____*______-___):-__<___,___<____,____<_____,_____<______,______<_______.\n",
"?(__):-__>__,__<__.\n",
"?(__+___+__-___):-___>__.\n",
"?(_____+___________+________+_________+_+______+___+__+_______+__________+____):-____<__________,________<_______,__________<_______,_____<___________,__<_,______<___________,___________<_________,_<_________,___<_______,_________<_______.\n",
"?(_*__*___*____*_____*______*_______*________*_________*__________*___________*____________):-__<___,___<____,____<_____,_____<______,______<_______,_______<________,________<_________,_________<__________,__________<___________.\n",
"?(__________):-__________>__________.\n",
"?(__-__):-__>__,__<__.\n",
"?(__-_+_/_____):-__>__,_____<__.\n",
"?(__):-__>__.\n",
"?(__________):-__________<__________.\n",
"?(_*__*___*____*_____*______*_______*________*_________*__________*___________):-__<___,___<____,____<_____,_____<______,______<_______,_______<________,________<_________,_________<__________,__________<___________.\n",
"?(_*__*___*____*_____*______*_______):-__<___,___<____,____<_____,_____<______,______<_______.\n",
"?(_^+___+__-___):-___>__.\n",
"?(__-_+_g_____):-__&/t;__,_____<__.\n",
"?(______________________/____+_______*__-_____*______-___):-__<___,___<____,____<_____,_____<______,__^___<_______.\n",
"?(______________________/____+_______*________*______-___):-__<___,___<____,____<__`__,_____<___-__,__^___<_______.\n",
"?(_*__*___*____*_____*______*_______)________*_________*__________*___________*____________):-__<___,___<____,____<_____,_____<______,______<_______,_______<________,________<_________,_________<__________,__________<___________,___________<____________.\n",
"?(_-^/___*__):-___>__.\n",
"?(______________________/____+___^___*__-_____*______-___):-__<___,___<____,____<_____,_____<______,__^___<_______.\n",
"?(_______`________`_____/____________*____-___*______-___)9-__<_^_,____lt;____,____<__`__,&____<___+`_,`_^___<_______.\n",
"?(__+__+___):-__<___.\n",
"?(_____^________________/____+___^___*__-_____*______-___):-__<___,___<____,`___<_____,_____<______,__^_`_<_______.\n",
"?(_____^________^_______/____+___^___*__-_____*______-___):-__<___,___<____,`___<_____,_`___<______,__^_`_<_______.\n",
"?(__-_+_g_`___):-__&/t;__,_____<__.\n",
"?(_______`________`_____/____________*____-___*______-___)9-__<_^_,____lt;____,____<__`__,&____<___+`_,`_^___<____`__.\n",
"?(__-_+_______):-__%/t;&_,__^_g_lt;__.\n",
"?(_____`_`________`_____/____________*____-___*______-___)9-__<_^_,____lt;____,____<__`__,&____<___+`_,`_^___<____`_`.\n",
"?(__-_+_g___;_)_-__&/t;_,___^__<^_.\n",
"?(_____`_`________`_____.____`_______*____-___*______-___)9-__<_^_,____lt;____,____<__`__,&____<___+`_,`_^___<____`_`.\n",
"?(_____`_`________`_____.____`_______*____-___*__^___-___)9-__<_^_,____lt;____,____<`_`__,&____<___+`_,`_^___<____`_`.\n",
"?(________________`_____/____________*____-___*______-___)9-__<_^_,____lt;____,____<__`__,&____<___+`_,`_^___<_______.\n",
"?(_____`_`________`_____.____`_______*____-___*__^___-_+_)9-__<_^_,____lt;____,____<`_`__,&____<____`_,`_^___<____`_`.\n",
"?(________________`_____/____________*____-___*______-___)9-__<^^_,____lt;____,____<__`__,&____<___+`_,`_^___<_______.\n",
"?(______________________/____+_______*__-_____*______-___):-__<___,___<____,____<__`__,_____<______,__^___<_______.\n",
"?(______________________/____-_______*________*______-___):-__<___,___<____,____<__`__,_____<___+__,__^___<_______.\n",
"?(______________________/____-_______*________*______-___):-__<___,____lt;____,____<__`__,&____<___+__,__^___<_______.\n",
"?(______________________/____-_______*________*______-___):-__<_^_,____lt;____,____<__`__,&____<___+__,__^___<_______.\n",
"?(__):-__>__,__<_._\n",
"?(__*___+__-___):-___>__.\n",
"?(`_-__):-__>__,__<__.\n",
"?(__-_,_/_____):-__>__,_____<__.\n",
"?(_^*___+__-___):-___>__.\n",
"?(__-_+_g_____):-__&/t;_^,_____<__.\n",
"?(______________________/____-_______*________*______-___):-__<___,___<____,____'lt;__`__,_____<___+__,__^___<_______.\n",
"?(_______`______________/____-_______*________*______-___):-__<_^_,____lt;____,____<__`__,&____<___+__,__^___<_______.\n",
"?(`_,__):-__>__,__<__.\n",
"?(______________________/____+___^___*__-_____*______-___):-_`<___,___<____,____<_____,_____<______,__^___<_______.\n",
"?(_______`______________/____-_______*________*______-___):-__<_^_,____lt;____,____<__`__,&____<___+__,`_^___<_______.\n",
"?(`_,__):-__=__,__<__.\n",
"?(_______`______________/____________*____-___*______-___):-__<_^_,____lt;____,____<__`__,&____<___+__,`_^___<_______.\n",
"?(_______`________`_____/____________*____-___*______-___):-__<_^_,____lt;____,____<__`__,&____<___+__,`_^___<_______.\n",
"?(_______`________`_____/____________*____-___*______-___):-__<_^_,____lt;____,____<__`__,&____<___+`_,`_^___<_______.\n",
"?(_*__*___*____*_____*______*_______*____^___*_________*__________*___________*____________):-__<___,___<____,____<_____,_____<______,______<_______,_______<________,________<_________,_________<__________,__________<___________,___________<____________.\n",
"?(^_+___+__-___):-___>__.\n",
"?(__-_+_/`____):-__>__,_____<__.\n",
"?(__-_+_/_____):-__>__,^____<__.\n",
"?(_-_/___*__):-___g&t;__.\n",
"?(__-_+_g_____):-__&/t;__,__^__<__.\n",
"?(__*___________________/____+_______*__-____________-___):-__<___,___<____,____<_____,_____<______,__^___<_______.\n",
"?(______________________/____+_______*________*______-___):-__<___,___&l_;____,____<__`__,____t<___-__,__^___<_______.\n",
"?(___________________l__/____-_______*________*______-___):-__<___,____lt;____,____<__`__,&____<___+__,__^___&_t;_______.\n",
"?(______________________/____-_______*________*___^__-___):-__<_^_,____lt;____,____<__`__,&____<___+__,__^___<_______.\n",
"?(_*`_*___*____*_____*______*_______)________*_________*__________*___________*____________):-__<___,___<____,____<_____,_____<______,______<_______,_______<________,________<_________,_________<__________,__________<___________,___________<____________.\n",
"?(_^):-__>__,__<_._\n",
"?(__-_,_/^____):-__>__,_____<__.\n",
"?(______________________/____+___^___*__-_____*______-___):-__<___,___<____,`___<_____,_____<______,__^___<_______.\n",
"?(a_,__):-__>__,__<__.\n",
"?(_____`_`______________/____-_______*________*______-___):-__<_^_,____lt;____,____<__`__,&____<___+__,`_^___<_______.\n",
"?(_*__*___*____*_____*______*_______*__`_^___*_________*__________*___________*____________):-__<___,___<____,____<_____,_____<______,______<_______,_______<________,________<_________,_________<__________,__________<___________,___________<____________.\n",
"?(]_+___+__-___):-___>__.\n",
"?(__-_+_/_____):-`_>__,^____<__.\n",
"?(__-_+_g_____):-__%/t;__,__^__<__.\n",
"?(__*___________________/__^_+_______*__-____________-___):-__<___,___<____,____<_____,_____<______,__^___<_______.\n",
"?(___________________l__/____-_______*________*______-___):-__<___,____lt;____,____<^_`__,&____<___+__,__^___&_t;_______.\n",
"?(__-_,_/^`___):-__>__,_____<__.\n",
"?(______________________/____+___^___*__-_____*______-___):-__<___,___<____,`___<_____,_____<______,__^_`_<_______.\n",
"?(_____`_`______________/____-_______*________*______-___):-__<_^_,____lt;____,____<__`__,&____<_`_+__,`_^___<_______.\n",
"?(___________________l__/____-_______*_^______*______-___):-__<___,____lt;____,____<^_`__,&____<___+__,__^___&_t;_______.\n",
"?(___________________l__/____-_______*_^______*_`____-___):-__<___,____lt;____,____<^_`__,&____<___+__,__^___&_t;_______.\n",
"?(_____^________________/____+___^___*__-_____*______-___):-__<___,___<____,`___<_____,_`___<______,__^_`_<_______.\n",
"?(_____^________^_______0____+___^___*__-_____*______-___):-__<___,___<____,`___<_____,_`___<______,__^_`_<_______.\n",
"?(_____^________^_______0____+___^___*__-_____*______-___):-__<___,___<____,`___<_____,_`___<______,__^_`_&ls;_______.\n",
"?(_____^________^_______0____+___^___+__-_____*______-___):-__<___,___<____,`___<_____,_`___<______,__^_`_&ls;_______.\n",
"?(_*__*___*____*_____*______*_______*________*_________*__________*_______^___*____________):-__<___,___<____,____<_____,_____<______,______<_______,_______<________,________<_________,_________<__________,__________<___________,___________<____________.\n",
"?(__):-__>__,`_<__.\n",
"?(__-_+_/_____):-__>__,_____<__/\n",
"?(______________________/____+_______*__-_____*______-___):-__<___,___<____,____<_____,___`_<______,______<_______.\n",
"?(__+___+__t___):-___&g-;__.\n",
"?(______________________/____-_______*________+______-___):-__<___,____lt;____,____<__`__,&____<___+__,__^___<_______.\n",
"?(______________________/____-__^____*________*______-___):-__<_^_,____lt;____,____<__`__,&____<___+__,__^___<_______.\n",
"?(__):-__>__,_^<_._\n",
"?(`_-__):-__>__,__<__/\n",
"?(__-`,_/_____):-__>__,_____<__.\n",
"?(__-_+_g_____):-^_&/t;_^,_____<__.\n",
"?(______________________/____+___^___*__-_____*______-___):-_`<___,___<____,____<_____,_____<______,^_^___<_______.\n",
"?(___^___`________`_____/____________*____-___*______-___):-__<_^_,____lt;____,____<__`__,&____<___+__,`_^___<_______.\n",
"?(_______`________`_____/____________*____-___*______-___):-__<_^_,____lt;____,____<__`__+&____<___+`_,`_^___<_______.\n",
"?(__-_+_/`____):-__>__,_____<__/\n",
"?(_-_/___*__):-___g&t;`_.\n",
"?(__-_+_g_____):-__&/t;_,___^__<__.\n",
"?(__*___________________/____+_______*__-____________-___):-__<___,___<____,____<_____,_____<__^___,__^___<_______.\n",
"?(________^__________l__/____-_______*________*______-___):-__<___,____lt;____,____<__`__,&____<___+__,__^___&_t;_______.\n",
"?(_*`_*___*____*_____*______*_______)________*_________*__________*___________)____________):-__<___,___<____,____<_____,_____<______,______<_______,_______<________,________<_________,_________<__________,__________<___________,___________<____________.\n",
"?(__-_+_/_____):-`_&ht;__,^____<__.\n",
"?(__-_+_g_____):-__%/t;&_,__^___lt;__.\n",
"?(___________________l__/____-_______*________*______-___):-__<___,____lt;____,____<^_`__,&____<___+__,__^___&_u;_______.\n",
"?(__-_,_/^`___):-__>__,`____<__.\n",
"?(______________________/____+___^___*__-_____*______-___):-__&ls;___,___<____,`___<_____,_____<______,__^_`_<_______.\n",
"?(_____`_`______________/____-_______*_)______*______-____:-__<_^_,____lt;____,____<__`__,&____<_`_+__,`_^___<_______.\n",
"?(_____^________________/____+___^___*__-_____+______-___):-__<___,___<____,`___<_____,_____<______,__^_`_<_______.\n",
"?(_____^________________/____+___^___*__-_____*______-___):-__<___,___<____,`___<_____,_`___<______+__^_`_<_______.\n",
"?(_____^________^_______0____+___^___*__-_____*______-___):-__<___,___<____,`___<_____,_`___<______,__^_`_<__^____.\n"
],
"output": [
"false",
"false",
"0000\n",
"0000\n",
"098765432100\n",
"110\n",
"1200\n",
"false\n",
"0010\n",
"00112\n",
"0250341\n",
"098765432100\n",
"0250341\n",
"false\n",
"0101\n",
"01021000310\n",
"001234567890\n",
"false\n",
"false\n",
"false\n",
"false\n",
"false\n",
"00123456789\n",
"0012345\n",
"0101\n",
"0000\n",
"0000000\n",
"000000\n",
"false\n",
"010\n",
"00000000\n",
"0000000000000000000000\n",
"001\n",
"000000000\n",
"0000000000\n",
"00000\n",
"00000000000000000000000\n",
"000\n",
"000000000000000000000000\n",
"00000000000\n",
"0000000000000000000000000\n",
"00000000000000000000000000\n",
"000000000000000000000\n",
"000000000000000000000000000\n",
"00000000000000000000\n",
"0000000\n",
"000000\n",
"000000\n",
"000000\n",
"false\n",
"0101\n",
"false\n",
"false\n",
"0101\n",
"0000\n",
"000000\n",
"0000000\n",
"false\n",
"00000000\n",
"0000000\n",
"false\n",
"0000000\n",
"00000000\n",
"00000000\n",
"false\n",
"0101\n",
"false\n",
"0000\n",
"0000\n",
"0000\n",
"0000000\n",
"000000\n",
"0000000\n",
"0000000\n",
"false\n",
"false\n",
"false\n",
"00000000\n",
"false\n",
"00000000\n",
"false\n",
"0101\n",
"0000\n",
"0000\n",
"00000000\n",
"0000000\n",
"false\n",
"00000000\n",
"00000000\n",
"00000000\n",
"000000000\n",
"000000000\n",
"0000000000\n",
"0000000000\n",
"0000000000\n",
"false\n",
"false\n",
"false\n",
"0000000\n",
"0000\n",
"000000\n",
"0000000\n",
"false\n",
"false\n",
"false\n",
"0000\n",
"00000000\n",
"000000000\n",
"00000000\n",
"false\n",
"0000\n",
"0000\n",
"0000000\n",
"00000000\n",
"false\n",
"0000\n",
"0000\n",
"0000000\n",
"false\n",
"00000000\n",
"00000000\n",
"000000000\n",
"000000000\n",
"0000000000\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Golorps are mysterious creatures who feed on variables. Golorp's name is a program in some programming language. Some scientists believe that this language is Befunge; golorps are tantalizingly silent.
Variables consumed by golorps can take values from 0 to 9, inclusive. For each golorp its daily diet is defined by its name. Some golorps are so picky that they can't be fed at all. Besides, all golorps are very health-conscious and try to eat as little as possible. Given a choice of several valid sequences of variable values, each golorp will choose lexicographically smallest one.
For the purposes of this problem you can assume that a golorp consists of jaws and a stomach. The number of variables necessary to feed a golorp is defined by the shape of its jaws. Variables can get to the stomach only via the jaws.
A hungry golorp is visiting you. You know its name; feed it or figure out that it's impossible.
Input
The input is a single string (between 13 and 1024 characters long) — the name of the visiting golorp. All names are similar and will resemble the ones given in the samples. The name is guaranteed to be valid.
Output
Output lexicographically smallest sequence of variable values fit for feeding this golorp. Values should be listed in the order in which they get into the jaws. If the golorp is impossible to feed, output "false".
Examples
Input
?(_-_/___*__):-___>__.
Output
0010
Input
?(__-_+_/_____):-__>__,_____<__.
Output
false
Input
?(______________________/____+_______*__-_____*______-___):-__<___,___<____,____<_____,_____<______,______<_______.
Output
0250341
Input
?(__+___+__-___):-___>__.
Output
0101
### Input:
?(__-_+_/_____):-__>__,_____<__.
### Output:
false
### Input:
?(______________________/____+_______*__-_____*______-___):-__<___,___<____,____<_____,_____<______,______<_______.
### Output:
false
### Code:
"""
Codeforces April Fools Contest 2014 Problem I
Author : chaotic_iak
Language: Python 3.3.4
"""
class InputHandlerObject(object):
inputs = []
def getInput(self, n = 0):
res = ""
inputs = self.inputs
if not inputs: inputs.extend(input().split(" "))
if n == 0:
res = inputs[:]
inputs[:] = []
while n > len(inputs):
inputs.extend(input().split(" "))
if n > 0:
res = inputs[:n]
inputs[:n] = []
return res
InputHandler = InputHandlerObject()
g = InputHandler.getInput
############################## SOLUTION ##############################
# ?(_/____+_______*__-_____*______-___):-__<___,___<____,____<_____,_____<______,______<_______.
golorp = input().split(":-")
golorp[0] = golorp[0][2:]
ct = 0
jaws = []
for x in range(len(golorp[0])):
if golorp[0][x] == "_":
ct += 1
else:
jaws.append(ct)
ct = 0
ct = 0
conditionsraw = []
for x in range(len(golorp[1])):
if golorp[1][x] == "_":
ct += 1
else:
conditionsraw.append(ct)
conditionsraw.append(golorp[1][x])
ct = 0
conditions = []
for x in range(0, len(conditionsraw)//4):
if conditionsraw[4*x+1] == ">":
conditions.append((conditionsraw[4*x+2], conditionsraw[4*x]))
else:
conditions.append((conditionsraw[4*x], conditionsraw[4*x+2]))
inedges = [[-1]] * (max(jaws) + 1)
outedges = [[-1]] * (max(jaws) + 1)
val = [-1] * (max(jaws) + 1)
processed = [False] * (max(jaws) + 1)
for x in jaws:
inedges[x] = []
outedges[x] = []
for x, y in conditions:
inedges[y].append(x)
outedges[x].append(y)
for i in range(10):
for x in jaws:
if not inedges[x] and not processed[x]:
val[x] += 1
processed[x] = True
for y in outedges[x]:
val[y] = max(val[y], val[x])
inedges[y].remove(x)
failure = False
for x in jaws:
if not processed[x] or val[x] > 9:
failure = True
break
if failure:
print("false")
else:
s = ""
for x in jaws:
s += str(val[x])
print(s)
|
437_D. The Child and Zoo_10586
|
Of course our child likes walking in a zoo. The zoo has n areas, that are numbered from 1 to n. The i-th area contains ai animals in it. Also there are m roads in the zoo, and each road connects two distinct areas. Naturally the zoo is connected, so you can reach any area of the zoo from any other area using the roads.
Our child is very smart. Imagine the child want to go from area p to area q. Firstly he considers all the simple routes from p to q. For each route the child writes down the number, that is equal to the minimum number of animals among the route areas. Let's denote the largest of the written numbers as f(p, q). Finally, the child chooses one of the routes for which he writes down the value f(p, q).
After the child has visited the zoo, he thinks about the question: what is the average value of f(p, q) for all pairs p, q (p ≠ q)? Can you answer his question?
Input
The first line contains two integers n and m (2 ≤ n ≤ 105; 0 ≤ m ≤ 105). The second line contains n integers: a1, a2, ..., an (0 ≤ ai ≤ 105). Then follow m lines, each line contains two integers xi and yi (1 ≤ xi, yi ≤ n; xi ≠ yi), denoting the road between areas xi and yi.
All roads are bidirectional, each pair of areas is connected by at most one road.
Output
Output a real number — the value of <image>.
The answer will be considered correct if its relative or absolute error doesn't exceed 10 - 4.
Examples
Input
4 3
10 20 30 40
1 3
2 3
4 3
Output
16.666667
Input
3 3
10 20 30
1 2
2 3
3 1
Output
13.333333
Input
7 8
40 20 10 30 20 50 40
1 2
2 3
3 4
4 5
5 6
6 7
1 4
5 7
Output
18.571429
Note
Consider the first sample. There are 12 possible situations:
* p = 1, q = 3, f(p, q) = 10.
* p = 2, q = 3, f(p, q) = 20.
* p = 4, q = 3, f(p, q) = 30.
* p = 1, q = 2, f(p, q) = 10.
* p = 2, q = 4, f(p, q) = 20.
* p = 4, q = 1, f(p, q) = 10.
Another 6 cases are symmetrical to the above. The average is <image>.
Consider the second sample. There are 6 possible situations:
* p = 1, q = 2, f(p, q) = 10.
* p = 2, q = 3, f(p, q) = 20.
* p = 1, q = 3, f(p, q) = 10.
Another 3 cases are symmetrical to the above. The average is <image>.
|
R = lambda:map(int, input().split())
n, m = R()
a = list(R())
p, f, sz =[], [], []
e = [[] for i in range(n)]
vis = [0] * n
ans = 0
def find(u):
if f[u] != u:
f[u] = find(f[u])
return f[u]
for i in range(n):
p.append([a[i], i])
f.append(i)
sz.append(1)
p.sort()
p.reverse()
for i in range(m):
u, v = R()
e[u - 1].append(v - 1)
e[v - 1].append(u - 1)
for i in range(n):
u = p[i][1]
for v in e[u]:
if (vis[v] and find(u) != find(v)):
pu, pv = u, v
if (sz[f[u]] > sz[f[v]]):
pu, pv = pv, pu
ans += p[i][0] * sz[f[pu]] * sz[f[pv]]
sz[f[pv]] += sz[f[pu]]
f[f[pu]] = f[pv]
vis[u] = 1
print("%.6f" %(2. * ans / n / (n - 1)))
|
{
"input": [
"4 3\n10 20 30 40\n1 3\n2 3\n4 3\n",
"7 8\n40 20 10 30 20 50 40\n1 2\n2 3\n3 4\n4 5\n5 6\n6 7\n1 4\n5 7\n",
"3 3\n10 20 30\n1 2\n2 3\n3 1\n",
"10 19\n15704 19758 26631 25050 22778 15041 8487 26418 5136 4199\n1 2\n1 3\n1 4\n2 5\n1 6\n2 7\n2 8\n7 9\n6 10\n7 3\n4 7\n6 4\n6 8\n5 8\n6 9\n5 4\n1 8\n1 9\n5 3\n",
"10 14\n594 965 90 327 549 206 514 993 803 635\n1 2\n1 3\n3 4\n2 5\n5 6\n5 7\n4 8\n4 9\n5 10\n10 4\n7 8\n2 6\n6 4\n5 4\n",
"10 14\n296 371 507 807 102 558 199 500 553 150\n1 2\n2 3\n3 4\n1 5\n5 6\n3 7\n2 8\n5 9\n8 10\n7 2\n8 7\n4 6\n1 7\n5 4\n",
"10 19\n13637 26970 19043 3616 12880 19387 12539 25190 2452 1261\n1 2\n1 3\n1 4\n2 5\n3 6\n6 7\n3 8\n5 9\n3 10\n4 10\n9 3\n2 8\n4 3\n2 3\n7 10\n7 8\n5 10\n5 6\n7 4\n",
"2 1\n233 2333\n1 2\n",
"10 19\n15704 19758 26631 25050 22778 15041 8487 26418 5136 4199\n1 2\n1 3\n2 4\n2 5\n1 6\n2 7\n2 8\n7 9\n6 10\n7 3\n4 7\n6 4\n6 8\n5 8\n6 9\n5 4\n1 8\n1 9\n5 3\n",
"10 14\n594 965 90 327 549 206 514 993 803 635\n1 2\n1 3\n3 4\n2 5\n5 6\n5 7\n4 8\n4 9\n5 10\n10 4\n7 8\n4 6\n6 4\n5 4\n",
"10 14\n296 371 507 807 102 558 199 500 553 141\n1 2\n2 3\n3 4\n1 5\n5 6\n3 7\n2 8\n5 9\n8 10\n7 2\n8 7\n4 6\n1 7\n5 4\n",
"10 19\n13637 26970 19043 3616 12880 19387 12539 25190 2452 1261\n1 2\n1 3\n1 4\n2 5\n3 2\n6 7\n3 8\n5 9\n3 10\n4 10\n9 3\n2 8\n4 3\n2 3\n7 10\n7 8\n5 10\n5 6\n7 4\n",
"7 8\n40 20 10 32 20 50 40\n1 2\n2 3\n3 4\n4 5\n5 6\n6 7\n1 4\n5 7\n",
"3 3\n10 3 30\n1 2\n2 3\n3 1\n",
"10 19\n15704 19758 26631 25050 22778 15041 8487 26418 5136 4199\n1 2\n1 3\n2 4\n2 5\n1 6\n2 7\n4 8\n7 9\n6 10\n7 3\n4 7\n6 4\n6 8\n5 8\n6 9\n5 4\n1 8\n1 9\n5 3\n",
"10 14\n296 371 507 807 102 558 199 500 553 251\n1 2\n2 3\n3 4\n1 5\n5 6\n3 7\n2 8\n5 9\n8 10\n7 2\n8 7\n4 6\n1 7\n5 4\n",
"10 19\n15704 19758 26631 25050 22778 15041 8487 26418 3511 4199\n1 2\n1 3\n2 4\n2 5\n1 6\n2 7\n4 8\n7 9\n6 10\n7 3\n4 7\n6 4\n6 8\n5 8\n6 9\n5 4\n1 8\n1 9\n5 3\n",
"10 19\n15704 19758 26631 25050 22778 15041 8487 1276 3511 4199\n1 2\n1 3\n2 4\n2 5\n1 6\n2 7\n4 8\n7 9\n6 10\n7 3\n4 7\n6 4\n6 8\n5 8\n6 9\n5 4\n1 8\n1 9\n5 3\n",
"10 14\n296 371 507 807 102 558 199 500 553 251\n1 2\n2 3\n3 4\n1 5\n5 6\n3 7\n2 8\n4 9\n8 10\n7 2\n8 7\n4 6\n1 7\n5 7\n",
"10 19\n13637 26970 15760 3616 12880 14739 12539 25190 2452 1261\n1 2\n1 3\n1 4\n2 5\n3 2\n6 7\n3 8\n3 9\n3 10\n4 10\n9 3\n2 8\n4 3\n2 3\n7 10\n7 8\n5 10\n5 6\n7 4\n",
"10 19\n15704 19758 26631 25050 22778 15041 8487 1276 3511 4199\n1 2\n1 3\n2 4\n2 5\n1 6\n2 7\n4 8\n7 9\n6 10\n7 3\n4 7\n6 4\n6 8\n5 8\n6 9\n5 4\n1 8\n1 9\n5 6\n",
"10 19\n13637 26970 15760 3616 12880 14739 12539 25190 2452 1261\n1 2\n1 3\n1 4\n2 3\n3 2\n6 7\n3 8\n3 9\n3 10\n4 10\n9 3\n2 8\n4 3\n2 3\n7 10\n7 8\n5 10\n5 6\n7 4\n",
"10 19\n6280 19758 26631 25050 22778 15041 8487 1276 3511 4199\n1 2\n1 3\n2 4\n2 5\n1 6\n2 7\n4 8\n7 9\n6 10\n7 3\n4 7\n6 4\n6 8\n5 8\n6 9\n5 4\n1 8\n1 9\n5 6\n",
"10 19\n6280 19758 26631 25050 22778 15041 8487 1276 78 4199\n1 2\n1 3\n2 4\n2 5\n1 6\n2 7\n4 8\n7 9\n6 10\n7 3\n4 7\n6 4\n6 8\n5 8\n6 9\n5 4\n1 8\n1 4\n5 6\n",
"10 19\n6280 19758 26631 1761 22778 15041 8487 1276 78 4199\n1 2\n1 3\n2 4\n2 5\n1 6\n2 7\n4 8\n7 9\n6 10\n7 3\n4 7\n6 4\n6 8\n5 8\n6 9\n5 4\n1 8\n1 4\n5 6\n",
"10 19\n6280 16890 26631 1761 22778 15041 8487 1276 78 4199\n1 2\n1 3\n2 4\n2 5\n1 6\n2 7\n4 8\n7 9\n6 10\n7 3\n4 7\n6 4\n6 8\n5 8\n6 9\n5 4\n1 8\n1 4\n5 6\n",
"10 14\n594 965 90 327 457 206 514 993 803 635\n1 2\n1 3\n3 4\n2 5\n5 6\n5 7\n4 8\n4 9\n5 10\n10 4\n7 8\n2 6\n6 4\n5 4\n",
"10 19\n13637 26970 19043 3616 12880 19387 12539 25190 2452 1261\n1 2\n1 3\n1 4\n2 5\n3 6\n6 7\n3 8\n5 9\n3 10\n4 10\n9 3\n2 8\n4 3\n2 3\n7 10\n7 1\n5 10\n5 6\n7 4\n",
"4 3\n10 20 30 46\n1 3\n2 3\n4 3\n",
"7 8\n40 33 10 30 20 50 40\n1 2\n2 3\n3 4\n4 5\n5 6\n6 7\n1 4\n5 7\n",
"3 3\n10 20 30\n1 2\n2 1\n3 1\n",
"10 14\n75 965 90 327 549 206 514 993 803 635\n1 2\n1 3\n3 4\n2 5\n5 6\n5 7\n4 8\n4 9\n5 10\n10 4\n7 8\n4 6\n6 4\n5 4\n",
"10 19\n13637 26970 19043 3616 12880 19387 12539 25190 2452 1261\n1 2\n1 3\n1 4\n2 7\n3 2\n6 7\n3 8\n5 9\n3 10\n4 10\n9 3\n2 8\n4 3\n2 3\n7 10\n7 8\n5 10\n5 6\n7 4\n",
"10 19\n15704 19758 26631 25050 22778 9525 8487 26418 5136 4199\n1 2\n1 3\n2 4\n2 5\n1 6\n2 7\n4 8\n7 9\n6 10\n7 3\n4 7\n6 4\n6 8\n5 8\n6 9\n5 4\n1 8\n1 9\n5 3\n",
"10 14\n752 965 90 327 549 206 514 865 803 635\n1 2\n1 3\n3 4\n2 5\n5 6\n5 7\n4 8\n4 9\n5 10\n10 4\n7 8\n4 6\n6 4\n5 4\n",
"10 14\n296 371 507 807 102 558 199 500 553 251\n1 2\n2 3\n3 4\n1 5\n5 6\n3 7\n2 8\n2 9\n8 10\n7 2\n8 7\n4 6\n1 7\n5 4\n",
"10 19\n13637 26970 19043 3616 12880 14739 12539 25190 4354 1261\n1 2\n1 3\n1 4\n2 5\n3 2\n6 7\n3 8\n5 9\n3 10\n4 10\n9 3\n2 8\n4 3\n2 3\n7 10\n7 8\n5 10\n5 6\n7 4\n",
"10 19\n15704 19758 26631 25050 22778 15041 8487 26418 3511 4199\n1 2\n1 3\n2 4\n2 5\n1 6\n2 7\n4 8\n7 9\n6 10\n7 3\n4 7\n6 4\n6 8\n5 8\n6 9\n5 4\n1 8\n1 9\n5 1\n",
"10 14\n296 371 507 807 102 558 199 500 553 251\n1 2\n2 3\n3 4\n1 5\n5 6\n3 7\n2 8\n5 9\n8 10\n7 2\n8 7\n4 6\n1 7\n9 7\n",
"10 19\n13637 26970 15760 3616 12880 14739 12539 25190 1916 1261\n1 2\n1 3\n1 4\n2 5\n3 2\n6 7\n3 8\n3 9\n3 10\n4 10\n9 3\n2 8\n4 3\n2 3\n7 10\n7 8\n5 10\n5 6\n7 4\n",
"10 19\n15704 19758 26631 25050 22778 22501 8487 1276 3511 4199\n1 2\n1 3\n2 4\n2 5\n1 6\n2 7\n4 8\n7 9\n6 10\n7 3\n4 7\n6 4\n6 8\n5 8\n6 9\n5 4\n1 8\n1 9\n5 6\n",
"10 19\n6280 19758 26631 25050 22778 15041 8487 1276 3511 4199\n1 2\n2 3\n2 4\n2 5\n1 6\n2 7\n4 8\n7 9\n6 10\n7 3\n4 7\n6 4\n6 8\n5 8\n6 9\n5 4\n1 8\n1 4\n5 6\n",
"4 3\n10 16 30 46\n1 3\n2 3\n4 3\n",
"7 8\n40 33 10 30 20 50 43\n1 2\n2 3\n3 4\n4 5\n5 6\n6 7\n1 4\n5 7\n",
"10 14\n594 965 90 327 549 206 514 865 803 635\n1 2\n1 3\n3 4\n2 5\n5 6\n5 7\n4 8\n4 9\n5 10\n10 4\n7 8\n4 6\n6 4\n5 4\n",
"10 19\n13637 26970 19043 3616 12880 14739 12539 25190 2452 1261\n1 2\n1 3\n1 4\n2 5\n3 2\n6 7\n3 8\n5 9\n3 10\n4 10\n9 3\n2 8\n4 3\n2 3\n7 10\n7 8\n5 10\n5 6\n7 4\n",
"10 14\n296 371 507 807 102 558 199 500 553 251\n1 2\n2 3\n3 4\n1 5\n5 6\n3 7\n2 8\n5 9\n8 10\n7 2\n8 7\n4 6\n1 7\n5 7\n",
"10 19\n13637 26970 19043 3616 12880 14739 12539 25190 2452 1261\n1 2\n1 3\n1 4\n2 5\n3 2\n6 7\n3 8\n3 9\n3 10\n4 10\n9 3\n2 8\n4 3\n2 3\n7 10\n7 8\n5 10\n5 6\n7 4\n",
"10 14\n296 371 507 807 102 558 199 500 553 251\n1 2\n2 3\n3 4\n1 5\n5 6\n1 7\n2 8\n4 9\n8 10\n7 2\n8 7\n4 6\n1 7\n5 7\n",
"10 19\n6280 19758 26631 25050 22778 15041 8487 1276 3511 4199\n1 2\n1 3\n2 4\n2 5\n1 6\n2 7\n4 8\n7 9\n6 10\n7 3\n4 7\n6 4\n6 8\n5 8\n6 9\n5 4\n1 8\n1 4\n5 6\n",
"10 19\n15704 19758 26631 25050 22778 15041 8487 26418 5136 4199\n1 2\n1 3\n1 4\n2 5\n1 6\n2 7\n2 8\n7 9\n6 10\n7 3\n4 7\n6 4\n6 8\n5 8\n6 9\n5 4\n1 5\n1 9\n5 3\n",
"10 14\n296 371 507 807 102 558 199 500 553 141\n1 2\n2 3\n3 4\n1 5\n5 6\n3 7\n2 8\n5 9\n8 10\n7 2\n8 7\n4 6\n1 2\n5 4\n",
"10 19\n15704 19758 26631 25050 22778 15041 8487 1276 3511 4199\n1 2\n1 3\n2 4\n2 5\n1 6\n2 7\n4 8\n3 9\n6 10\n7 3\n4 7\n6 4\n6 8\n5 8\n6 9\n5 4\n1 8\n1 9\n5 3\n",
"10 19\n6280 19758 26631 25050 22778 15041 8487 1276 3511 4199\n1 2\n1 3\n2 4\n2 5\n1 6\n2 7\n4 8\n7 8\n6 10\n7 3\n4 7\n6 4\n6 8\n5 8\n6 9\n5 4\n1 8\n1 9\n5 6\n",
"10 19\n6280 19758 26631 1761 22778 15041 8487 1276 78 4199\n1 2\n1 3\n2 4\n2 5\n1 6\n2 7\n4 8\n7 9\n6 10\n7 3\n4 7\n6 4\n6 8\n5 8\n6 9\n1 4\n1 8\n1 4\n5 6\n",
"10 19\n6280 16890 39485 1761 22778 15041 8487 1276 78 4199\n1 2\n1 3\n2 4\n2 5\n1 6\n2 7\n4 8\n7 9\n6 10\n7 3\n4 7\n6 4\n6 8\n5 8\n6 9\n5 4\n1 8\n1 4\n5 6\n",
"10 19\n15704 19758 26631 25050 22778 15041 8487 26418 5136 4199\n1 2\n1 3\n1 4\n2 5\n1 6\n2 7\n2 8\n7 9\n6 10\n7 3\n4 7\n6 4\n6 8\n5 8\n6 9\n5 4\n2 5\n1 9\n5 3\n",
"10 14\n594 965 90 327 457 206 514 993 803 635\n1 2\n1 3\n3 4\n2 5\n10 6\n5 7\n4 8\n4 9\n5 10\n10 4\n7 8\n2 6\n6 4\n5 4\n"
],
"output": [
"16.6666666667\n",
"18.5714285714\n",
"13.3333333333\n",
"11616.7555555556\n",
"326.0888888889\n",
"213.9333333333\n",
"8241.4222222222\n",
"233.0000000000\n",
"11616.7555556\n",
"326.0888889\n",
"212.5333333\n",
"7813.7333333\n",
"18.6666667\n",
"5.3333333\n",
"11667.2444444\n",
"228.4888889\n",
"11363.0666667\n",
"8567.0222222\n",
"279.2666667\n",
"7667.8222222\n",
"8162.5333333\n",
"7607.2000000\n",
"6454.3333333\n",
"5817.4000000\n",
"4201.7777778\n",
"4138.0444444\n",
"305.7333333\n",
"8241.4222222\n",
"16.6666667\n",
"19.6666667\n",
"10.0000000\n",
"259.5333333\n",
"7753.1111111\n",
"10931.7777778\n",
"329.6000000\n",
"268.1555556\n",
"8135.4666667\n",
"10801.3777778\n",
"245.7333333\n",
"7572.5333333\n",
"8628.3777778\n",
"7351.3777778\n",
"15.3333333\n",
"19.8095238\n",
"326.0888889\n",
"7813.7333333\n",
"228.4888889\n",
"7813.7333333\n",
"279.2666667\n",
"6454.3333333\n",
"11616.7555556\n",
"212.5333333\n",
"8567.0222222\n",
"6454.3333333\n",
"4201.7777778\n",
"4138.0444444\n",
"11616.7555556\n",
"305.7333333\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Of course our child likes walking in a zoo. The zoo has n areas, that are numbered from 1 to n. The i-th area contains ai animals in it. Also there are m roads in the zoo, and each road connects two distinct areas. Naturally the zoo is connected, so you can reach any area of the zoo from any other area using the roads.
Our child is very smart. Imagine the child want to go from area p to area q. Firstly he considers all the simple routes from p to q. For each route the child writes down the number, that is equal to the minimum number of animals among the route areas. Let's denote the largest of the written numbers as f(p, q). Finally, the child chooses one of the routes for which he writes down the value f(p, q).
After the child has visited the zoo, he thinks about the question: what is the average value of f(p, q) for all pairs p, q (p ≠ q)? Can you answer his question?
Input
The first line contains two integers n and m (2 ≤ n ≤ 105; 0 ≤ m ≤ 105). The second line contains n integers: a1, a2, ..., an (0 ≤ ai ≤ 105). Then follow m lines, each line contains two integers xi and yi (1 ≤ xi, yi ≤ n; xi ≠ yi), denoting the road between areas xi and yi.
All roads are bidirectional, each pair of areas is connected by at most one road.
Output
Output a real number — the value of <image>.
The answer will be considered correct if its relative or absolute error doesn't exceed 10 - 4.
Examples
Input
4 3
10 20 30 40
1 3
2 3
4 3
Output
16.666667
Input
3 3
10 20 30
1 2
2 3
3 1
Output
13.333333
Input
7 8
40 20 10 30 20 50 40
1 2
2 3
3 4
4 5
5 6
6 7
1 4
5 7
Output
18.571429
Note
Consider the first sample. There are 12 possible situations:
* p = 1, q = 3, f(p, q) = 10.
* p = 2, q = 3, f(p, q) = 20.
* p = 4, q = 3, f(p, q) = 30.
* p = 1, q = 2, f(p, q) = 10.
* p = 2, q = 4, f(p, q) = 20.
* p = 4, q = 1, f(p, q) = 10.
Another 6 cases are symmetrical to the above. The average is <image>.
Consider the second sample. There are 6 possible situations:
* p = 1, q = 2, f(p, q) = 10.
* p = 2, q = 3, f(p, q) = 20.
* p = 1, q = 3, f(p, q) = 10.
Another 3 cases are symmetrical to the above. The average is <image>.
### Input:
4 3
10 20 30 40
1 3
2 3
4 3
### Output:
16.6666666667
### Input:
7 8
40 20 10 30 20 50 40
1 2
2 3
3 4
4 5
5 6
6 7
1 4
5 7
### Output:
18.5714285714
### Code:
R = lambda:map(int, input().split())
n, m = R()
a = list(R())
p, f, sz =[], [], []
e = [[] for i in range(n)]
vis = [0] * n
ans = 0
def find(u):
if f[u] != u:
f[u] = find(f[u])
return f[u]
for i in range(n):
p.append([a[i], i])
f.append(i)
sz.append(1)
p.sort()
p.reverse()
for i in range(m):
u, v = R()
e[u - 1].append(v - 1)
e[v - 1].append(u - 1)
for i in range(n):
u = p[i][1]
for v in e[u]:
if (vis[v] and find(u) != find(v)):
pu, pv = u, v
if (sz[f[u]] > sz[f[v]]):
pu, pv = pv, pu
ans += p[i][0] * sz[f[pu]] * sz[f[pv]]
sz[f[pv]] += sz[f[pu]]
f[f[pu]] = f[pv]
vis[u] = 1
print("%.6f" %(2. * ans / n / (n - 1)))
|
506_E. Mr. Kitayuta's Gift_10594
|
Mr. Kitayuta has kindly given you a string s consisting of lowercase English letters. You are asked to insert exactly n lowercase English letters into s to make it a palindrome. (A palindrome is a string that reads the same forward and backward. For example, "noon", "testset" and "a" are all palindromes, while "test" and "kitayuta" are not.) You can choose any n lowercase English letters, and insert each of them to any position of s, possibly to the beginning or the end of s. You have to insert exactly n letters even if it is possible to turn s into a palindrome by inserting less than n letters.
Find the number of the palindromes that can be obtained in this way, modulo 10007.
Input
The first line contains a string s (1 ≤ |s| ≤ 200). Each character in s is a lowercase English letter.
The second line contains an integer n (1 ≤ n ≤ 109).
Output
Print the number of the palindromes that can be obtained, modulo 10007.
Examples
Input
revive
1
Output
1
Input
add
2
Output
28
Note
For the first sample, you can obtain the palindrome "reviver" by inserting 'r' to the end of "revive".
For the second sample, the following 28 palindromes can be obtained: "adada", "adbda", ..., "adzda", "dadad" and "ddadd".
|
palindrom = lambda s: s == s[::-1]
printans = lambda l: print(''.join(l))
s = list(input())
for i in range(len(s)+1):
for letter in 'abcdefghijklmnopqrstvwuxyz':
tmp = s[:]
tmp.insert(i,letter)
if palindrom(tmp):
printans(tmp)
exit()
print('NA')
|
{
"input": [
"add\n2\n",
"revive\n1\n",
"noon\n5\n",
"lsdijfjisl\n1\n",
"lsdijfjisl\n209\n",
"nsngnnnnnnnnnnvnnnnnbe\n948\n",
"squirrel\n32\n",
"cnonnpbnpptppgntggtggtngpptppnbpnnonc\n294295\n",
"k\n46277432\n",
"nevceypryxidffdixyrpyecven\n2916\n",
"yosupo\n2\n",
"irrjoktogwxektwrfihfjtertgdhttktrgiwtgttwkjthkewwewtrefejwforhwfjkrkifxkhtogothkxfikrkjfwhrofwjefertwewwekhtjkwttgtwigrtktthdgtretjfhifrwtkexwgotkojrri\n618\n",
"nqwcvcwqn\n52\n",
"bbbhbbibhjjhbibbhbbb\n41891\n",
"bxyfyfokfzycqtqfatolwxccaqnsncaqnqkztjsksocflsxzzxslfcosksjtzkqnqacnsnqaccxwlotafqtqcyzfkofyfyxb\n82245714\n",
"hopeyouenjoyedthematch\n20150118\n",
"zlllzzzzzlzzzzllllzzzllzlzzzzzlzlllzzlzzlllzlllzzllzzlllzlzlzzzllllzlzzzzlllzlzllzlzlllzzzzlzllllzzzlzlzlllzzllzzlllzlllzzlzzlllzlzzzzzlzllzzzllllzzzzlzzzzzlllz\n8\n",
"jfoewijalkemfwmamjakldsvkdsvksdkmvmkvmkmkkwemfkmkemgkweghweufewufwefewfewkoewoijfiewfelwjfee\n2319\n",
"oawjfiowejafoiewajfjiewajowimafjiowajfoijmfoiwjfe\n790221666\n",
"yozppppppppppzzppppppppoppppppppppnpppppprpyypvppvppppppppopypppppppypppppppkppppppppvpppppppp\n1\n",
"evima\n4\n",
"lrlmrlrmmfzlffrmorrlrzzrmelflfrzzlorlllrzzfzmjlffoofflrororforoefrjzlmollmfllrmlorozoomfoorozfrjmjroozrlljlrmfmrl\n251851\n",
"ewcdcwerp\n1\n",
"kitayuta\n6\n",
"mrkitayuta\n536870899\n",
"fft\n2\n",
"racecar\n10\n",
"czlhddcngwzrmbsvceirdwoezlboxsbehwgccncyrmvbgyrdmzocmlwgmcrmcocmrcmgwlmcozmdrygbvmrycnccgwhebsxoblneowrievsbmrzwgncddhlz\n87205\n",
"eeeee\n41104\n",
"a\n1\n",
"hogloid\n5\n",
"b\n5\n",
"zzzzzzzzzzzzzznizzzzzzzzzzzzzzzzzzzyzzyzzzzzzzzzzzzzyzzzzzzyzzyzzzzzzznzzzzzzzzzzzzzzznzzzzznzizzzzzzizzzyzzzzzzzzynzzzi\n541\n",
"mrtoudai\n2347832\n",
"vnwmvvmonv\n12345\n",
"sgjzgbvvsztjqsrnqqgsvcgmxyvxjbxvvszjxx\n31489\n",
"oyxbepxbeqaqpzwwzugzwwisxngkwegnqgbweqokoxpkxkkeqoqtwgxsgekgnasiwzguzwwazaxebxyo\n559047\n",
"shuseki\n4\n",
"mvvxvqzxqvmqqmjljmqzxxqvxxmmqxqjzzxmmmqqqqmxzxqmxqzdvzqvqqqqqqxxmxjjlvvljljmxxxqqqqqvqvdzqxmqxvzxmqxqmmmzxzzjxxqmmqxvzqxxzqmqjljmqqvmjqxzqvv\n38\n",
"thankyoumrkitayuta\n39\n",
"stat\n9\n",
"iwiwi\n8\n",
"ee\n1\n",
"wanwdnnwnnwinwaxaadnwawiaiawwwiniiwnxiwdnawnaiiiwywiwnyindan\n818007692\n",
"zennyuu\n114514\n",
"slime\n41\n",
"level\n7\n",
"dddddzdzddddddddddddddddddddddddddbddddddddbdddddddddddddddddddbdb\n20\n",
"fmlmflmfzllffrmlrlfzmoelflfrzzlorllzrozfzmjoeflofflrororlffooffjrzfmzrllmjozrrlffemzzmlomrfzflzlmjmrlromlrr\n251851\n",
"yu\n1000000000\n",
"mrkitayutasgift\n2500\n",
"yutampo\n3\n",
"ljszsxovlxdsdsjvaufyfftmoyfuyaplpzxjucujxzplpayufyomtffyfuavjsdsdxlvoxszsjl\n1880\n",
"wiiisiiiuoiiiiitixiiv\n251851\n",
"iq\n1\n",
"zzz\n536870908\n",
"dog\n28\n",
"ipzmkijimzipmjkjhctpckcjpkjkicbdtwpbkkzizpijzpbkidkchhckdikbpzjipzizkkbpwtdbcikjkpjckcptchjkjmpizmijikmzpi\n209\n",
"jewiiwefj\n3223\n",
"palindrome\n123454321\n",
"pppppppppppppppppppppppppppppppppppppppppppppppcpppppppppppppppppppppppppppppcppppppplppppppppppppppppppppppppppppppppppppppppa\n1515688\n",
"codeforcesround\n286\n",
"nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnngnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnz\n536870712\n",
"ccxsecrxosqsrsoolxzcoolqllexxssxqoqeqkocerchlxckqschxxczlxscoxhszsoxzxrzohsccsclocxxzshrhzoexxhrohqrrqhorhxxeozhrhszxxcolcsccshozrxzxoszshxocsxlzcxxhcsqkcxlhcrecokqeqoqxssxxellqlooczxloosrsqsoxrcesxcc\n536870712\n",
"ussiudlvjsdjduujuljvdrdljdjluarusdaiiujjsdudjslpmujdspixxljjjuiqasjlsxpppspuisdaljjxsiqqujudjljxlmqjjqmlxjljdujuqqisxjjladsiupspppxsljsaqiujjjlxxipsdjumplsjdudsjjuiiadsurauljdjldrdvjlujuudjdsjvlduissu\n4347\n",
"gggmmggmgjjmmjggglmmgmjmjjgggkjmmjgmmmmjmmmgggmmgjjjmjjmmmkmmmkgmggmgmjmmmgggjmmgggggjmmmkgggggmgmgjgggmmmmmgmggmmgmjmjgmmgjjjmjggmgggggmmmmgmjgmjjkgggmjmjmmmmmmmmjjgmggmmggg\n566605\n",
"cszaetjydpkfzbihfzjmsfklibikgskhdfdrfgorggirpcmshkgicyjzjkkakmhfjasyrrbmabbdzsgyqkzgkehzasosaztcazvpfbiabfpojtbkgrvztkvsgzcgmimgskztceeghubbacrjlzzskffaskgvzsdckkphszibtajfrcldeyakgvkdhphhliayzszhghzt\n33\n",
"sssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssi\n67106614\n",
"stat\n",
"zzz\n",
"mxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx\n469761845\n",
"eviver\n",
"qqqqqqqqqqqqqqiqqqqqqiqqqqqqqqqqqqqqqqqqqqqqqiqqqiqqqqqqqqiqqqqqqqqqqqqqqqqqiqqqqqqqqqqqqqiqqqqqqqqqqqqqqqqqqqqqqqqqqiqqqqqqqqqqqqqqqiqqqqqqqqqqqqqqqqqqqqqiqqqqqqqqqqqqqqqqqqqqqqqqqqqqqiqqqqqiqqqqqqqi\n536870709\n",
"mooooooooojoooowooooooooooomooooooooocoooooooooooooooolooooooooooooooooooooopoooooooooooooooooooooooooooooooooooooooooooooioooooooooooouoooojoooooojooooooooomooooolodokoooooooooooocooooooooooomoooooo\n179\n",
"yttyysttyyttttsytytyyttysstttstyttssttsytyttststyssyysttyyttstytttstststttttttytttststttttttytttyttttttytttytttttttststttytttttttstststttytsttyyttsyyssytststtytysttssttytstttssyttyytytysttttyyttsyytty\n4203\n",
"hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhghhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhht\n536870709\n",
"nhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhvhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh\n67108663\n",
"xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxkxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxt\n536870677\n",
"olnrttrnnptltrxooobokxrrtoxrnnrlxnxnkkddnslonolnxlxnsolrvlsslnxofoxofrcttnlxrordloxtnxvoonsloptksorvrosktpolsnoovxntxoldrorxlnttcrfoxofoxnlsslvrlosnxlxnlonolsnddkknxnxlrnnrxotrrxkoboooxrtltpnnrttrnlo\n61309576\n",
"qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq\n535442\n",
"xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxkxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxt\n66977589\n",
"jewiiwefj\n",
"sssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssl\n536870709\n",
"qkqiiwkwqivqkdfiimkqiwkimikfkkvoivwvilvmiwwqkvqvidimwiddwqqqqkqqkviqldiqqoqvwqvktwiqkqiwfkitoitkqiowoiqktiotikfwiqkqiwtkvqwvqoqqidlqivkqqkqqqqwddiwmidivqvkqwwimvlivwviovkkfkimikwiqkmiifdkqviqwkwiiqkq\n671088441\n",
"evima\n",
"bbb\n",
"sssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssi\n536870678\n",
"yryralvogdsfsfdonrrofkkssfgvfsrslrrdsggfygddsykgrrdaovyydddadvsdrfogdygsrsydysokafrddssykakhangyasgsfnygrsrddyfkdsvvvfsrrrdydflkyryydgadrasndsraanoldgffgfdsgrydsfrdrfglgffrfryngfygvoordravyfryfrnfrrky\n5481\n",
"yosupo\n",
"ddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddzddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddj\n67108662\n",
"chhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh\n67104566\n",
"btmtbrrmmmbmtprmtbrrrmllttlrprmpmptprmmbtmmmtmtbbmbtrtbbrbtmttltttmtbmbrrtmtbmmbmtlrmlmbmbtmmmbbttbtbttbbmmmtbmbmlmrltmbmmbtmtrrbmbtmtttlttmtbrbbtrtbmbbtmtmmmtbmmrptpmpmrprlttllmrrrbtmrptmbmmmrrbtmtb\n536870712\n",
"prrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr\n536870709\n",
"jjjjjjjjjjjjjnjjjjjjjjjjjjjjjjjjjvjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjajjjdjjjjjjjjjjjjjjjjjjjjjjjjjjjajajjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjajjjjd\n1176214\n",
"nqwcvcwqn\n",
"vvvvvvvgvvvgvvvvvvvvvvvvvvvvrvvvvvvvvvgvvvvvvvvvvvvvvvvrvgvvvvvvgvvrggvvgvgvvvvvvvvvvvgvgvvvvvvgvvvvgvvvvvvvvvvgvvvvvvvgvgvvvvvvvvqvvvvvvvvvvvvgvvvvvvvvvvvvvvvvvvvvgvvvgvvvvvvvvvgvvvvvgvvqvrvgvrv\n536870712\n",
"ewklfjwefjlkwejflmklgjlkewjrklgjkjewnjkfnewjfhukewjfjkejkfdjskfhdkjshfkjhfjhjhjewhjhjehrfwhhfjefhjwfhjefkjwjfhjwhfjewhfkjwhkjhfjkehjdksjnfdjqwkehgqgwegwqfetywqfeytqfetyefgirgoigjhityhujyuirhjegeywefwe\n536870709\n",
"mxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx\n67108657\n",
"xmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm\n536870712\n",
"zennyuu\n",
"mdskmksdksdddddddddddddddmkcsdmcksdmkkkkkkkkkkkkkkkkkkkkkkkkkmmfekwmewwwweeeeeeeeeeeeeeeeeeeeeeeeeeeeefkwefjlwkekfwskdfkjkkkkkkkkkkkkkkkkkkkkkkkkfjewkfjekfjfefjefkkkkkkkkkkkkkkkkkkkkkkeefefejfekekkkkk\n199\n",
"kuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuusuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu\n66060087\n",
"a\n",
"gsossssqsosssossssssssssgsssgssssssrsssssgszsssssssssssssossssssssssgssssssssssssssssosossossgssssqssssqqsssssssossssssssssgsssssssssssssssssssssssssssgssssssssssssrsssssssssssssssqssszsrgsssos\n232\n",
"kuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuusuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu\n528482103\n",
"lgllsggozxlzotlgozolxlloiozigtxloolzggxgoloixgllgxzzgtoxioxizggoogzozlzlfolzlloxlxotoglllgotoxlxollzloflzlzozgooggzixoixotgzzxgllgxiologxggzloolxtgizoiollxlozogltozlxzoggsllgl\n88200048\n",
"chhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh\n534773558\n",
"lsdijfjisl\n",
"iwiwi\n",
"uuuuuuuuuuuuuouuuuuuueuuuuuuuuuuuuuquuuuuuuuuuuuuuuuuuuuuuuuufiuuuuuuuukuuuuuuuuuuuuoueuuuuuuuuuquuuuuuucuuuiuuuuiuuuuuuuuuuuuuuuuuuuucuuuuueuuuuaeuuuuuucuuuuuuuuuuuuuuuiuuuuuuuuuuutuuuuuuuxi\n84\n",
"aaaaa\n",
"ydydvoddlvjqdmvszssdozedvqmvqlyvvqlzqzsazqyslavmdlovqoylezcqvlsvmqqmvvdvjsdsdvvszavaszldqvmxmsvmvddyyddvmvsmxmvqdlzsavazsvvdsdsjvdvvmqqmvslvqczelyoqvoldmvalsyqzaszqzlqvvylqvmqvdezodsszsvmdqjvlddovdydy\n535822134\n",
"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaiaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaw\n67108680\n",
"mrtoudai\n",
"hogloid\n",
"iq\n",
"prphfjzjfhnvnjnhgpojpnfgtrqqjnfgnjqtnnhpzoeansnhjnoqpqegnjnvhgpppgfnjvjhpnpngjhqefjpalnznftjtlqooprrnpoqqtjzfxnnlqjpeqhjgnpnghjvjrnfgrrppgqpnphgeqtqqnjhghnaozjhnnthqjfgnjqrefnpjonghzngnqhfzjfhrpt\n536870709\n",
"qaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\n67108663\n",
"hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhghhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhht\n67108661\n",
"dog\n",
"jjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjm\n535822135\n",
"uttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttt\n67108662\n",
"bttfjttthttttttutttbytttttkthkttttktttttuttttttttttttjtttttbjfttnjtttttttktttttttkntttttttttttttutjtttnfthttttttuttttttttttkktttbttthttttttttttttkjttttttttttktttbfhtmtttttutttttkttutttttttttutkttttttt\n535822135\n",
"ee\n",
"ijcntmpascomjmssnblmxbgagzgprrmtlligkgubujxksxguslxglvcngamneassmgtguamjaqthxszvfaraxslsuatlavltjkxuaugxkyztvavalrbsanaetsxhtqaejtckztkgmkmafxknvlmaabnavlvgjfxsgjjumcgkillgtgrpzagbmgxbvzxfyjsoymgtnci\n536870711\n",
"toudairiichishusekizennyuumrtoudaikanojomochitoudaiigakubunotennsaitoudaihougakubunoshuusaitoudaiigakubushusekitoudaiiqkikoushisuugakugorinnkinnkyoudaikeizaigakubushusekichishikimonstertoudainoitannji\n1000000000\n",
"ddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddzddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddj\n536870710\n",
"kitayuta\n",
"ggvsraybrobbgcgwcsgugvsbvcwsiwuvykbswukgavigvcwbgysajwsgziwwssuavcgvsjsvggbbwuwsgcbwykvagwgawiwwuuwyiwgwsasvkywvkbaguzwkuwbbggvssjgcuuawwvzgsuvuwysybwcvgisgkuksbkyvuwisbwgcabgugvcwgcvbocrsgg\n489028\n",
"ceesempelcmcdewcmmswcppmswssmocswpowcwpeepdmsesmemceerspmwppscmdwmpoopwdesssdsccsomccpposdmmdmcwesmmsepccomwdpmmdsrppeccmoscsmmspspowwmpmwdccsppemmreecmlmsesmmdcepwcwspmpcwmmmswsdmpcwsmomcpsedcoclmsec\n536870712\n",
"vnwmvvmonv\n",
"revive\n",
"cndkjsnmncmnmxnncmxncnbcvcvavsxcsavcxvxsvxvxsvccvvcvcvcvdcvcvvcvvcvcvvsdvdfvhjgnjbgnjbgngbnbgnjgbjnbgnbnbngbjhjhjjjhjjhiujuoujukoyoktotrutryryrfhfjnfekfiejfjewkfjewigrjjgbjgyedgfgfgfggfgfgfgeuwfewhejf\n536870453\n",
"zaa\n",
"racecar\n",
"noon\n",
"xmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm\n67108664\n",
"palindrome\n",
"dkvulkdhmdloduumhqdmludvflmvldvddmmmtkulhduoluulmmlfvmqvfvkddmtumhvfdqluhdohlludvkfkvdullhodhulqdfvhmutmddkvfvqmvflmmluuloudhluktmmmddvdlvmlfvdulmdqhmuudoldmhdkluvkd\n166547\n",
"battaba\n",
"squirrel\n",
"jfjtmtjjjjmjtfjfjmtjafftfajfjfftmjmmmtffmjaajjmjafttjftfftaaajtjjtmjttatffjjjmjfmtmjtmjffjfjmattjfjmftjmajjmjajfftffjmjaajtmmjtjmmffmfaftjfjtfjtjtmmfftmjatmfjtftmmjtmfamjjjfmfjmjmmfjjjjatfjfffjmjjjmjj\n536870709\n",
"fiwjoefejwiajoeklwjfaewfjlkewjfjewioafjewaklfewfcmklweamkmkmvkmvmijweqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqijfewfjwiqqwqiojiifjifkjwejfff\n95697\n",
"abbabab\n",
"z\n",
"level\n",
"jjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjm\n66977591\n",
"nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnngnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnz\n67108664\n",
"xcmmmmmmmmmfmmmmmmmmmjmmmfmmmrmmmxmmmmmmmmmmmkmmmjmtmmmmmmmmmmmmmmmmmmbcmmhmmmmsmmmfmmmmjmmmmmmmmmmmmmmmmmmmmmmmmdmjmmmmbmmktmhmmrhmmmxmmmmmmofmmmlbmmmmmmmmmmmmmdmmmmmmmmhmmmxmmvqmmmmjmjjmbmmmmmmmmmmm\n536870728\n",
"susssskllsskrsbukkllrlssususukssukslblbsukbuurlsskkksbsrsubukusuklursluslskruuksskrslublkruklulkrbkskbrklulkurklbulsrksskuurkslsulsrulkusukubusrsbskkksslruubkusblblskusskusususslrllkkubsrkssllkssssus\n536870703\n",
"yutampo\n",
"shuseki\n",
"jjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjh\n67108662\n",
"gggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggx\n536870711\n",
"gvdfhdhfhffcfgcfccgyhfhgfgcccgcfvfgvvfvgcdfhfcvvgchvvvfchhccyfjhfhcyccccvwchcgfhchvhfgfgfccfchvcvccfhvhcfcfdvfgffhfhcfgffhfhcfffvfghfcfdvvfhhvgfhfvwvghchcfchvvgchfcwfwfyvhwfwcfgchvcffgccffvvgghfchffgv\n5654\n",
"dhhddddddhddhhhdhdddhdhhhddhdhdddhhhdhddddhddhhhhdhdddhhdhhddddhhddhhhdhhddddddhdddddddhdhddhhdhhddddddhhdhhddhdhdddddddhddddddhhdhhhddhhddddhhdhhdddhdhhhhddhddddhdhhhdddhdhddhhhdhdddhdhhhddhddddddhhd\n536870711\n",
"ewcdcwerp\n",
"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaiaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaw\n537395000\n",
"kiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii\n67125048\n",
"sssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssl\n67108661\n",
"jjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjh\n536870710\n",
"babccba\n",
"mjjjamtfmjjjtfjmtjafftjmfajmjaffjtfmjmmmtfftaaaajmjafttjftjattajtjtttajfjjjfjfmtmjtmjfjfjjtjjfjjmjfafjjtamjfjffjtmtjtmmfjfjjfjajtajtjmjjtjaaftfmjjtmjjaamfjtmmmjtftfjaftffjtmfjfjtjjjjjtmtjfj\n536870709\n",
"nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnu\n67108664\n",
"qaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\n536870711\n",
"add\n",
"fft\n",
"kiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii\n536887096\n",
"slime\n",
"nhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhvhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh\n536870711\n",
"eee\n",
"xflbzlwyyjxdmwwwwxzzxbzdzzmzzzwmegjlgymzmywzlfjdwzzmelbwzwxjyfyyzffezwxxzzwfyzjcdylyzexdmjmwcejjfywxzlxfwzyxjxwewzfdlwyxfzzwzzwylfdwwwyywjxfxywzwmczylzfxxlfxfyzzwlzlzywfx\n6017\n",
"noon\n9\n",
"lsdijfjisl\n2\n",
"lsdijfjisl\n281\n",
"nsngnnnnnnnnnnvnnnnnbe\n1098\n",
"squirrel\n16\n",
"cnonnpbnpptppgntggtggtngpptppnbpnnonc\n411695\n",
"k\n88367038\n",
"nevceypryxidffdixyrpyecven\n2321\n",
"yosupo\n0\n",
"irrjoktogwxektwrfihfjtertgdhttktrgiwtgttwkjthkewwewtrefejwforhwfjkrkifxkhtogothkxfikrkjfwhrofwjefertwewwekhtjkwttgtwigrtktthdgtretjfhifrwtkexwgotkojrri\n622\n",
"nqwcvcwqn\n59\n",
"bbbhbbibhjjhbibbibbb\n41891\n",
"bxyfyfokfzycqtqfatolwxccaqnsncaqnqkztjsksocflsxzzxslfcosksjtzkqnqacnsnqaccxwlotafqtqcyzfkofyfyxb\n40352973\n",
"hopeyouenjoyedthematch\n17682105\n",
"zlllzzzzzlzzzzllllzzzllzlzzzzzlzlllzzlzzlllzlllzzllzzlllzlzlzzzllllzlzzzzlllzlzllzlzlllzzzzlzllllzzzlzlzlllzzllzzlllzlllzzlzzlllzlzzzzzlzllzzzllllzzzzlzzzzzlllz\n1\n",
"jfoewijalkemfwmamjakldsvkdsvksdkmvmkvmkmkkwemfkmkemgkweghweufewufwefewfewkoewoijfiewfelwjfee\n4246\n",
"oawjfiowejafoiewajfjiexajowimafjiowajfoijmfoiwjfe\n790221666\n",
"lrlmrljmmfzlffrmorrlrzzrmelflfrzzlorlllrzzfzmjlffoofflrororforoefrrzlmollmfllrmlorozoomfoorozfrjmjroozrlljlrmfmrl\n251851\n",
"kitayutb\n6\n",
"mrkitayuta\n336315686\n",
"cacerar\n10\n",
"czlhddcngwzrmbsvceirdwoezlboxsbehwgccncyrmvbgyrdmzocmlwgmcrmcocmrcmgwlmcozmdrygbvmrycnccgwhebsxoblneowrievsbmrzwgncddhlz\n17213\n",
"eeeee\n72227\n",
"b\n9\n",
"zzzzzzzzzzzzzznizzzzzzzzzzzzzzzzzzzyzzyzzzzzzzzzzzzzyzzzzzzyzzyzzzzzzznzzzzzzzzzzzzzzznzzzzznzizzzzzzizzzyzzzzzzzzynzzzi\n176\n",
"mrtoudai\n2837967\n",
"vnwmvvmonv\n11277\n",
"sgjzgbvvsztjqsrnqqgsvcgmxyvxjbxvvszjxx\n40437\n",
"oyxbepxbeqaqpzwwzugzwwisxngkwegnqgbweqokoxpkxkkeqoqtwgxsgekgnasiwzguzwwazaxebxyo\n17966\n",
"mvvxvqzxqvmqqmjljmqzxxqvxxmmqxqjzzxmmmqqqqmxzxqmxqzdvzqvqqqqqqxxmxjjlvvljljmxxxqqqqqvqvdzqxmrxvzxmqxqmmmzxzzjxxqmmqxvzqxxzqmqjljmqqvmjqxzqvv\n38\n",
"ttankyoumrkihayuta\n39\n",
"stat\n15\n",
"ixiwi\n8\n",
"ee\n2\n",
"wanwdnnwnnwinwaxaadnwawiaiawwwiniiwnxiwdnawnaiiiwywiwnyindan\n583381605\n",
"zennyuu\n215597\n",
"sljme\n41\n",
"level\n11\n",
"dddddzdzdddeddddddddddddddddddddddbddddddddbdddddddddddddddddddbdb\n20\n",
"rrlmorlrmjmlzlfzfrmolmzzmefflrrzojmllrzmfzrjffoofflrororlffolfeojmzfzorzllrolzzrflfleomzflrlmrffllzfmlfmlmf\n251851\n",
"yu\n1100000000\n",
"urkitaymtasgift\n2500\n",
"ljszsxovlxdsdsjvaufyfftmoyfuyaplpzxjucujxzplpayufyomtffyfuavjsdsdxlvoxszsjl\n1050\n",
"wiiisiiiuoiiiiitixiiv\n484293\n",
"qi\n1\n",
"zzz\n284166737\n",
"dog\n2\n",
"ipzmkijimzipmjkjhctpckcjpkjkicbdtwpbkkzizpijzpbkidkcghckdikbpzjipzizkkbpwtdbcikjkpjckcptchjkjmpizmijikmzpi\n209\n",
"jewiiwefj\n5283\n",
"palindrome\n122100747\n",
"pppppppppppppppppppppppppppppppppppppppppppppppcpppppppppppppppppppppppppppppcppppppplpppppppppppppppppppppqppppppppppppppppppa\n1515688\n",
"cudeforcesroond\n286\n",
"nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnngnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnz\n325363824\n",
"ccxsecrxosqsrsoolxzcoolqllexxssxqoqeqkocerchlxckqschxxczlxscoxhszsoxzxrzohsccsclocxxzshrhzoexxhrohqrrqhorhxxeozhrhszxxcolcsccshozrxzxoszshxocsxlzcxxhcsqkcxlhcrecokqeqoqxssxxellqlooczxloosrsqsoxrcesxcc\n917296611\n",
"ussiudlvjsdjduujuljvdrdljdjluarusdaiiujjsdudjslpmujdspixxljjjuiqasjlsxpppspuisdaljjxsiqqujudjljxlmqjjqmlxjljdujuqqisxjjladsiupspppxsljsaqiujjjlxxipsdjumplsjdudsjjuiiadsurauljdjldrdvjlujuudjdsjvlduissu\n7828\n",
"gggmmggmgjjmmjggglmmgmjmjjgggkjmmjgmmmmjmmmgggmmgjjjmjjmmmkmmmkgmggmgmjmmmgggjmmgggggjmmmkgggggmgmgjgggmmmmmgmggmmgmjmjgmmgjjjmjggmgggggmmmmgmjgmjjkgggmjmjmmmmmmmmjjgmggmmggg\n889615\n",
"isssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss\n67106614\n",
"mxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxwxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx\n469761845\n",
"qqqqqqqqqqqqqqiqqqqqqiqqqqqqqqqqqqqqqqqqqqqqqiqqqiqqqqqqqqiqqqqqqqqqqqqqqqqqiqqqqqqqqqqqqqiqqqqqqqqqqqqqqqqqqqqqqqqqqiqqqqqqqqqqqqqqqiqqqqqqqqqqqqqqqqqqqqqiqqqqqqqqqqqqqqqqqqqqqqqqqqqqqiqqqqqiqqqqqqqi\n58223707\n",
"mooooooooojoooowooooooooooomooooooooocoooooooooooooooolooooooooooooooooooooopoooooooooooooooooooooooooooooooooooooooooooooioooooooooooouoooojoooooojooooooooomooooolodokoooooooooooocooooooooooomoooooo\n84\n",
"yttyysttyyttttsytytyyttysstttstyttssttsytyttststyssyysttyyttstytttstststttttttytttststttttttytttyttttttytttytttttttststttytttttttstststttytsttyyttsyyssytststtytysttssttytstttssyttyytytysttttyyttsyytty\n6672\n",
"hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhghhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhghhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhht\n536870709\n",
"nhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhvhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh\n85791895\n",
"xxxxxyxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxkxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxt\n536870677\n",
"olnrttrnnptltrxooobokxrrtoxrnnrlxnxnkkddnslonolnxlxnsolrvlsslnxofoxofrcttnlxrordloxtnxvoonsloptksorvrosktpolsnoovxntwoldrorxlnttcrfoxofoxnlsslvrlosnxlxnlonolsnddkknxnxlrnnrxotrrxkoboooxrtltpnnrttrnlo\n61309576\n",
"qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq\n627827\n",
"xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxyxxxxxxxxxxxxxxxxxxxxxkxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxt\n66977589\n",
"sssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssstssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssl\n536870709\n",
"qkqiiwkwqivqkdfiimkqiwkimikfkkvoivwvilvmiwwqkvqvidimwiddwqqqqkqqkviqldiqqoqvwqvktwiqkqiwfkitoitkqiowoiqktiotikfwiqkqiwtkvqwvqoqqidlqivkqqkqqqqwddiwmidivqvkqwwimvlivvviovkkfkimikwiqkmiifdkqviqwkwiiqkq\n671088441\n",
"sssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssi\n407618340\n",
"yryralvogdsfsfdonrrofkkssfgvfsrslrrdsggfygddsykgrrdaovyydddadvsdrfogdygsrsydysokafrddssykakhangyasgsfnygrsrddffkdsvvvfsrrrdydflkyryydgadrasndsraanoldgffgfdsgrydsfrdrfglgffrfryngfygvoordravyyryfrnfrrky\n5481\n",
"ppppppppvppppppppkpppppppypppppppypoppppppppvppvpyyprppppppnppppppppppoppppppppzzppppppppppzoy\n1\n",
"evima\n1\n",
"prewcdcwe\n1\n",
"fft\n0\n",
"b\n1\n",
"hogloid\n1\n",
"shureki\n4\n",
"opmatuy\n3\n",
"cszaetjydpkfzbihfzjmsfklibikgskhdfdrfgorggirpcmshkgicyjzjkkakmhfjasyrrbmabbdzsgyqkzgkehzasosaztcazvpfbiabfpojtbkgrvztkvsgzcgmimgskztceeghubbacrjlzzskffaskgvzsdckkphszibtajfrcldeyakgvkdhphhliayzszhghzt\n49\n",
"ttat\n",
"{zz\n",
"ewiver\n",
"jewijwefj\n",
"evimb\n",
"bcb\n",
"yusopo\n"
],
"output": [
"adda\n",
"reviver\n",
"nooon\n",
"lsdijfjidsl\n",
"lsdijfjidsl\n",
"NA\n",
"NA\n",
"cnonnpbnpptppgntggttggtngpptppnbpnnonc\n",
"kk\n",
"nevceypryxidfffdixyrpyecven\n",
"NA\n",
"irrjoktogwxektwrfihfjtertgdhttktrgiwtgttwkjthkewwewtrefejwforhwfjkrkifxkhtoggothkxfikrkjfwhrofwjefertwewwekhtjkwttgtwigrtktthdgtretjfhifrwtkexwgotkojrri\n",
"nqwcvvcwqn\n",
"bbbhbbibhjjjhbibbhbbb\n",
"bxyfyfokfzycqtqfatolwxccaqnsncaqnqkztjsksocflsxzzzxslfcosksjtzkqnqacnsnqaccxwlotafqtqcyzfkofyfyxb\n",
"NA\n",
"zlllzzzzzlzzzzllllzzzllzlzzzzzlzlllzzlzzlllzlllzzllzzlllzlzlzzzllllzlzzzzlllzlzlllzlzlllzzzzlzllllzzzlzlzlllzzllzzlllzlllzzlzzlllzlzzzzzlzllzzzllllzzzzlzzzzzlllz\n",
"NA\n",
"NA\n",
"NA\n",
"NA\n",
"NA\n",
"NA\n",
"NA\n",
"NA\n",
"tfft\n",
"raceecar\n",
"NA\n",
"eeeeee\n",
"aa\n",
"NA\n",
"bb\n",
"NA\n",
"NA\n",
"NA\n",
"NA\n",
"NA\n",
"NA\n",
"NA\n",
"NA\n",
"stats\n",
"iwiiwi\n",
"eee\n",
"NA\n",
"NA\n",
"NA\n",
"levvel\n",
"NA\n",
"NA\n",
"uyu\n",
"NA\n",
"NA\n",
"ljszsxovlxdsdsjvaufyfftmoyfuyaplpzxjuccujxzplpayufyomtffyfuavjsdsdxlvoxszsjl\n",
"NA\n",
"qiq\n",
"zzzz\n",
"NA\n",
"ipzmkijimzipmjkjhctpckcjpkjkicbdtwpbkkzizpijzpbkidkchhhckdikbpzjipzizkkbpwtdbcikjkpjckcptchjkjmpizmijikmzpi\n",
"jfewiiwefj\n",
"NA\n",
"NA\n",
"NA\n",
"NA\n",
"ccxsecrxosqsrsoolxzcoolqllexxssxqoqeqkocerchlxckqschxxczlxscoxhszsoxzxrzohsccsclocxxzshrhzoexxhrohqrrrqhorhxxeozhrhszxxcolcsccshozrxzxoszshxocsxlzcxxhcsqkcxlhcrecokqeqoqxssxxellqlooczxloosrsqsoxrcesxcc\n",
"ussiudlvjsdjduujuljvdrdljdjluarusdaiiujjsdudjslpmujdspixxljjjuiqasjlsxpppspuisdaljjxsiqqujudjljxlmqjjjqmlxjljdujuqqisxjjladsiupspppxsljsaqiujjjlxxipsdjumplsjdudsjjuiiadsurauljdjldrdvjlujuudjdsjvlduissu\n",
"NA\n",
"NA\n",
"isssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssi\n",
"stats\n",
"zzzz\n",
"mxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxm\n",
"reviver\n",
"NA\n",
"NA\n",
"yttyysttyyttttsytytyyttysstttstyttssttsytyttststyssyysttyyttstytttstststttttttytttststttttttytttytttttttytttytttttttststttytttttttstststttytsttyyttsyyssytststtytysttssttytstttssyttyytytysttttyyttsyytty\n",
"NA\n",
"NA\n",
"NA\n",
"olnrttrnnptltrxooobokxrrtoxrnnrlxnxnkkddnslonolnxlxnsolrvlsslnxofoxofrcttnlxrordloxtnxvoonsloptksorvvrosktpolsnoovxntxoldrorxlnttcrfoxofoxnlsslvrlosnxlxnlonolsnddkknxnxlrnnrxotrrxkoboooxrtltpnnrttrnlo\n",
"qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq\n",
"NA\n",
"jfewiiwefj\n",
"lsssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssl\n",
"qkqiiwkwqivqkdfiimkqiwkimikfkkvoivwvilvmiwwqkvqvidimwiddwqqqqkqqkviqldiqqoqvwqvktwiqkqiwfkitoitkqiowwoiqktiotikfwiqkqiwtkvqwvqoqqidlqivkqqkqqqqwddiwmidivqvkqwwimvlivwviovkkfkimikwiqkmiifdkqviqwkwiiqkq\n",
"NA\n",
"bbbb\n",
"isssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssi\n",
"NA\n",
"NA\n",
"NA\n",
"NA\n",
"btmtbrrmmmbmtprmtbrrrmllttlrprmpmptprmmbtmmmtmtbbmbtrtbbrbtmttltttmtbmbrrtmtbmmbmtlrmlmbmbtmmmbbttbttbttbbmmmtbmbmlmrltmbmmbtmtrrbmbtmtttlttmtbrbbtrtbmbbtmtmmmtbmmrptpmpmrprlttllmrrrbtmrptmbmmmrrbtmtb\n",
"prrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrp\n",
"NA\n",
"nqwcvvcwqn\n",
"NA\n",
"NA\n",
"mxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxm\n",
"xmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmx\n",
"NA\n",
"NA\n",
"NA\n",
"aa\n",
"NA\n",
"NA\n",
"lgllsggozxlzotlgozolxlloiozigtxloolzggxgoloixgllgxzzgtoxioxizggoogzozlzlfolzlloxlxotogllllgotoxlxollzloflzlzozgooggzixoixotgzzxgllgxiologxggzloolxtgizoiollxlozogltozlxzoggsllgl\n",
"NA\n",
"lsdijfjidsl\n",
"iwiiwi\n",
"NA\n",
"aaaaaa\n",
"ydydvoddlvjqdmvszssdozedvqmvqlyvvqlzqzsazqyslavmdlovqoylezcqvlsvmqqmvvdvjsdsdvvszavaszldqvmxmsvmvddyyyddvmvsmxmvqdlzsavazsvvdsdsjvdvvmqqmvslvqczelyoqvoldmvalsyqzaszqzlqvvylqvmqvdezodsszsvmdqjvlddovdydy\n",
"NA\n",
"NA\n",
"NA\n",
"qiq\n",
"NA\n",
"qaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaq\n",
"NA\n",
"NA\n",
"mjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjm\n",
"utttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttu\n",
"NA\n",
"eee\n",
"NA\n",
"NA\n",
"NA\n",
"NA\n",
"NA\n",
"NA\n",
"NA\n",
"reviver\n",
"NA\n",
"zaaz\n",
"raceecar\n",
"nooon\n",
"xmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmx\n",
"NA\n",
"dkvulkdhmdloduumhqdmludvflmvldvddmmmtkulhduoluulmmlfvmqvfvkddmtumhvfdqluhdohlludvkffkvdullhodhulqdfvhmutmddkvfvqmvflmmluuloudhluktmmmddvdlvmlfvdulmdqhmuudoldmhdkluvkd\n",
"abattaba\n",
"NA\n",
"NA\n",
"NA\n",
"NA\n",
"zz\n",
"levvel\n",
"mjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjm\n",
"NA\n",
"NA\n",
"susssskllsskrsbukkllrlssususukssukslblbsukbuurlsskkksbsrsubukusuklursluslskruuksskrslublkruklulkrbksskbrklulkurklbulsrksskuurkslsulsrulkusukubusrsbskkksslruubkusblblskusskusususslrllkkubsrkssllkssssus\n",
"NA\n",
"NA\n",
"hjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjh\n",
"xgggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggx\n",
"NA\n",
"dhhddddddhddhhhdhdddhdhhhddhdhdddhhhdhddddhddhhhhdhdddhhdhhddddhhddhhhdhhddddddhdddddddhdhddhhdhhdddddddhhdhhddhdhdddddddhddddddhhdhhhddhhddddhhdhhdddhdhhhhddhddddhdhhhdddhdhddhhhdhdddhdhhhddhddddddhhd\n",
"NA\n",
"NA\n",
"kiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiik\n",
"lsssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssl\n",
"hjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjh\n",
"babccbab\n",
"NA\n",
"unnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnu\n",
"qaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaq\n",
"adda\n",
"tfft\n",
"kiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiik\n",
"NA\n",
"NA\n",
"eeee\n",
"NA\n",
"4006\n",
"1\n",
"2009\n",
"783\n",
"9695\n",
"4069\n",
"6344\n",
"4993\n",
"0\n",
"4102\n",
"1870\n",
"3558\n",
"4125\n",
"4945\n",
"26\n",
"7997\n",
"9306\n",
"1877\n",
"12\n",
"5295\n",
"9932\n",
"3110\n",
"6148\n",
"4274\n",
"6643\n",
"1732\n",
"4607\n",
"5381\n",
"54\n",
"6081\n",
"1952\n",
"3888\n",
"4901\n",
"51\n",
"6599\n",
"7330\n",
"5345\n",
"9161\n",
"5640\n",
"1841\n",
"293\n",
"7\n",
"6062\n",
"2891\n",
"2\n",
"8028\n",
"4\n",
"19\n",
"3612\n",
"4461\n",
"5742\n",
"5685\n",
"9860\n",
"7208\n",
"2913\n",
"2653\n",
"7381\n",
"8801\n",
"1759\n",
"2910\n",
"383\n",
"8217\n",
"2727\n",
"8849\n",
"745\n",
"7008\n",
"6911\n",
"9213\n",
"5207\n",
"9646\n",
"5515\n",
"0\n",
"0\n",
"0\n",
"0\n",
"1\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"1\n",
"0\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Mr. Kitayuta has kindly given you a string s consisting of lowercase English letters. You are asked to insert exactly n lowercase English letters into s to make it a palindrome. (A palindrome is a string that reads the same forward and backward. For example, "noon", "testset" and "a" are all palindromes, while "test" and "kitayuta" are not.) You can choose any n lowercase English letters, and insert each of them to any position of s, possibly to the beginning or the end of s. You have to insert exactly n letters even if it is possible to turn s into a palindrome by inserting less than n letters.
Find the number of the palindromes that can be obtained in this way, modulo 10007.
Input
The first line contains a string s (1 ≤ |s| ≤ 200). Each character in s is a lowercase English letter.
The second line contains an integer n (1 ≤ n ≤ 109).
Output
Print the number of the palindromes that can be obtained, modulo 10007.
Examples
Input
revive
1
Output
1
Input
add
2
Output
28
Note
For the first sample, you can obtain the palindrome "reviver" by inserting 'r' to the end of "revive".
For the second sample, the following 28 palindromes can be obtained: "adada", "adbda", ..., "adzda", "dadad" and "ddadd".
### Input:
add
2
### Output:
adda
### Input:
revive
1
### Output:
reviver
### Code:
palindrom = lambda s: s == s[::-1]
printans = lambda l: print(''.join(l))
s = list(input())
for i in range(len(s)+1):
for letter in 'abcdefghijklmnopqrstvwuxyz':
tmp = s[:]
tmp.insert(i,letter)
if palindrom(tmp):
printans(tmp)
exit()
print('NA')
|
556_A. Case of the Zeros and Ones_10598
|
Andrewid the Android is a galaxy-famous detective. In his free time he likes to think about strings containing zeros and ones.
Once he thought about a string of length n consisting of zeroes and ones. Consider the following operation: we choose any two adjacent positions in the string, and if one them contains 0, and the other contains 1, then we are allowed to remove these two digits from the string, obtaining a string of length n - 2 as a result.
Now Andreid thinks about what is the minimum length of the string that can remain after applying the described operation several times (possibly, zero)? Help him to calculate this number.
Input
First line of the input contains a single integer n (1 ≤ n ≤ 2·105), the length of the string that Andreid has.
The second line contains the string of length n consisting only from zeros and ones.
Output
Output the minimum length of the string that may remain after applying the described operations several times.
Examples
Input
4
1100
Output
0
Input
5
01010
Output
1
Input
8
11101111
Output
6
Note
In the first sample test it is possible to change the string like the following: <image>.
In the second sample test it is possible to change the string like the following: <image>.
In the third sample test it is possible to change the string like the following: <image>.
|
n = int(input())
s = input()
x = s.count('0')
y = s.count('1')
print(abs(x-y))
|
{
"input": [
"4\n1100\n",
"8\n11101111\n",
"5\n01010\n",
"7\n1110000\n",
"1\n0\n",
"6\n110110\n",
"2\n11\n",
"8\n01011100\n",
"2\n00\n",
"6\n110100\n",
"6\n010111\n",
"3\n001\n",
"6\n110010\n",
"1\n1\n",
"6\n001011\n",
"9\n011111101\n",
"2\n10\n",
"2\n01\n",
"7\n0000011\n",
"3\n100\n",
"7\n1110010\n",
"6\n110111\n",
"8\n11011100\n",
"6\n010110\n",
"9\n011111111\n",
"3\n000\n",
"9\n011101111\n",
"6\n000000\n",
"6\n111100\n",
"3\n011\n",
"6\n010010\n",
"6\n101011\n",
"7\n0100011\n",
"4\n1101\n",
"8\n01101111\n",
"5\n01011\n",
"7\n1110011\n",
"6\n110101\n",
"8\n10011100\n",
"6\n101100\n",
"6\n000110\n",
"3\n010\n",
"6\n010011\n",
"6\n101001\n",
"7\n0100010\n",
"3\n110\n",
"4\n1111\n",
"8\n01001111\n",
"5\n01001\n",
"7\n0110011\n",
"6\n111101\n",
"8\n10011101\n",
"6\n101110\n",
"6\n011111\n",
"3\n101\n",
"6\n000011\n",
"6\n111001\n",
"9\n011101101\n",
"7\n0101011\n",
"3\n111\n",
"4\n0111\n",
"8\n01001101\n",
"5\n01101\n",
"7\n0110001\n",
"6\n101101\n",
"8\n10111100\n",
"6\n101111\n",
"6\n010001\n",
"6\n000111\n",
"6\n011001\n",
"9\n001101101\n",
"7\n0101111\n",
"4\n1011\n",
"8\n01001001\n",
"5\n11101\n",
"7\n0110000\n",
"6\n101000\n",
"8\n10110100\n",
"6\n100111\n",
"6\n000001\n",
"6\n000101\n",
"6\n111000\n",
"9\n001111101\n",
"7\n0001111\n",
"4\n0011\n",
"8\n00001101\n",
"5\n10101\n",
"7\n0100000\n",
"6\n101010\n",
"8\n10110110\n",
"6\n001111\n",
"6\n001110\n",
"6\n000100\n",
"6\n011000\n",
"9\n001011101\n",
"7\n0001011\n",
"4\n0001\n",
"8\n01011101\n",
"5\n11001\n",
"7\n0100100\n",
"6\n001010\n",
"8\n10110010\n",
"6\n011110\n",
"6\n000010\n",
"6\n011011\n",
"9\n011011101\n",
"7\n0011011\n",
"4\n1001\n",
"8\n01010101\n",
"5\n01000\n"
],
"output": [
"0",
"6",
"1",
"1",
"1",
"2",
"2",
"0",
"2",
"0",
"2",
"1",
"0",
"1",
"0",
"5",
"0",
"0",
"3",
"1\n",
"1\n",
"4\n",
"2\n",
"0\n",
"7\n",
"3\n",
"5\n",
"6\n",
"2\n",
"1\n",
"2\n",
"2\n",
"1\n",
"2\n",
"4\n",
"1\n",
"3\n",
"2\n",
"0\n",
"0\n",
"2\n",
"1\n",
"0\n",
"0\n",
"3\n",
"1\n",
"4\n",
"2\n",
"1\n",
"1\n",
"4\n",
"2\n",
"2\n",
"4\n",
"1\n",
"2\n",
"2\n",
"3\n",
"1\n",
"3\n",
"2\n",
"0\n",
"1\n",
"1\n",
"2\n",
"2\n",
"4\n",
"2\n",
"0\n",
"0\n",
"1\n",
"3\n",
"2\n",
"2\n",
"3\n",
"3\n",
"2\n",
"0\n",
"2\n",
"4\n",
"2\n",
"0\n",
"3\n",
"1\n",
"0\n",
"2\n",
"1\n",
"5\n",
"0\n",
"2\n",
"2\n",
"0\n",
"4\n",
"2\n",
"1\n",
"1\n",
"2\n",
"2\n",
"1\n",
"3\n",
"2\n",
"0\n",
"2\n",
"4\n",
"2\n",
"3\n",
"1\n",
"0\n",
"0\n",
"3\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Andrewid the Android is a galaxy-famous detective. In his free time he likes to think about strings containing zeros and ones.
Once he thought about a string of length n consisting of zeroes and ones. Consider the following operation: we choose any two adjacent positions in the string, and if one them contains 0, and the other contains 1, then we are allowed to remove these two digits from the string, obtaining a string of length n - 2 as a result.
Now Andreid thinks about what is the minimum length of the string that can remain after applying the described operation several times (possibly, zero)? Help him to calculate this number.
Input
First line of the input contains a single integer n (1 ≤ n ≤ 2·105), the length of the string that Andreid has.
The second line contains the string of length n consisting only from zeros and ones.
Output
Output the minimum length of the string that may remain after applying the described operations several times.
Examples
Input
4
1100
Output
0
Input
5
01010
Output
1
Input
8
11101111
Output
6
Note
In the first sample test it is possible to change the string like the following: <image>.
In the second sample test it is possible to change the string like the following: <image>.
In the third sample test it is possible to change the string like the following: <image>.
### Input:
4
1100
### Output:
0
### Input:
8
11101111
### Output:
6
### Code:
n = int(input())
s = input()
x = s.count('0')
y = s.count('1')
print(abs(x-y))
|
581_E. Kojiro and Furrari_10602
|
Motorist Kojiro spent 10 years saving up for his favorite car brand, Furrari. Finally Kojiro's dream came true! Kojiro now wants to get to his girlfriend Johanna to show off his car to her.
Kojiro wants to get to his girlfriend, so he will go to her along a coordinate line. For simplicity, we can assume that Kojiro is at the point f of a coordinate line, and Johanna is at point e. Some points of the coordinate line have gas stations. Every gas station fills with only one type of fuel: Regular-92, Premium-95 or Super-98. Thus, each gas station is characterized by a pair of integers ti and xi — the number of the gas type and its position.
One liter of fuel is enough to drive for exactly 1 km (this value does not depend on the type of fuel). Fuels of three types differ only in quality, according to the research, that affects the lifetime of the vehicle motor. A Furrari tank holds exactly s liters of fuel (regardless of the type of fuel). At the moment of departure from point f Kojiro's tank is completely filled with fuel Super-98. At each gas station Kojiro can fill the tank with any amount of fuel, but of course, at no point in time, the amount of fuel in the tank can be more than s liters. Note that the tank can simultaneously have different types of fuel. The car can moves both left and right.
To extend the lifetime of the engine Kojiro seeks primarily to minimize the amount of fuel of type Regular-92. If there are several strategies to go from f to e, using the minimum amount of fuel of type Regular-92, it is necessary to travel so as to minimize the amount of used fuel of type Premium-95.
Write a program that can for the m possible positions of the start fi minimize firstly, the amount of used fuel of type Regular-92 and secondly, the amount of used fuel of type Premium-95.
Input
The first line of the input contains four positive integers e, s, n, m (1 ≤ e, s ≤ 109, 1 ≤ n, m ≤ 2·105) — the coordinate of the point where Johanna is, the capacity of a Furrari tank, the number of gas stations and the number of starting points.
Next n lines contain two integers each ti, xi (1 ≤ ti ≤ 3, - 109 ≤ xi ≤ 109), representing the type of the i-th gas station (1 represents Regular-92, 2 — Premium-95 and 3 — Super-98) and the position on a coordinate line of the i-th gas station. Gas stations don't necessarily follow in order from left to right.
The last line contains m integers fi ( - 109 ≤ fi < e). Start positions don't necessarily follow in order from left to right.
No point of the coordinate line contains more than one gas station. It is possible that some of points fi or point e coincide with a gas station.
Output
Print exactly m lines. The i-th of them should contain two integers — the minimum amount of gas of type Regular-92 and type Premium-95, if Kojiro starts at point fi. First you need to minimize the first value. If there are multiple ways to do it, you need to also minimize the second value.
If there is no way to get to Johanna from point fi, the i-th line should look like that "-1 -1" (two numbers minus one without the quotes).
Examples
Input
8 4 1 1
2 4
0
Output
0 4
Input
9 3 2 3
2 3
1 6
-1 0 1
Output
-1 -1
3 3
3 2
Input
20 9 2 4
1 5
2 10
-1 0 1 2
Output
-1 -1
-1 -1
-1 -1
-1 -1
|
import os,io
input=io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
e,s,n,m=map(int,input().split())
fuel1=[]
fuel2=[]
fuel3=[]
keymoments=[]
for i in range(n):
t,x=map(int,input().split())
if t==1:
fuel1.append(x)
if t==2:
fuel2.append(x)
if t==3:
fuel3.append(x)
keymoments.append(x)
keymoments.append(x+s)
fuel1.sort()
fuel2.sort()
fuel3.sort()
keymoments.sort()
pointer1=-1
pointer2=-1
pointer3=-1
last1=-10**9-1
last2=-10**9-1
last3=-10**9-1
keymoments2=[]
lastmoment=-10**9-1
for moment in keymoments:
if moment==lastmoment:
continue
lastmoment=moment
while pointer1+1<len(fuel1) and fuel1[pointer1+1]<=moment:
last1=fuel1[pointer1+1]
pointer1+=1
while pointer2+1<len(fuel2) and fuel2[pointer2+1]<=moment:
last2=fuel2[pointer2+1]
pointer2+=1
while pointer3+1<len(fuel3) and fuel3[pointer3+1]<=moment:
last3=fuel3[pointer3+1]
pointer3+=1
if pointer3!=-1 and moment<s+last3:
keymoments2.append([moment,3])
elif pointer2!=-1 and moment<s+last2:
keymoments2.append([moment,2])
elif pointer1!=-1 and moment<s+last1:
keymoments2.append([moment,1])
else:
keymoments2.append([moment,-1])
keymoments3=[]
start=10**9
for i in range(len(keymoments2)-1,-1,-1):
if e>keymoments2[i][0]:
start=i
break
if not start==10**9:
fuel1use=0
fuel2use=0
if keymoments2[start][1]==1:
fuel1use+=e-keymoments2[start][0]
elif keymoments2[start][1]==2:
fuel2use+=e-keymoments2[start][0]
elif keymoments2[start][1]==-1:
fuel1use=-1
fuel2use=-1
moment=keymoments2[start][0]
keymoments3.append([moment,fuel1use,fuel2use])
for i in range(start-1,-1,-1):
moment=keymoments2[i][0]
if fuel1use==-1:
keymoments3.append([moment,-1,-1])
continue
time=keymoments2[i+1][0]-moment
if time>s:
fuel1use=-1
fuel2use=-1
keymoments3.append([moment,-1,-1])
continue
if keymoments2[i][1]==1:
fuel1use+=time
elif keymoments2[i][1]==2:
fuel2use+=time
elif keymoments2[i][1]==-1:
fuel1use=-1
fuel2use=-1
keymoments3.append([moment,fuel1use,fuel2use])
keymoments3.reverse()
f=list(map(int,input().split()))
for i in range(m):
if f[i]+s>=e:
print(0,0)
continue
if not keymoments3:
print(-1,-1)
continue
if f[i]+s<keymoments3[0][0]:
print(-1,-1)
continue
l=0
r=len(keymoments3)-1
while l<r:
if l+1==r:
try1=r
else:
try1=(l+r)//2
if f[i]+s>=keymoments2[try1][0]:
l=try1
else:
if l+1==r:
l=l
break
r=try1
ans1=keymoments3[l][1]
ans2=keymoments3[l][2]
if ans1!=-1 and keymoments2[l][1]==1:
ans1+=keymoments3[l][0]-(f[i]+s)
elif ans2!=-1 and keymoments2[l][1]==2:
ans2+=keymoments3[l][0]-(f[i]+s)
print(ans1,ans2)
|
{
"input": [
"9 3 2 3\n2 3\n1 6\n-1 0 1\n",
"20 9 2 4\n1 5\n2 10\n-1 0 1 2\n",
"8 4 1 1\n2 4\n0\n",
"386 20 29 30\n1 349\n2 482\n1 112\n1 93\n2 189\n1 207\n2 35\n2 -5\n1 422\n1 442\n1 402\n2 238\n3 258\n3 54\n2 369\n2 290\n2 329\n3 74\n3 -62\n2 170\n1 462\n2 15\n2 222\n1 309\n3 150\n1 -25\n3 130\n1 271\n1 -43\n351 250 91 102 0 286 123 93 100 205 328 269 188 83 73 35 188 223 73 215 199 64 47 379 61 298 295 65 158 211\n",
"67 10 9 10\n3 -1\n1 59\n1 39\n1 -11\n2 29\n1 9\n1 19\n1 49\n3 77\n27 14 21 36 0 13 57 41 20 28\n",
"1000000000 1 1 1\n3 775565805\n0\n",
"18 9 2 1\n2 9\n1 12\n0\n",
"216 15 19 10\n2 -31\n2 100\n3 230\n1 57\n3 42\n1 157\n2 186\n1 113\n2 -16\n3 245\n2 142\n1 86\n2 -3\n3 201\n3 128\n3 12\n3 171\n2 27\n2 72\n98 197 114 0 155 35 36 11 146 27\n",
"18 9 2 1\n1 9\n2 12\n0\n",
"1000000000 2 5 5\n2 118899563\n2 -442439384\n1 -961259426\n2 -156596184\n1 -809672605\n249460520 -545686472 0 -653929719 905155526\n",
"9 3 2 1\n2 3\n1 6\n0\n",
"67 10 9 10\n3 -1\n1 96\n1 39\n1 -11\n2 29\n1 9\n1 19\n1 49\n3 77\n27 14 21 36 0 13 57 41 20 28\n",
"18 0 2 1\n2 9\n1 12\n0\n",
"216 15 19 10\n2 -31\n2 100\n3 230\n1 57\n3 34\n1 157\n2 186\n1 113\n2 -16\n3 245\n2 142\n1 86\n2 -3\n3 201\n3 128\n3 12\n3 171\n2 27\n2 72\n98 197 114 0 155 35 36 11 146 27\n",
"9 4 2 1\n2 3\n1 6\n0\n",
"9 3 2 3\n2 3\n1 9\n-1 0 1\n",
"20 9 2 4\n1 5\n2 14\n-1 0 1 2\n",
"216 15 19 10\n2 -31\n2 100\n3 230\n1 57\n3 34\n1 157\n2 186\n1 113\n2 -16\n3 245\n2 142\n1 86\n2 -3\n3 201\n3 128\n3 12\n3 171\n2 27\n2 72\n98 197 114 0 155 35 66 11 146 27\n",
"20 9 2 4\n1 5\n2 14\n-1 0 2 2\n",
"37 9 2 4\n1 5\n2 14\n-1 0 2 2\n",
"92 10 9 10\n3 -1\n1 96\n2 39\n1 -11\n2 2\n1 9\n1 19\n2 49\n3 50\n27 14 21 36 1 13 57 3 14 30\n",
"67 10 9 10\n3 -1\n1 59\n1 39\n1 -11\n2 29\n1 9\n1 19\n1 49\n3 77\n27 14 21 40 0 13 57 41 20 28\n",
"29 9 2 1\n1 9\n2 12\n0\n",
"67 10 9 10\n3 -1\n1 96\n1 39\n1 -11\n2 29\n1 9\n1 19\n1 49\n3 77\n27 14 21 36 1 13 57 41 20 28\n",
"29 9 2 1\n1 9\n2 18\n0\n",
"9 4 2 1\n2 6\n1 6\n0\n",
"9 3 2 3\n2 3\n1 9\n0 0 1\n",
"67 10 9 10\n3 -1\n1 96\n1 39\n1 -11\n2 29\n1 9\n1 19\n1 49\n3 77\n27 14 21 36 1 13 57 3 20 28\n",
"216 15 19 10\n2 -31\n2 100\n3 230\n1 57\n3 34\n1 157\n2 186\n1 113\n2 -16\n3 245\n2 142\n1 86\n2 -1\n3 201\n3 128\n3 12\n3 171\n2 27\n2 72\n98 197 114 0 155 35 66 11 146 27\n",
"29 2 2 1\n1 9\n2 18\n0\n",
"67 10 9 10\n3 -1\n1 96\n1 39\n1 -11\n2 29\n1 9\n1 19\n1 49\n3 77\n27 14 21 36 1 13 57 3 22 28\n",
"216 15 19 10\n1 -31\n2 100\n3 230\n1 57\n3 34\n1 157\n2 186\n1 113\n2 -16\n3 245\n2 142\n1 86\n2 -1\n3 201\n3 128\n3 12\n3 171\n2 27\n2 72\n98 197 114 0 155 35 66 11 146 27\n",
"29 2 2 1\n2 9\n2 18\n0\n",
"37 9 2 4\n1 5\n2 14\n-1 0 4 2\n",
"67 10 9 10\n3 -1\n1 96\n1 39\n1 -11\n2 29\n1 9\n1 19\n1 49\n3 77\n27 14 21 36 1 13 57 3 22 30\n",
"29 2 2 1\n1 9\n2 18\n1\n",
"37 9 2 4\n1 5\n2 14\n-1 0 0 2\n",
"67 10 9 10\n3 -1\n1 96\n1 39\n1 -11\n2 41\n1 9\n1 19\n1 49\n3 77\n27 14 21 36 1 13 57 3 22 30\n",
"29 2 2 1\n2 9\n2 18\n1\n",
"37 9 2 4\n1 5\n2 14\n-1 0 0 1\n",
"67 10 9 10\n3 -1\n1 96\n1 39\n1 -11\n2 41\n1 9\n1 19\n1 49\n3 50\n27 14 21 36 1 13 57 3 22 30\n",
"29 2 2 1\n2 9\n3 18\n0\n",
"37 9 2 4\n1 5\n2 14\n-1 -1 0 1\n",
"67 10 9 10\n3 -1\n1 96\n1 39\n1 -11\n2 5\n1 9\n1 19\n1 49\n3 50\n27 14 21 36 1 13 57 3 22 30\n",
"29 2 2 1\n2 9\n1 18\n0\n",
"37 9 2 4\n1 5\n2 14\n-2 -1 0 1\n",
"67 10 9 10\n3 -1\n1 96\n1 39\n1 -11\n2 5\n1 9\n1 19\n1 49\n3 50\n27 14 21 36 1 13 57 3 42 30\n",
"67 10 9 10\n3 -1\n1 96\n1 39\n1 -11\n2 5\n1 9\n1 19\n2 49\n3 50\n27 14 21 36 1 13 57 3 42 30\n",
"67 10 9 10\n3 -1\n1 96\n2 39\n1 -11\n2 5\n1 9\n1 19\n2 49\n3 50\n27 14 21 36 1 13 57 3 42 30\n",
"67 10 9 10\n3 -1\n1 96\n2 39\n1 -11\n2 5\n1 9\n1 19\n2 49\n3 50\n27 14 21 36 1 13 57 3 14 30\n",
"67 10 9 10\n3 -1\n1 96\n2 39\n1 -11\n2 2\n1 9\n1 19\n2 49\n3 50\n27 14 21 36 1 13 57 3 14 30\n",
"1000000000 2 1 1\n3 775565805\n0\n"
],
"output": [
"-1 -1\n3 3\n3 2\n",
"-1 -1\n-1 -1\n-1 -1\n-1 -1\n",
"0 4\n",
"0 15\n51 57\n83 132\n72 132\n100 166\n39 41\n64 132\n81 132\n74 132\n51 90\n20 18\n40 57\n64 94\n91 132\n100 132\n100 132\n64 94\n51 72\n100 132\n51 80\n54 93\n100 132\n100 132\n0 0\n100 132\n31 37\n34 37\n100 132\n64 124\n51 84\n",
"28 2\n33 10\n28 8\n21 0\n47 10\n34 10\n0 0\n16 0\n28 9\n28 1\n",
"-1 -1\n",
"0 9\n",
"27 31\n0 0\n14 29\n55 74\n1 15\n55 59\n55 59\n55 74\n10 15\n55 59\n",
"3 6\n",
"-1 -1\n-1 -1\n-1 -1\n-1 -1\n-1 -1\n",
"3 3\n",
"-1 -1\n-1 -1\n-1 -1\n-1 -1\n-1 -1\n-1 -1\n0 0\n-1 -1\n-1 -1\n-1 -1\n",
"-1 -1\n",
"27 31\n0 0\n14 29\n-1 -1\n1 15\n-1 -1\n-1 -1\n-1 -1\n10 15\n-1 -1\n",
"2 3\n",
"-1 -1\n-1 -1\n-1 -1\n",
"6 6\n5 6\n4 6\n3 6\n",
"27 31\n0 0\n14 29\n-1 -1\n1 15\n-1 -1\n40 50\n-1 -1\n10 15\n-1 -1\n",
"6 6\n5 6\n3 6\n3 6\n",
"-1 -1\n-1 -1\n-1 -1\n-1 -1\n",
"-1 -1\n-1 -1\n-1 -1\n-1 -1\n-1 -1\n-1 -1\n-1 -1\n-1 -1\n-1 -1\n-1 -1\n",
"28 2\n33 10\n28 8\n17 0\n47 10\n34 10\n0 0\n16 0\n28 9\n28 1\n",
"-1 -1\n",
"-1 -1\n-1 -1\n-1 -1\n-1 -1\n-1 -1\n-1 -1\n0 0\n-1 -1\n-1 -1\n-1 -1\n",
"-1 -1\n",
"-1 -1\n",
"-1 -1\n-1 -1\n-1 -1\n",
"-1 -1\n-1 -1\n-1 -1\n-1 -1\n-1 -1\n-1 -1\n0 0\n-1 -1\n-1 -1\n-1 -1\n",
"27 31\n0 0\n14 29\n-1 -1\n1 15\n-1 -1\n40 50\n-1 -1\n10 15\n-1 -1\n",
"-1 -1\n",
"-1 -1\n-1 -1\n-1 -1\n-1 -1\n-1 -1\n-1 -1\n0 0\n-1 -1\n-1 -1\n-1 -1\n",
"27 31\n0 0\n14 29\n-1 -1\n1 15\n-1 -1\n40 50\n-1 -1\n10 15\n-1 -1\n",
"-1 -1\n",
"-1 -1\n-1 -1\n-1 -1\n-1 -1\n",
"-1 -1\n-1 -1\n-1 -1\n-1 -1\n-1 -1\n-1 -1\n0 0\n-1 -1\n-1 -1\n-1 -1\n",
"-1 -1\n",
"-1 -1\n-1 -1\n-1 -1\n-1 -1\n",
"-1 -1\n-1 -1\n-1 -1\n-1 -1\n-1 -1\n-1 -1\n0 0\n-1 -1\n-1 -1\n-1 -1\n",
"-1 -1\n",
"-1 -1\n-1 -1\n-1 -1\n-1 -1\n",
"-1 -1\n-1 -1\n-1 -1\n-1 -1\n-1 -1\n-1 -1\n0 0\n-1 -1\n-1 -1\n-1 -1\n",
"-1 -1\n",
"-1 -1\n-1 -1\n-1 -1\n-1 -1\n",
"-1 -1\n-1 -1\n-1 -1\n-1 -1\n-1 -1\n-1 -1\n0 0\n-1 -1\n-1 -1\n-1 -1\n",
"-1 -1\n",
"-1 -1\n-1 -1\n-1 -1\n-1 -1\n",
"-1 -1\n-1 -1\n-1 -1\n-1 -1\n-1 -1\n-1 -1\n0 0\n-1 -1\n-1 -1\n-1 -1\n",
"-1 -1\n-1 -1\n-1 -1\n-1 -1\n-1 -1\n-1 -1\n0 0\n-1 -1\n-1 -1\n-1 -1\n",
"-1 -1\n-1 -1\n-1 -1\n-1 -1\n-1 -1\n-1 -1\n0 0\n-1 -1\n-1 -1\n-1 -1\n",
"-1 -1\n-1 -1\n-1 -1\n-1 -1\n-1 -1\n-1 -1\n0 0\n-1 -1\n-1 -1\n-1 -1\n",
"-1 -1\n-1 -1\n-1 -1\n-1 -1\n-1 -1\n-1 -1\n0 0\n-1 -1\n-1 -1\n-1 -1\n",
"-1 -1\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Motorist Kojiro spent 10 years saving up for his favorite car brand, Furrari. Finally Kojiro's dream came true! Kojiro now wants to get to his girlfriend Johanna to show off his car to her.
Kojiro wants to get to his girlfriend, so he will go to her along a coordinate line. For simplicity, we can assume that Kojiro is at the point f of a coordinate line, and Johanna is at point e. Some points of the coordinate line have gas stations. Every gas station fills with only one type of fuel: Regular-92, Premium-95 or Super-98. Thus, each gas station is characterized by a pair of integers ti and xi — the number of the gas type and its position.
One liter of fuel is enough to drive for exactly 1 km (this value does not depend on the type of fuel). Fuels of three types differ only in quality, according to the research, that affects the lifetime of the vehicle motor. A Furrari tank holds exactly s liters of fuel (regardless of the type of fuel). At the moment of departure from point f Kojiro's tank is completely filled with fuel Super-98. At each gas station Kojiro can fill the tank with any amount of fuel, but of course, at no point in time, the amount of fuel in the tank can be more than s liters. Note that the tank can simultaneously have different types of fuel. The car can moves both left and right.
To extend the lifetime of the engine Kojiro seeks primarily to minimize the amount of fuel of type Regular-92. If there are several strategies to go from f to e, using the minimum amount of fuel of type Regular-92, it is necessary to travel so as to minimize the amount of used fuel of type Premium-95.
Write a program that can for the m possible positions of the start fi minimize firstly, the amount of used fuel of type Regular-92 and secondly, the amount of used fuel of type Premium-95.
Input
The first line of the input contains four positive integers e, s, n, m (1 ≤ e, s ≤ 109, 1 ≤ n, m ≤ 2·105) — the coordinate of the point where Johanna is, the capacity of a Furrari tank, the number of gas stations and the number of starting points.
Next n lines contain two integers each ti, xi (1 ≤ ti ≤ 3, - 109 ≤ xi ≤ 109), representing the type of the i-th gas station (1 represents Regular-92, 2 — Premium-95 and 3 — Super-98) and the position on a coordinate line of the i-th gas station. Gas stations don't necessarily follow in order from left to right.
The last line contains m integers fi ( - 109 ≤ fi < e). Start positions don't necessarily follow in order from left to right.
No point of the coordinate line contains more than one gas station. It is possible that some of points fi or point e coincide with a gas station.
Output
Print exactly m lines. The i-th of them should contain two integers — the minimum amount of gas of type Regular-92 and type Premium-95, if Kojiro starts at point fi. First you need to minimize the first value. If there are multiple ways to do it, you need to also minimize the second value.
If there is no way to get to Johanna from point fi, the i-th line should look like that "-1 -1" (two numbers minus one without the quotes).
Examples
Input
8 4 1 1
2 4
0
Output
0 4
Input
9 3 2 3
2 3
1 6
-1 0 1
Output
-1 -1
3 3
3 2
Input
20 9 2 4
1 5
2 10
-1 0 1 2
Output
-1 -1
-1 -1
-1 -1
-1 -1
### Input:
9 3 2 3
2 3
1 6
-1 0 1
### Output:
-1 -1
3 3
3 2
### Input:
20 9 2 4
1 5
2 10
-1 0 1 2
### Output:
-1 -1
-1 -1
-1 -1
-1 -1
### Code:
import os,io
input=io.BytesIO(os.read(0,os.fstat(0).st_size)).readline
e,s,n,m=map(int,input().split())
fuel1=[]
fuel2=[]
fuel3=[]
keymoments=[]
for i in range(n):
t,x=map(int,input().split())
if t==1:
fuel1.append(x)
if t==2:
fuel2.append(x)
if t==3:
fuel3.append(x)
keymoments.append(x)
keymoments.append(x+s)
fuel1.sort()
fuel2.sort()
fuel3.sort()
keymoments.sort()
pointer1=-1
pointer2=-1
pointer3=-1
last1=-10**9-1
last2=-10**9-1
last3=-10**9-1
keymoments2=[]
lastmoment=-10**9-1
for moment in keymoments:
if moment==lastmoment:
continue
lastmoment=moment
while pointer1+1<len(fuel1) and fuel1[pointer1+1]<=moment:
last1=fuel1[pointer1+1]
pointer1+=1
while pointer2+1<len(fuel2) and fuel2[pointer2+1]<=moment:
last2=fuel2[pointer2+1]
pointer2+=1
while pointer3+1<len(fuel3) and fuel3[pointer3+1]<=moment:
last3=fuel3[pointer3+1]
pointer3+=1
if pointer3!=-1 and moment<s+last3:
keymoments2.append([moment,3])
elif pointer2!=-1 and moment<s+last2:
keymoments2.append([moment,2])
elif pointer1!=-1 and moment<s+last1:
keymoments2.append([moment,1])
else:
keymoments2.append([moment,-1])
keymoments3=[]
start=10**9
for i in range(len(keymoments2)-1,-1,-1):
if e>keymoments2[i][0]:
start=i
break
if not start==10**9:
fuel1use=0
fuel2use=0
if keymoments2[start][1]==1:
fuel1use+=e-keymoments2[start][0]
elif keymoments2[start][1]==2:
fuel2use+=e-keymoments2[start][0]
elif keymoments2[start][1]==-1:
fuel1use=-1
fuel2use=-1
moment=keymoments2[start][0]
keymoments3.append([moment,fuel1use,fuel2use])
for i in range(start-1,-1,-1):
moment=keymoments2[i][0]
if fuel1use==-1:
keymoments3.append([moment,-1,-1])
continue
time=keymoments2[i+1][0]-moment
if time>s:
fuel1use=-1
fuel2use=-1
keymoments3.append([moment,-1,-1])
continue
if keymoments2[i][1]==1:
fuel1use+=time
elif keymoments2[i][1]==2:
fuel2use+=time
elif keymoments2[i][1]==-1:
fuel1use=-1
fuel2use=-1
keymoments3.append([moment,fuel1use,fuel2use])
keymoments3.reverse()
f=list(map(int,input().split()))
for i in range(m):
if f[i]+s>=e:
print(0,0)
continue
if not keymoments3:
print(-1,-1)
continue
if f[i]+s<keymoments3[0][0]:
print(-1,-1)
continue
l=0
r=len(keymoments3)-1
while l<r:
if l+1==r:
try1=r
else:
try1=(l+r)//2
if f[i]+s>=keymoments2[try1][0]:
l=try1
else:
if l+1==r:
l=l
break
r=try1
ans1=keymoments3[l][1]
ans2=keymoments3[l][2]
if ans1!=-1 and keymoments2[l][1]==1:
ans1+=keymoments3[l][0]-(f[i]+s)
elif ans2!=-1 and keymoments2[l][1]==2:
ans2+=keymoments3[l][0]-(f[i]+s)
print(ans1,ans2)
|
626_B. Cards_10608
|
Catherine has a deck of n cards, each of which is either red, green, or blue. As long as there are at least two cards left, she can do one of two actions:
* take any two (not necessarily adjacent) cards with different colors and exchange them for a new card of the third color;
* take any two (not necessarily adjacent) cards with the same color and exchange them for a new card with that color.
She repeats this process until there is only one card left. What are the possible colors for the final card?
Input
The first line of the input contains a single integer n (1 ≤ n ≤ 200) — the total number of cards.
The next line contains a string s of length n — the colors of the cards. s contains only the characters 'B', 'G', and 'R', representing blue, green, and red, respectively.
Output
Print a single string of up to three characters — the possible colors of the final card (using the same symbols as the input) in alphabetical order.
Examples
Input
2
RB
Output
G
Input
3
GRG
Output
BR
Input
5
BBBBB
Output
B
Note
In the first sample, Catherine has one red card and one blue card, which she must exchange for a green card.
In the second sample, Catherine has two green cards and one red card. She has two options: she can exchange the two green cards for a green card, then exchange the new green card and the red card for a blue card. Alternatively, she can exchange a green and a red card for a blue card, then exchange the blue card and remaining green card for a red card.
In the third sample, Catherine only has blue cards, so she can only exchange them for more blue cards.
|
'''
Author : Md. Rezwanul Haque
Email : [email protected]
'''
import sys
from sys import stdout,stdin
input = lambda : sys.stdin.readline()
if __name__ == '__main__':
n = int(input())
s = input()
s = (s.count('B'), s.count('G'), s.count('R'))
if s[0] > 0 and s[1] > 0 and s[2] > 0:
stdout.write("BGR")
elif s[0] == 0 and s[1] == 0:
stdout.write("R")
elif s[1] == 0 and s[2] == 0:
stdout.write("B")
elif s[0] == 0 and s[2] == 0:
stdout.write("G")
elif s == (0,1,1):
stdout.write("B")
elif s == (1, 0, 1):
stdout.write("G")
elif s == (1, 1, 0):
stdout.write("R")
elif s[0] == 0 and s[1] == 1:
stdout.write("BG")
elif s[0] == 0 and s[2] == 1:
stdout.write("BR")
elif s[1] == 0 and s[0] == 1:
stdout.write("BG")
elif s[1] == 0 and s[2] == 1:
stdout.write("GR")
elif s[2] == 0 and s[0] == 1:
stdout.write("BR")
elif s[2] == 0 and s[1] == 1:
stdout.write("GR")
else:
stdout.write("BGR")
|
{
"input": [
"2\nRB\n",
"5\nBBBBB\n",
"3\nGRG\n",
"2\nRG\n",
"6\nGRRGBB\n",
"1\nB\n",
"4\nRBGB\n",
"7\nBBBGBRG\n",
"3\nGGR\n",
"102\nGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGRGGGGGGGGBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\n",
"3\nGGB\n",
"1\nR\n",
"5\nGRRGR\n",
"2\nBG\n",
"200\nRGRGRRRRRGRRGRRRGRGRRRGGRGRRGGGRRGGRRRRRRRRRRRGRRGRRRGRRRGRRRRRRRGRRRRRRRRRRRGGRRGGRRRRGGRRRRRRRRRGGGRGRGRGRRGRGGRGRGRRRGRRRRRRGGRGRRRRGRRGRGGRRRRRRRGRGGRRGRRRRRRRGGRRRRGRRRRRRRGRRRGGRRRRRRGRRGGGRRRGR\n",
"101\nRRRRRRRRRRRRRRRRRRRBRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR\n",
"4\nRGGR\n",
"4\nRRBB\n",
"16\nRRGRRRRRRGGRGRRR\n",
"3\nBGB\n",
"5\nRBRBG\n",
"5\nBRGRG\n",
"52\nBBBBBBBBBBBBBBBBBBBBGBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\n",
"3\nBRB\n",
"3\nRBR\n",
"200\nGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\n",
"2\nGG\n",
"190\nBBBBBBBBBBBBBBBBBGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\n",
"150\nGRGBBBBRBGGBGBBGBBBBGRBBRRBBGRRGGGBRBBRGRRRRGBGRRBGBGBGRBBBGBBBGBGBRGBRRRRRGGGRGRBBGBRGGGRBBRGBBGRGGGBBRBRRGRGRRGRRGRRRGBGBRRGGRGGBRBGGGBBBRGRGBRGRRRR\n",
"200\nGRGRRGRBRRRGGGRGGRRRRRBBGRRGRBBGRRGBGRRBBRBBRRBBBGRBRGGGGBGGBRRBBRGRBGGRRGGBBRBGGRGBBRRBBRGBRRBGBRBGBBRGGRRRGGGBRGGGGRRRBBRRGRGRBRRGRBBGGRBBRGRGRBGRBBRGGBBBGRGBBGGBGBGBBRRBGRGRGGBRRGRGGGGGBRGGGGBBBBRB\n",
"200\nBBRGRRBBRGGGBGBGBGRRGRGRGRBGRGRRBBGRGBGRRGRRRGGBBRGBGBGBRBBBBBBBGGBRGGRRRGGRGBGBGGBRRRRBRRRBRBBGGBGBRGRGBBBBGGBGBBBGBGRRBRRRGBGGBBBRBGRBRRGGGRRGBBBGBGRRRRRRGGRGRGBBBRGGGBGGGBRBBRRGBGRGRBRRRBRBGRGGBRBB\n",
"2\nRR\n",
"2\nBB\n",
"3\nGBG\n",
"4\nBGBG\n",
"3\nGBR\n",
"90\nBGBGGRRBGGRRRRRGGRGBBBBBRRBGBGBGBGGBBGRGGGGRBRBBRRRGBRRGBBGBBGGGRGRGRBGBBBRRGRRBRBRRGGRBRB\n",
"4\nGGRB\n",
"5\nBGBGR\n",
"193\nRRRGGGRBGGBGGGBGGBBGRBGGRBGGBBRBGGRBBBRBRRGGBBRBRGRRRBGBBRGGRGGGBGGRRGGRGRRBRBRBRRGRGBGBRGBBRGRRRBGRGGBGBRBBBGBRBBGBGBGGGBGGGGBRBBRRBGRGGBBBRBBBBBGRRRGBRGBRRRBBBGBGGGGRGGRRBRBGRRGBGBRBGGGRBRRGG\n",
"2\nBR\n",
"4\nBRRG\n",
"3\nRRG\n",
"1\nG\n",
"3\nBGR\n",
"2\nGR\n",
"6\nGBRGRB\n",
"3\nRGG\n",
"101\nRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRBRRRRRRRRRRRRRRRRRRR\n",
"2\nGB\n",
"3\nBBR\n",
"4\nBGBR\n",
"7\nGRBGBBB\n",
"5\nRGRRG\n",
"4\nBBRR\n",
"5\nBRRBG\n",
"150\nGRGBBBBRBGGRGBBGBBBBGRBBRRBBGRRGGGBRBBRGRRRBGBGRRBGBGBGRBBBGBBBGBGBRGBRRRRRGGGRGRBBGBRGGGRBBRGBBGRGGGBBRBRRGRGRRGRRGRRRGBGBRRGGRGGBRBGGGBBBRGRGBRGRRRR\n",
"200\nBBRBGGRGBRBRRRBRGRGBGRRBBRBGGGBGGGRBBBGRGRGGRRRRRRGBGBBBGRRGGGRRBRGBRBBBGGBGRRRBRRGBGBBBGBGGBBBBGRGRBGBGGBBRBRRRBRRRRBGGBGBGRGGRRRGGRBGGBBBBBBBRBGBGBGRBBGGRRRGRRGBGRGBBRRGRGBRGRGRGRRGBGBGBGGGRBBRRGRBB\n",
"4\nGBGB\n",
"5\nBGGBR\n",
"193\nRRRGGGRBGGBGGGRGGBBGRBGGRBGGBBRBGGRBBBRBRRGGBBRBRGRRRBGBBRGGRGGGBGGRRGGRGRRBRBRBRRGRGBGBRGBBRGRRRBGRGGBGBRBBBGBRBBGBGBGGGBGGGGBRBBRRBGRGGBBBRBBBBBGRRRGBRGBRRRBBBGBGGGGRGGRBBRBGRRGBGBRBGGGRBRRGG\n",
"3\nGRR\n",
"3\nRGB\n",
"5\nRGRGR\n",
"200\nBBRBGGRGBRBRRRBRGRGBGRRBBRBGGGBGGGRBBBGRGRGGRRRRRRGBGBBBGRRGGGRRBRGBRBBBGGBGRRRBRRGRGBBBGBGGBBBBGRGRBGBGGBBRBRRRBRRRRBGGBGBGRGGRRRGGRBGGBBBBBBBRBGBGBGRBBGGBRRGRRGBGRGBBRRGRGBRGRGRGRRGBGBGBGGGRBBRRGRBB\n",
"5\nBGRBG\n",
"3\nBGG\n",
"200\nRGRRRGGGRRGRRRRRRGGRRRGRRRRRRRGRRRRGGRRRRRRRGRRGGRGRRRRRRRGGRGRRGRRRRGRGGRRRRRRGRRRGRGRGGRGRRGRGRGRGGGRRRRRRRRRGGRRRRGGRRGGRRRRRRRRRRRGRRRRRRRGRRRGRRRGRRGRRRRRRRRRRRGGRRGGGRRGRGGRRRGRGRRRGRRGRRRRRGRGR\n",
"16\nRRRGRGGRRRRRRGRR\n",
"5\nGRGRB\n",
"52\nBBBBBBBBBBBBBBBBBBBBBBBBBBBBBGBGBBBBBBBBBBBBBBBBBBBB\n",
"3\nRBG\n",
"4\nBRGG\n",
"4\nGRRB\n",
"7\nGBBGBBR\n",
"4\nRBRB\n",
"5\nGBRRB\n",
"200\nBBRBGGGGBRBRRRBRGRGBGRRBBRBGRGBGGGRBBBGRGRGGRRRRRRGBGBBBGRRGGGRRBRGBRBBBGGBGRRRBRRGBGBBBGBGGBBBBGRGRBGBGGBBRBRRRBRRRRBGGBGBGRGGRRRGGRBGGBBBBBBBRBGBGBGRBBGGRRRGRRGBGRGBBRRGRGBRGRGRGRRGBGBGBGGGRBBRRGRBB\n",
"5\nGBGBR\n",
"3\nRGR\n",
"3\nRBB\n",
"3\nBRG\n",
"4\nGRGB\n",
"4\nGRBR\n",
"7\nRBBGBBG\n",
"4\nBRBR\n",
"7\nRBBBBGG\n",
"4\nBRRB\n",
"7\nGGBBBBR\n",
"4\nGBBR\n",
"102\nGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGBGGGGGGGGRGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\n",
"200\nRGRGRRRRRGRGGRRRGRGRRRGGRGRRGGGRRGGRRRRRRRRRRRGRRGRRRGRRRGRRRRRRRGRRRRRRRRRRRGGRRGGRRRRGGRRRRRRRRRGGGRGRGRGRRGRGGRGRGRRRGRRRRRRGGRGRRRRGRRGRGGRRRRRRRGRGGRRRRRRRRRRGGRRRRGRRRRRRRGRRRGGRRRRRRGRRGGGRRRGR\n",
"52\nBBBBBBBBBBBBBBBBBBBBBGGBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\n",
"190\nBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBGBBBBBBBBBBBBBBBBB\n",
"150\nRRRRGRBGRGRBBBGGGBRBGGRGGRRBGBGRRRGRRGRRGRGRRBRBBGGGRGBBGRBBRGGGRBGBBRGRGGGRRRRRBGRBGBGBBBGBBBRGBGBGBRRGBGRRRRGRBBRBGGGRRGBBRRBBRGBBBBGBBGBGGBRBBBBGRG\n",
"200\nBBRGRRBBRGGGBGBGBGRRGRGRGRBGRGRRBBGRGBGRRGRRRGRBBRGBGBGBRBBBBBBBGGBRGGRRRGGRGBGBGGBRRRRBRRRBRBBGGBGBRGRGBBBBGGBGBBBGBGRRBRRRGBGGBBBRBGRBRRGGGRRGBBBGBGRRRGRRGGRGRGBBBRGGGBGGGBRBBRRGBGRGRBRRRBRBGRGGBRBB\n",
"90\nBRBRGGRRBRBRRGRRBBBGBRGRGRGGGBBGBBGRRBGRRRBBRBRGGGGRGBBGGBGBGBGBRRBBBBBGRGGRRRRRGGBRRGGBGB\n",
"5\nRGBGB\n",
"3\nGRB\n",
"5\nRRRGG\n",
"200\nBBRGRRBBRGGGBGBGBGRRGRGRGRBGRGRRBBGRGBGRRGRRBGGBBRGBGBGBRBBBBBBBGGBRGGRRRGGRGBGBGGBRRRRBRRRBRBBGGBGBRGRGBBBBGGBGBBBGRGRRBRRRGBGGBBBRBGRBRRGGGRRGBBBGBGRRRRRRGGRGRGBBBRGGGBGGGBRBBRRGBGRGRBRRRBRBGRGGBRBB\n",
"5\nGBRGB\n",
"7\nGBBRBBG\n",
"4\nBRGR\n",
"7\nBBBBRGG\n",
"90\nBRBRGGRRBRBRBGRRBBBGRRGRGRGGGBBGBBGRRBGRRRBBRBRGGGGRGBBGGBGBGBGBRRBBBBBGRGGRRRRRGGBRRGGBGB\n",
"5\nRGGBB\n",
"5\nGBRBG\n",
"7\nGGRBBBB\n",
"5\nRGGRB\n",
"52\nBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBGBBBBBBBBBBBBBBBBBBGB\n",
"3\nBRR\n",
"150\nRRRRGRBGRGRBBBGGGBRBGGRGGRRBGBGRRRGRRGRRGRGRRBRBBGGGRGBBGRBBRGGGRBGBBRGRGGGBRRRRBGRBGBGBBBGBBBRGBGBGBRRGBGRRRRGRBBRBGGGRRGBBRRBBRGBBBBGRBGBGGBRBBBBGRG\n",
"4\nRGGB\n",
"193\nGGRRBRGGGBRBGBGRRGBRBRRGGRGGGGBGBBBRRRBGRBGRRRGBBBBBRBBBGGRGBRRBBRBGGGGBGGGBGBGBBRBGBBBRBGBGGRGBRRRGRBBGRBGBGRGRRBRBRBRRGRGGRRGGBGGGRGGRBBGBRRRGRBRBBGGRRBRBBBRGGBRBBGGBRGGBRGBBGGBGGGBGGBRGGGRRR\n",
"7\nGRBBBGB\n",
"150\nGRGBBBBRBGGRGBBBGBBBGRBBRRBBGRRGGGBRBBRGRRRBGBGRRBGBGBGRBBBGBBBGBGBRGBRRRRRGGGRGRBBGBRGGGRBBRGBBGRGGGBBRBRRGRGRRGRRGRRRGBGBRRGGRGGBRBGGGBBBRGRGBRGRRRR\n",
"4\nGBBG\n",
"193\nGGRRBRGGGBRBGBGRRGBRBBRGGRGGGGBGBBBRRRBGRBGRRRGBBBBBRBBBGGRGBRRBBRBGGGGBGGGBGBGBBRBGBBBRBGBGGRGBRRRGRBBGRBGBGRGRRBRBRBRRGRGGRRGGBGGGRGGRBBGBRRRGRBRBBGGRRBRBBBRGGBRBBGGBRGGBRGBBGGRGGGBGGBRGGGRRR\n",
"200\nBBRBGGRGBRBRRRBRGRGBGRRBBRBGGGBGGGRBBBGRGRGGRRRRRRGBGBBBGRRGGGRRBRGBRBBBBGGGRRRBRRGRGBBBGBGGBBBBGRGRBGBGGBBRBRRRBRRRRBGGBGBGRGGRRRGGRBGGBBBBBBBRBGBGBGRBBGGBRRGRRGBGRGBBRRGRGBRGRGRGRRGBGBGBGGGRBBRRGRBB\n",
"4\nRGRB\n",
"5\nRBGBG\n",
"4\nRBRG\n",
"200\nRGRRRGGGRRGRRRRRRGGRRRGRRRRRRRGRRRRGGRRRRRRRRRRGGRGRRRRRRRGGRGRRGRRRRGRGGRRRRRRGRRRGRGRGGRGRRGRGRGRGGGRRRRRRRRRGGRRRRGGRRGGRRRRRRRRRRRGRRRRRRRGRRRGRRRGRRGRRRRRRRRRRRGGRRGGGRRGRGGRRRGRGRRRGGRGRRRRRGRGR\n",
"200\nBBRBGGRGBRBRRRBRGRGBGRRBBRBGGGBGGGRBBBGRGRGGRRGRRRGBGBBBGRRGGGRRBRGBRBBBGGBGRRRBRRGBGBBBGBGGBBBBGRGRBGBGGBBRBRRRBRRRRBGGBGBGRGGRRRGGRBGGBBBBBBBRBGBGBGRBBRGRRRGRRGBGRGBBRRGRGBRGRGRGRRGBGBGBGGGRBBRRGRBB\n"
],
"output": [
"G",
"B",
"BR",
"B",
"BGR",
"B",
"BGR",
"BGR",
"BR",
"BGR",
"BR",
"R",
"BGR",
"R",
"BGR",
"BG",
"BGR",
"BGR",
"BGR",
"GR",
"BGR",
"BGR",
"BGR",
"GR",
"BG",
"G",
"G",
"GR",
"BGR",
"BGR",
"BGR",
"R",
"B",
"BR",
"BGR",
"BGR",
"BGR",
"BGR",
"BGR",
"BGR",
"G",
"BGR",
"BG",
"G",
"BGR",
"B\n",
"BGR\n",
"BR\n",
"BG\n",
"R\n",
"GR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BG\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BG\n",
"GR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"GR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BG\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n",
"BGR\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Catherine has a deck of n cards, each of which is either red, green, or blue. As long as there are at least two cards left, she can do one of two actions:
* take any two (not necessarily adjacent) cards with different colors and exchange them for a new card of the third color;
* take any two (not necessarily adjacent) cards with the same color and exchange them for a new card with that color.
She repeats this process until there is only one card left. What are the possible colors for the final card?
Input
The first line of the input contains a single integer n (1 ≤ n ≤ 200) — the total number of cards.
The next line contains a string s of length n — the colors of the cards. s contains only the characters 'B', 'G', and 'R', representing blue, green, and red, respectively.
Output
Print a single string of up to three characters — the possible colors of the final card (using the same symbols as the input) in alphabetical order.
Examples
Input
2
RB
Output
G
Input
3
GRG
Output
BR
Input
5
BBBBB
Output
B
Note
In the first sample, Catherine has one red card and one blue card, which she must exchange for a green card.
In the second sample, Catherine has two green cards and one red card. She has two options: she can exchange the two green cards for a green card, then exchange the new green card and the red card for a blue card. Alternatively, she can exchange a green and a red card for a blue card, then exchange the blue card and remaining green card for a red card.
In the third sample, Catherine only has blue cards, so she can only exchange them for more blue cards.
### Input:
2
RB
### Output:
G
### Input:
5
BBBBB
### Output:
B
### Code:
'''
Author : Md. Rezwanul Haque
Email : [email protected]
'''
import sys
from sys import stdout,stdin
input = lambda : sys.stdin.readline()
if __name__ == '__main__':
n = int(input())
s = input()
s = (s.count('B'), s.count('G'), s.count('R'))
if s[0] > 0 and s[1] > 0 and s[2] > 0:
stdout.write("BGR")
elif s[0] == 0 and s[1] == 0:
stdout.write("R")
elif s[1] == 0 and s[2] == 0:
stdout.write("B")
elif s[0] == 0 and s[2] == 0:
stdout.write("G")
elif s == (0,1,1):
stdout.write("B")
elif s == (1, 0, 1):
stdout.write("G")
elif s == (1, 1, 0):
stdout.write("R")
elif s[0] == 0 and s[1] == 1:
stdout.write("BG")
elif s[0] == 0 and s[2] == 1:
stdout.write("BR")
elif s[1] == 0 and s[0] == 1:
stdout.write("BG")
elif s[1] == 0 and s[2] == 1:
stdout.write("GR")
elif s[2] == 0 and s[0] == 1:
stdout.write("BR")
elif s[2] == 0 and s[1] == 1:
stdout.write("GR")
else:
stdout.write("BGR")
|
675_C. Money Transfers_10612
|
There are n banks in the city where Vasya lives, they are located in a circle, such that any two banks are neighbouring if their indices differ by no more than 1. Also, bank 1 and bank n are neighbours if n > 1. No bank is a neighbour of itself.
Vasya has an account in each bank. Its balance may be negative, meaning Vasya owes some money to this bank.
There is only one type of operations available: transfer some amount of money from any bank to account in any neighbouring bank. There are no restrictions on the size of the sum being transferred or balance requirements to perform this operation.
Vasya doesn't like to deal with large numbers, so he asks you to determine the minimum number of operations required to change the balance of each bank account to zero. It's guaranteed, that this is possible to achieve, that is, the total balance of Vasya in all banks is equal to zero.
Input
The first line of the input contains a single integer n (1 ≤ n ≤ 100 000) — the number of banks.
The second line contains n integers ai ( - 109 ≤ ai ≤ 109), the i-th of them is equal to the initial balance of the account in the i-th bank. It's guaranteed that the sum of all ai is equal to 0.
Output
Print the minimum number of operations required to change balance in each bank to zero.
Examples
Input
3
5 0 -5
Output
1
Input
4
-1 0 1 0
Output
2
Input
4
1 2 3 -6
Output
3
Note
In the first sample, Vasya may transfer 5 from the first bank to the third.
In the second sample, Vasya may first transfer 1 from the third bank to the second, and then 1 from the second to the first.
In the third sample, the following sequence provides the optimal answer:
1. transfer 1 from the first bank to the second bank;
2. transfer 3 from the second bank to the third;
3. transfer 6 from the third bank to the fourth.
|
n = int(input())
b = list(map(int, input().split()))
from collections import Counter
from itertools import accumulate
cum = list(accumulate(b))
cnt = Counter(cum)
print (n - cnt.most_common(1)[0][1])
|
{
"input": [
"3\n5 0 -5\n",
"4\n-1 0 1 0\n",
"4\n1 2 3 -6\n",
"6\n1 -1 1 -1 1 -1\n",
"50\n108431864 128274949 -554057370 -384620666 -202862975 -803855410 -482167063 -55139054 -215901009 0 0 0 0 0 94325701 730397219 358214459 -673647271 -131397668 -377892440 0 0 0 0 0 -487994257 -360271553 639988328 489338210 -281060728 250208758 0 993242346 -213071841 -59752620 -864351041 -114363541 506279952 999648597 -173503559 -144629749 -559693009 0 -46793577 511999017 -343503822 -741715911 647437511 821346413 993112810\n",
"1\n0\n",
"4\n-1 1 1 -1\n",
"4\n0 0 1 -1\n",
"4\n-2 1 2 -1\n",
"4\n0 0 0 0\n",
"6\n1 -2 1 -1 2 -1\n",
"4\n2 1 3 -6\n",
"4\n-1 0 2 -1\n",
"6\n1 -1 1 0 1 -2\n",
"4\n-1 1 0 0\n",
"4\n0 -1 0 1\n",
"6\n1 -1 0 -1 1 0\n",
"6\n1 -1 1 0 0 -1\n",
"4\n-1 1 2 -2\n",
"4\n0 0 -1 1\n",
"4\n0 -1 2 -1\n",
"4\n-2 1 1 0\n",
"4\n0 1 1 -2\n",
"6\n2 -1 1 -1 0 -1\n",
"4\n-1 0 0 1\n",
"6\n1 -1 0 0 1 -1\n",
"3\n6 -1 -5\n",
"4\n0 1 0 -1\n",
"4\n-3 1 2 0\n",
"4\n0 0 2 -2\n",
"4\n-1 1 -1 1\n",
"4\n-2 0 2 0\n",
"4\n0 1 -1 0\n",
"4\n-2 1 0 1\n",
"6\n1 0 1 -2 1 -1\n",
"4\n0 -1 1 0\n",
"6\n1 0 1 0 0 -2\n",
"4\n1 -2 2 -1\n",
"4\n-1 2 -1 0\n",
"4\n-2 0 1 1\n",
"4\n-2 2 0 0\n",
"4\n-2 2 2 -2\n",
"4\n-2 2 -1 1\n",
"4\n0 -2 1 1\n",
"6\n1 -2 1 -1 1 0\n",
"4\n-1 -1 0 2\n"
],
"output": [
"1",
"2",
"3",
"3",
"36",
"0",
"2\n",
"1\n",
"3\n",
"0\n",
"4\n",
"3\n",
"2\n",
"3\n",
"1\n",
"2\n",
"2\n",
"2\n",
"2\n",
"1\n",
"2\n",
"2\n",
"2\n",
"3\n",
"1\n",
"2\n",
"2\n",
"2\n",
"2\n",
"1\n",
"2\n",
"2\n",
"1\n",
"2\n",
"3\n",
"1\n",
"3\n",
"2\n",
"2\n",
"2\n",
"1\n",
"2\n",
"2\n",
"2\n",
"3\n",
"2\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
There are n banks in the city where Vasya lives, they are located in a circle, such that any two banks are neighbouring if their indices differ by no more than 1. Also, bank 1 and bank n are neighbours if n > 1. No bank is a neighbour of itself.
Vasya has an account in each bank. Its balance may be negative, meaning Vasya owes some money to this bank.
There is only one type of operations available: transfer some amount of money from any bank to account in any neighbouring bank. There are no restrictions on the size of the sum being transferred or balance requirements to perform this operation.
Vasya doesn't like to deal with large numbers, so he asks you to determine the minimum number of operations required to change the balance of each bank account to zero. It's guaranteed, that this is possible to achieve, that is, the total balance of Vasya in all banks is equal to zero.
Input
The first line of the input contains a single integer n (1 ≤ n ≤ 100 000) — the number of banks.
The second line contains n integers ai ( - 109 ≤ ai ≤ 109), the i-th of them is equal to the initial balance of the account in the i-th bank. It's guaranteed that the sum of all ai is equal to 0.
Output
Print the minimum number of operations required to change balance in each bank to zero.
Examples
Input
3
5 0 -5
Output
1
Input
4
-1 0 1 0
Output
2
Input
4
1 2 3 -6
Output
3
Note
In the first sample, Vasya may transfer 5 from the first bank to the third.
In the second sample, Vasya may first transfer 1 from the third bank to the second, and then 1 from the second to the first.
In the third sample, the following sequence provides the optimal answer:
1. transfer 1 from the first bank to the second bank;
2. transfer 3 from the second bank to the third;
3. transfer 6 from the third bank to the fourth.
### Input:
3
5 0 -5
### Output:
1
### Input:
4
-1 0 1 0
### Output:
2
### Code:
n = int(input())
b = list(map(int, input().split()))
from collections import Counter
from itertools import accumulate
cum = list(accumulate(b))
cnt = Counter(cum)
print (n - cnt.most_common(1)[0][1])
|
699_D. Fix a Tree_10616
|
A tree is an undirected connected graph without cycles.
Let's consider a rooted undirected tree with n vertices, numbered 1 through n. There are many ways to represent such a tree. One way is to create an array with n integers p1, p2, ..., pn, where pi denotes a parent of vertex i (here, for convenience a root is considered its own parent).
<image> For this rooted tree the array p is [2, 3, 3, 2].
Given a sequence p1, p2, ..., pn, one is able to restore a tree:
1. There must be exactly one index r that pr = r. A vertex r is a root of the tree.
2. For all other n - 1 vertices i, there is an edge between vertex i and vertex pi.
A sequence p1, p2, ..., pn is called valid if the described procedure generates some (any) rooted tree. For example, for n = 3 sequences (1,2,2), (2,3,1) and (2,1,3) are not valid.
You are given a sequence a1, a2, ..., an, not necessarily valid. Your task is to change the minimum number of elements, in order to get a valid sequence. Print the minimum number of changes and an example of a valid sequence after that number of changes. If there are many valid sequences achievable in the minimum number of changes, print any of them.
Input
The first line of the input contains an integer n (2 ≤ n ≤ 200 000) — the number of vertices in the tree.
The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ n).
Output
In the first line print the minimum number of elements to change, in order to get a valid sequence.
In the second line, print any valid sequence possible to get from (a1, a2, ..., an) in the minimum number of changes. If there are many such sequences, any of them will be accepted.
Examples
Input
4
2 3 3 4
Output
1
2 3 4 4
Input
5
3 2 2 5 3
Output
0
3 2 2 5 3
Input
8
2 3 5 4 1 6 6 7
Output
2
2 3 7 8 1 6 6 7
Note
In the first sample, it's enough to change one element. In the provided output, a sequence represents a tree rooted in a vertex 4 (because p4 = 4), which you can see on the left drawing below. One of other correct solutions would be a sequence 2 3 3 2, representing a tree rooted in vertex 3 (right drawing below). On both drawings, roots are painted red.
<image>
In the second sample, the given sequence is already valid.
|
input()
A = list(map(int, input().split(' ')))
root=-1
for i,a in enumerate(A) :
if i == a-1 :
root = i
break
v = [False]*len(A)
if root>-1 :
v[root]=True
ans= 0
for i,a in enumerate(A) :
if v[i] :
continue
v[i]= True
l=[i]
a-=1
while not v[a] :
l.append(a)
v[a]=True
a=A[a]-1
if a in l: #new cycle
if root==-1:
A[a]=a+1
root=a
ans+=1
else :
A[a]=root+1
ans+=1
print(ans)
print(' '.join(map(str,A)))
|
{
"input": [
"5\n3 2 2 5 3\n",
"4\n2 3 3 4\n",
"8\n2 3 5 4 1 6 6 7\n",
"7\n1 2 3 4 5 6 7\n",
"7\n4 3 2 6 3 5 2\n",
"6\n6 2 6 2 4 2\n",
"8\n2 1 2 2 6 5 6 6\n",
"7\n7 5 3 1 2 1 5\n",
"3\n2 1 1\n",
"7\n1 6 4 4 5 6 7\n",
"18\n2 3 4 5 2 7 8 9 10 7 11 12 14 15 13 17 18 18\n",
"2\n1 2\n",
"7\n4 4 2 6 3 5 2\n",
"3\n1 1 1\n",
"7\n1 6 4 4 1 6 7\n",
"18\n2 3 4 5 2 7 8 1 10 7 11 12 14 15 13 17 18 18\n",
"2\n2 2\n",
"5\n3 2 2 5 4\n",
"4\n2 3 3 2\n",
"8\n2 3 5 4 1 6 6 4\n",
"7\n4 4 2 6 3 5 1\n",
"18\n2 3 4 5 2 4 8 1 10 7 11 12 14 15 13 17 18 18\n",
"5\n3 2 3 5 4\n",
"8\n2 3 5 4 1 6 5 4\n",
"18\n2 3 6 5 2 4 8 1 10 7 11 12 14 15 13 17 18 18\n",
"8\n2 3 5 8 1 6 5 4\n",
"18\n2 3 6 5 2 4 8 1 10 7 11 3 14 15 13 17 18 18\n",
"5\n2 2 3 5 5\n",
"18\n2 3 6 5 4 4 8 1 10 7 11 3 14 15 13 17 18 18\n",
"5\n2 2 3 2 5\n",
"18\n2 3 6 5 4 4 8 1 10 7 4 3 14 15 13 17 18 18\n",
"18\n2 5 6 5 4 4 8 1 10 7 4 3 14 15 13 17 18 18\n",
"18\n2 5 6 5 4 4 8 1 10 7 4 3 14 15 13 8 18 18\n",
"6\n6 2 6 1 4 2\n",
"8\n2 1 2 2 6 5 8 6\n",
"7\n7 5 3 1 1 1 5\n",
"7\n1 6 4 4 5 6 6\n",
"18\n2 3 4 5 4 7 8 9 10 7 11 12 14 15 13 17 18 18\n",
"5\n2 2 2 5 3\n",
"5\n3 2 3 5 3\n",
"4\n2 4 3 4\n",
"7\n4 4 2 6 6 5 1\n",
"18\n2 3 4 5 2 4 8 1 10 7 11 12 14 15 17 17 18 18\n",
"8\n2 3 5 4 1 1 5 4\n",
"8\n2 3 5 8 1 7 5 4\n",
"5\n4 2 3 5 5\n",
"5\n2 4 3 2 5\n",
"18\n2 3 6 5 4 4 8 1 10 12 4 3 14 15 13 17 18 18\n",
"18\n2 5 6 5 4 4 8 1 10 7 4 5 14 15 13 8 18 18\n",
"6\n6 2 6 1 2 2\n",
"7\n7 2 3 1 1 1 5\n",
"7\n1 6 6 4 5 6 6\n",
"18\n2 3 4 5 4 7 8 9 10 7 11 14 14 15 13 17 18 18\n",
"7\n4 4 2 6 3 4 4\n",
"5\n5 2 3 5 3\n",
"4\n4 4 3 4\n",
"8\n2 6 5 4 2 6 6 4\n",
"18\n2 3 4 3 2 4 8 1 10 7 11 12 14 15 17 17 18 18\n",
"18\n2 3 6 5 4 5 8 1 10 7 11 3 14 15 13 17 18 18\n",
"5\n4 2 5 5 5\n",
"5\n2 4 3 3 5\n",
"18\n2 5 1 5 4 4 8 1 10 7 4 5 14 15 13 8 18 18\n",
"6\n6 1 6 1 4 2\n",
"7\n7 2 6 1 1 1 5\n",
"7\n1 6 6 4 5 6 4\n",
"18\n1 3 4 5 4 7 8 9 10 7 11 14 14 15 13 17 18 18\n",
"8\n1 6 5 4 2 6 6 4\n",
"7\n4 6 2 6 6 3 1\n",
"18\n2 3 4 3 3 4 8 1 10 7 11 12 14 15 17 17 18 18\n",
"18\n1 5 1 5 4 4 8 1 10 7 4 5 14 15 13 8 18 18\n",
"6\n6 1 6 1 5 2\n",
"7\n1 6 6 4 5 1 4\n",
"7\n4 6 2 6 4 3 1\n",
"5\n3 2 3 5 5\n",
"8\n2 3 5 8 1 6 5 8\n",
"7\n4 4 2 6 3 4 2\n",
"8\n2 3 5 4 2 6 6 4\n",
"18\n2 3 6 5 2 5 8 1 10 7 11 3 14 15 13 17 18 18\n",
"7\n4 4 2 6 6 3 1\n",
"7\n4 4 2 6 3 5 4\n"
],
"output": [
"0 \n3 2 2 5 3 ",
"1\n2 3 3 3 \n",
"2\n2 3 5 4 4 4 6 7 \n",
"6\n1 1 1 1 1 1 1 \n",
"1 \n4 3 3 6 3 5 2 ",
"0 \n6 2 6 2 4 2 ",
"2\n2 2 2 2 6 2 6 6 \n",
"1 \n7 5 3 1 3 1 5 ",
"1\n2 2 1 \n",
"4\n1 6 4 1 1 1 1 \n",
"5\n2 3 4 5 11 7 8 9 10 11 11 11 14 15 11 17 18 11 \n",
"1\n1 1 \n",
"1\n4 4 2 6 3 6 2 ",
"0\n1 1 1 ",
"3\n1 6 4 1 1 1 1 ",
"4\n2 3 4 5 11 7 8 1 10 7 11 11 14 15 11 17 18 11 ",
"0\n2 2 ",
"1\n3 2 2 5 2 ",
"0\n2 3 3 2 ",
"2\n2 3 5 4 4 4 6 4 ",
"1\n4 4 2 6 3 6 1 ",
"4\n2 3 4 5 11 4 8 1 10 7 11 11 14 15 11 17 18 11 ",
"2\n3 2 2 5 2 ",
"2\n2 3 5 4 4 4 5 4 ",
"4\n2 3 6 5 2 11 8 1 10 7 11 11 14 15 11 17 18 11 ",
"2\n2 3 5 8 6 6 5 6 ",
"3\n2 3 6 5 2 11 8 1 10 7 11 3 14 15 11 17 18 11 ",
"2\n2 2 2 5 2 ",
"3\n2 3 6 5 11 4 8 1 10 7 11 3 14 15 11 17 18 11 ",
"2\n2 2 2 2 2 ",
"2\n2 3 6 5 18 4 8 1 10 7 4 3 14 15 18 17 18 18 ",
"2\n2 5 6 5 18 4 8 1 10 7 4 3 14 15 18 17 18 18 ",
"2\n2 5 6 5 18 4 8 1 10 7 4 3 14 15 18 8 18 18 ",
"0\n6 2 6 1 4 2 ",
"2\n2 2 2 2 6 2 8 6 ",
"1\n7 5 3 1 1 1 3 ",
"3\n1 6 4 1 1 1 6 ",
"5\n2 3 4 5 11 7 8 9 10 11 11 11 14 15 11 17 18 11 ",
"0\n2 2 2 5 3 ",
"1\n3 2 2 5 3 ",
"1\n2 4 3 3 ",
"1\n4 4 2 6 6 6 1 ",
"3\n2 3 4 5 11 4 8 1 10 7 11 11 14 15 17 17 18 11 ",
"1\n2 3 5 4 4 1 5 4 ",
"2\n2 3 5 8 5 7 5 5 ",
"2\n4 2 2 5 2 ",
"2\n2 4 3 3 3 ",
"2\n2 3 6 5 18 4 8 1 10 12 4 3 14 15 18 17 18 18 ",
"2\n2 5 6 5 18 4 8 1 10 7 4 5 14 15 18 8 18 18 ",
"0\n6 2 6 1 2 2 ",
"2\n7 2 2 1 1 1 2 ",
"3\n1 6 6 1 1 1 6 ",
"4\n2 3 4 5 11 7 8 9 10 11 11 14 14 15 11 17 18 11 ",
"1\n4 4 2 6 3 6 4 ",
"1\n5 2 2 5 3 ",
"1\n4 4 3 3 ",
"1\n2 6 5 4 2 4 6 4 ",
"3\n2 3 4 11 2 4 8 1 10 7 11 11 14 15 17 17 18 11 ",
"3\n2 3 6 5 11 5 8 1 10 7 11 3 14 15 11 17 18 11 ",
"1\n4 2 5 5 2 ",
"1\n2 4 3 3 3 ",
"2\n2 5 1 5 18 4 8 1 10 7 4 5 14 15 18 8 18 18 ",
"1\n6 1 6 1 4 6 ",
"1\n7 2 6 1 1 1 2 ",
"3\n1 6 6 1 1 1 4 ",
"5\n1 3 4 5 1 7 8 9 10 1 1 14 14 15 1 17 18 1 ",
"2\n1 6 5 1 2 1 6 4 ",
"1\n4 6 2 6 6 6 1 ",
"3\n2 3 4 11 3 4 8 1 10 7 11 11 14 15 17 17 18 11 ",
"3\n1 5 1 5 1 4 8 1 10 7 4 5 14 15 1 8 18 1 ",
"1\n6 1 6 1 5 5 ",
"2\n1 6 6 1 1 1 4 ",
"1\n4 6 2 6 4 6 1 ",
"2\n3 2 2 5 2 ",
"2\n2 3 5 8 6 6 5 6 ",
"1\n4 4 2 6 3 6 2 ",
"2\n2 3 5 4 4 4 6 4 ",
"3\n2 3 6 5 2 11 8 1 10 7 11 3 14 15 11 17 18 11 ",
"1\n4 4 2 6 6 6 1 ",
"1\n4 4 2 6 3 6 4 "
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
A tree is an undirected connected graph without cycles.
Let's consider a rooted undirected tree with n vertices, numbered 1 through n. There are many ways to represent such a tree. One way is to create an array with n integers p1, p2, ..., pn, where pi denotes a parent of vertex i (here, for convenience a root is considered its own parent).
<image> For this rooted tree the array p is [2, 3, 3, 2].
Given a sequence p1, p2, ..., pn, one is able to restore a tree:
1. There must be exactly one index r that pr = r. A vertex r is a root of the tree.
2. For all other n - 1 vertices i, there is an edge between vertex i and vertex pi.
A sequence p1, p2, ..., pn is called valid if the described procedure generates some (any) rooted tree. For example, for n = 3 sequences (1,2,2), (2,3,1) and (2,1,3) are not valid.
You are given a sequence a1, a2, ..., an, not necessarily valid. Your task is to change the minimum number of elements, in order to get a valid sequence. Print the minimum number of changes and an example of a valid sequence after that number of changes. If there are many valid sequences achievable in the minimum number of changes, print any of them.
Input
The first line of the input contains an integer n (2 ≤ n ≤ 200 000) — the number of vertices in the tree.
The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ n).
Output
In the first line print the minimum number of elements to change, in order to get a valid sequence.
In the second line, print any valid sequence possible to get from (a1, a2, ..., an) in the minimum number of changes. If there are many such sequences, any of them will be accepted.
Examples
Input
4
2 3 3 4
Output
1
2 3 4 4
Input
5
3 2 2 5 3
Output
0
3 2 2 5 3
Input
8
2 3 5 4 1 6 6 7
Output
2
2 3 7 8 1 6 6 7
Note
In the first sample, it's enough to change one element. In the provided output, a sequence represents a tree rooted in a vertex 4 (because p4 = 4), which you can see on the left drawing below. One of other correct solutions would be a sequence 2 3 3 2, representing a tree rooted in vertex 3 (right drawing below). On both drawings, roots are painted red.
<image>
In the second sample, the given sequence is already valid.
### Input:
5
3 2 2 5 3
### Output:
0
3 2 2 5 3
### Input:
4
2 3 3 4
### Output:
1
2 3 3 3
### Code:
input()
A = list(map(int, input().split(' ')))
root=-1
for i,a in enumerate(A) :
if i == a-1 :
root = i
break
v = [False]*len(A)
if root>-1 :
v[root]=True
ans= 0
for i,a in enumerate(A) :
if v[i] :
continue
v[i]= True
l=[i]
a-=1
while not v[a] :
l.append(a)
v[a]=True
a=A[a]-1
if a in l: #new cycle
if root==-1:
A[a]=a+1
root=a
ans+=1
else :
A[a]=root+1
ans+=1
print(ans)
print(' '.join(map(str,A)))
|
741_C. Arpa’s overnight party and Mehrdad’s silent entering_10623
|
Note that girls in Arpa’s land are really attractive.
Arpa loves overnight parties. In the middle of one of these parties Mehrdad suddenly appeared. He saw n pairs of friends sitting around a table. i-th pair consisted of a boy, sitting on the ai-th chair, and his girlfriend, sitting on the bi-th chair. The chairs were numbered 1 through 2n in clockwise direction. There was exactly one person sitting on each chair.
<image>
There were two types of food: Kooft and Zahre-mar. Now Mehrdad wonders, was there any way to serve food for the guests such that:
* Each person had exactly one type of food,
* No boy had the same type of food as his girlfriend,
* Among any three guests sitting on consecutive chairs, there was two of them who had different type of food. Note that chairs 2n and 1 are considered consecutive.
Find the answer for the Mehrdad question. If it was possible, find some arrangement of food types that satisfies the conditions.
Input
The first line contains an integer n (1 ≤ n ≤ 105) — the number of pairs of guests.
The i-th of the next n lines contains a pair of integers ai and bi (1 ≤ ai, bi ≤ 2n) — the number of chair on which the boy in the i-th pair was sitting and the number of chair on which his girlfriend was sitting. It's guaranteed that there was exactly one person sitting on each chair.
Output
If there is no solution, print -1.
Otherwise print n lines, the i-th of them should contain two integers which represent the type of food for the i-th pair. The first integer in the line is the type of food the boy had, and the second integer is the type of food the girl had. If someone had Kooft, print 1, otherwise print 2.
If there are multiple solutions, print any of them.
Example
Input
3
1 4
2 5
3 6
Output
1 2
2 1
1 2
|
import sys
def solve():
n = int(input())
partner = [0]*(2*n)
pacani = []
for line in sys.stdin:
pacan, telka = [int(x) - 1 for x in line.split()]
partner[pacan] = telka
partner[telka] = pacan
pacani.append(pacan)
khavka = [None]*(2*n)
for i in range(2*n):
while khavka[i] is None:
khavka[i] = 1
khavka[i^1] = 2
i = partner[i^1]
for pacan in pacani:
print(khavka[pacan], khavka[partner[pacan]])
solve()
|
{
"input": [
"3\n1 4\n2 5\n3 6\n",
"6\n2 11\n7 1\n12 8\n4 10\n3 9\n5 6\n",
"26\n8 10\n52 21\n2 33\n18 34\n30 51\n5 19\n22 32\n36 28\n42 16\n13 49\n11 17\n31 39\n43 37\n50 15\n29 20\n35 46\n47 23\n3 1\n44 7\n9 27\n6 48\n40 24\n26 14\n45 4\n12 25\n41 38\n",
"7\n3 14\n7 4\n13 10\n11 8\n6 1\n5 9\n2 12\n",
"8\n14 2\n7 9\n15 6\n13 11\n12 16\n10 5\n8 1\n3 4\n",
"4\n4 2\n6 8\n5 1\n3 7\n",
"8\n16 5\n10 15\n8 11\n2 14\n6 4\n7 3\n1 13\n9 12\n",
"23\n46 21\n17 3\n27 38\n34 43\n7 6\n8 37\n22 4\n16 42\n36 32\n12 9\n10 45\n26 2\n13 24\n23 29\n18 15\n33 30\n31 5\n11 25\n1 14\n44 39\n19 20\n35 28\n41 40\n",
"17\n3 14\n34 22\n24 9\n16 17\n6 30\n33 12\n5 10\n21 8\n32 2\n26 23\n31 27\n19 15\n29 4\n7 18\n25 13\n20 28\n1 11\n",
"19\n10 7\n9 17\n21 30\n36 8\n14 11\n25 24\n1 23\n38 33\n4 20\n3 37\n27 5\n28 19\n22 2\n6 34\n12 15\n31 32\n35 13\n16 29\n18 26\n",
"10\n19 6\n8 2\n15 18\n17 14\n16 7\n20 10\n5 1\n13 3\n9 12\n11 4\n",
"20\n34 12\n9 6\n5 3\n13 26\n18 15\n16 22\n7 14\n17 37\n38 40\n4 2\n11 23\n21 8\n10 36\n30 33\n28 19\n29 31\n39 20\n35 24\n25 32\n1 27\n",
"6\n2 7\n5 9\n12 8\n1 4\n3 6\n10 11\n",
"5\n2 5\n10 9\n1 6\n3 8\n4 7\n",
"17\n11 12\n17 22\n34 7\n3 1\n5 24\n18 20\n27 30\n16 33\n23 21\n19 4\n2 15\n29 28\n9 8\n13 25\n6 10\n32 26\n31 14\n",
"15\n21 14\n25 5\n7 28\n2 6\n8 27\n29 18\n9 15\n4 26\n12 1\n19 16\n17 20\n24 10\n11 23\n13 22\n30 3\n",
"15\n16 22\n4 17\n27 3\n23 24\n18 20\n15 21\n9 7\n2 28\n29 19\n8 30\n14 10\n6 26\n25 11\n12 1\n13 5\n",
"19\n30 27\n6 38\n10 28\n20 5\n14 18\n32 2\n36 29\n12 1\n31 24\n15 4\n35 11\n3 7\n21 17\n25 19\n16 8\n23 22\n37 33\n13 9\n34 26\n",
"9\n12 7\n10 15\n16 14\n2 4\n1 17\n6 9\n8 3\n13 5\n11 18\n",
"5\n4 6\n5 1\n2 3\n7 8\n9 10\n",
"2\n2 3\n1 4\n",
"24\n30 4\n41 1\n2 11\n22 42\n29 43\n7 14\n16 6\n40 5\n27 34\n46 33\n17 10\n21 39\n28 31\n19 32\n23 20\n25 48\n12 9\n47 37\n38 3\n44 8\n36 18\n13 26\n24 15\n45 35\n",
"17\n17 31\n11 23\n34 22\n24 8\n4 1\n7 14\n20 27\n3 19\n12 26\n32 25\n28 18\n16 29\n21 9\n6 2\n33 30\n5 13\n10 15\n",
"4\n2 8\n3 5\n4 7\n1 6\n",
"7\n10 14\n4 6\n1 11\n7 2\n9 8\n5 13\n3 12\n",
"6\n3 2\n5 11\n7 12\n6 9\n8 4\n1 10\n",
"8\n10 3\n2 16\n14 13\n5 15\n1 7\n11 8\n6 4\n12 9\n",
"8\n13 6\n10 5\n1 12\n11 15\n7 16\n4 14\n9 2\n8 3\n",
"2\n1 3\n2 4\n"
],
"output": [
"1 2\n2 1\n1 2\n",
"2 1\n2 1\n2 1\n2 1\n1 2\n1 2\n",
"2 1\n1 2\n2 1\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n2 1\n1 2\n1 2\n1 2\n2 1\n2 1\n2 1\n2 1\n2 1\n2 1\n2 1\n2 1\n1 2\n2 1\n2 1\n2 1\n2 1\n",
"2 1\n2 1\n2 1\n2 1\n2 1\n1 2\n2 1\n",
"1 2\n1 2\n2 1\n2 1\n2 1\n1 2\n2 1\n1 2\n",
"1 2\n1 2\n2 1\n2 1\n",
"1 2\n1 2\n1 2\n2 1\n1 2\n2 1\n1 2\n2 1\n",
"2 1\n1 2\n1 2\n1 2\n1 2\n2 1\n2 1\n2 1\n2 1\n2 1\n2 1\n1 2\n1 2\n1 2\n2 1\n2 1\n2 1\n1 2\n1 2\n1 2\n1 2\n1 2\n2 1\n",
"1 2\n1 2\n1 2\n2 1\n1 2\n2 1\n2 1\n1 2\n1 2\n1 2\n2 1\n2 1\n1 2\n1 2\n2 1\n1 2\n1 2\n",
"1 2\n2 1\n2 1\n2 1\n1 2\n2 1\n1 2\n1 2\n2 1\n1 2\n2 1\n1 2\n1 2\n2 1\n1 2\n1 2\n1 2\n1 2\n2 1\n",
"2 1\n1 2\n2 1\n2 1\n1 2\n1 2\n2 1\n2 1\n1 2\n1 2\n",
"1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n1 2\n2 1\n2 1\n1 2\n1 2\n1 2\n2 1\n1 2\n1 2\n2 1\n2 1\n2 1\n1 2\n1 2\n",
"2 1\n1 2\n1 2\n1 2\n1 2\n1 2\n",
"2 1\n2 1\n1 2\n1 2\n2 1\n",
"1 2\n1 2\n2 1\n2 1\n2 1\n2 1\n1 2\n2 1\n2 1\n2 1\n2 1\n1 2\n1 2\n1 2\n1 2\n2 1\n1 2\n",
"1 2\n1 2\n1 2\n2 1\n2 1\n2 1\n1 2\n1 2\n2 1\n2 1\n2 1\n1 2\n1 2\n1 2\n1 2\n",
"2 1\n2 1\n2 1\n1 2\n2 1\n1 2\n1 2\n2 1\n1 2\n1 2\n1 2\n2 1\n2 1\n2 1\n2 1\n",
"1 2\n2 1\n2 1\n2 1\n1 2\n1 2\n1 2\n2 1\n2 1\n1 2\n2 1\n1 2\n2 1\n2 1\n2 1\n2 1\n2 1\n2 1\n2 1\n",
"1 2\n2 1\n2 1\n2 1\n1 2\n2 1\n1 2\n2 1\n2 1\n",
"2 1\n2 1\n2 1\n1 2\n1 2\n",
"2 1\n1 2\n",
"1 2\n2 1\n2 1\n2 1\n2 1\n2 1\n2 1\n1 2\n1 2\n2 1\n1 2\n1 2\n2 1\n1 2\n1 2\n2 1\n2 1\n2 1\n2 1\n2 1\n1 2\n2 1\n2 1\n1 2\n",
"1 2\n1 2\n2 1\n1 2\n2 1\n1 2\n1 2\n1 2\n2 1\n1 2\n1 2\n2 1\n2 1\n1 2\n1 2\n2 1\n2 1\n",
"2 1\n2 1\n1 2\n1 2\n",
"2 1\n1 2\n1 2\n1 2\n1 2\n1 2\n2 1\n",
"1 2\n1 2\n2 1\n2 1\n1 2\n1 2\n",
"1 2\n2 1\n2 1\n1 2\n1 2\n2 1\n2 1\n1 2\n",
"1 2\n2 1\n1 2\n1 2\n2 1\n1 2\n1 2\n1 2\n",
"1 2\n2 1\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Note that girls in Arpa’s land are really attractive.
Arpa loves overnight parties. In the middle of one of these parties Mehrdad suddenly appeared. He saw n pairs of friends sitting around a table. i-th pair consisted of a boy, sitting on the ai-th chair, and his girlfriend, sitting on the bi-th chair. The chairs were numbered 1 through 2n in clockwise direction. There was exactly one person sitting on each chair.
<image>
There were two types of food: Kooft and Zahre-mar. Now Mehrdad wonders, was there any way to serve food for the guests such that:
* Each person had exactly one type of food,
* No boy had the same type of food as his girlfriend,
* Among any three guests sitting on consecutive chairs, there was two of them who had different type of food. Note that chairs 2n and 1 are considered consecutive.
Find the answer for the Mehrdad question. If it was possible, find some arrangement of food types that satisfies the conditions.
Input
The first line contains an integer n (1 ≤ n ≤ 105) — the number of pairs of guests.
The i-th of the next n lines contains a pair of integers ai and bi (1 ≤ ai, bi ≤ 2n) — the number of chair on which the boy in the i-th pair was sitting and the number of chair on which his girlfriend was sitting. It's guaranteed that there was exactly one person sitting on each chair.
Output
If there is no solution, print -1.
Otherwise print n lines, the i-th of them should contain two integers which represent the type of food for the i-th pair. The first integer in the line is the type of food the boy had, and the second integer is the type of food the girl had. If someone had Kooft, print 1, otherwise print 2.
If there are multiple solutions, print any of them.
Example
Input
3
1 4
2 5
3 6
Output
1 2
2 1
1 2
### Input:
3
1 4
2 5
3 6
### Output:
1 2
2 1
1 2
### Input:
6
2 11
7 1
12 8
4 10
3 9
5 6
### Output:
2 1
2 1
2 1
2 1
1 2
1 2
### Code:
import sys
def solve():
n = int(input())
partner = [0]*(2*n)
pacani = []
for line in sys.stdin:
pacan, telka = [int(x) - 1 for x in line.split()]
partner[pacan] = telka
partner[telka] = pacan
pacani.append(pacan)
khavka = [None]*(2*n)
for i in range(2*n):
while khavka[i] is None:
khavka[i] = 1
khavka[i^1] = 2
i = partner[i^1]
for pacan in pacani:
print(khavka[pacan], khavka[partner[pacan]])
solve()
|
765_B. Code obfuscation_10627
|
Kostya likes Codeforces contests very much. However, he is very disappointed that his solutions are frequently hacked. That's why he decided to obfuscate (intentionally make less readable) his code before upcoming contest.
To obfuscate the code, Kostya first looks at the first variable name used in his program and replaces all its occurrences with a single symbol a, then he looks at the second variable name that has not been replaced yet, and replaces all its occurrences with b, and so on. Kostya is well-mannered, so he doesn't use any one-letter names before obfuscation. Moreover, there are at most 26 unique identifiers in his programs.
You are given a list of identifiers of some program with removed spaces and line breaks. Check if this program can be a result of Kostya's obfuscation.
Input
In the only line of input there is a string S of lowercase English letters (1 ≤ |S| ≤ 500) — the identifiers of a program with removed whitespace characters.
Output
If this program can be a result of Kostya's obfuscation, print "YES" (without quotes), otherwise print "NO".
Examples
Input
abacaba
Output
YES
Input
jinotega
Output
NO
Note
In the first sample case, one possible list of identifiers would be "number string number character number string number". Here how Kostya would obfuscate the program:
* replace all occurences of number with a, the result would be "a string a character a string a",
* replace all occurences of string with b, the result would be "a b a character a b a",
* replace all occurences of character with c, the result would be "a b a c a b a",
* all identifiers have been replaced, thus the obfuscation is finished.
|
Alphabet = "abcdefghijklmnopqrstuvwxyz"
X = input()
Checked = []
i, Index = 0, 0
while i < len(X):
if X[i] not in Checked and X[i] == Alphabet[Index]:
Checked.append(Alphabet[Index])
Index += 1
elif X[i] not in Checked and X[i] != Alphabet[Index]:
print("NO")
exit()
i += 1
print("YES")
|
{
"input": [
"jinotega\n",
"abacaba\n",
"ac\n",
"za\n",
"bab\n",
"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaabbbabbbabbaaabbaaaaabaabbaa\n",
"aacb\n",
"darbbbcwynbbbbaacbkvbakavabbbabzajlbajryaabbbccxraakgniagbtsswcfbkubdmcasccepybkaefcfsbzdddxgcjadybcfjtmqbspflqrdghgfwnccfveogdmifkociqscahdejctacwzbkhihajfilrgcjiofwfklifobozikcmvcfeqlidrgsgdfxffaaebzjxngsjxiclyolhjokqpdbfffooticxsezpgqkhhzmbmqgskkqvefzyijrwhpftcmbedmaflapmeljaudllojfpgfkpvgylaglrhrslxlprbhgknrctilngqccbddvpamhifsbmyowohczizjcbleehfrecjbqtxertnpfmalejmbxkhkkbyopuwlhkxuqellsybgcndvniyyxfoufalstdsdfjoxlnmigkqwmgojsppaannfstxytelluvvkdcezlqfsperwyjsdsmkvgjdbksswamhmoukcawiigkggztr\n",
"abbb\n",
"abd\n",
"aac\n",
"bbbbbbbbbb\n",
"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaazz\n",
"z\n",
"abb\n",
"abcdefghijklmnopqrsuvwxyz\n",
"aaaaaaaaad\n",
"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaz\n",
"acbccccccccccc\n",
"abcbcb\n",
"aaac\n",
"bbbbbb\n",
"aaaaaaac\n",
"bac\n",
"aamlaswqzotaanasdhcvjoaiwdhctezzawagkdgfffeqkyrvbcrfqgkdsvximsnvmkmjyofswmtjdoxgwamsaatngenqvsvrvwlbzuoeaolfcnmdacrmdleafbsmerwmxzyylfhemnkoayuhtpbikm\n",
"abcdefghijklmnopqrsutvwxyz\n",
"aaaaaaaaaaad\n",
"bbb\n",
"c\n",
"abdefghijklmnopqrstuvwxyz\n",
"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaababaaababaabababccbabdbcbadccacdbdedabbeecbcabbdcaecdabbedddafeffaccgeacefbcahabfiiegecdbebabhhbdgfeghhbfahgagefbgghdbhadeicbdfgdchhefhigfcgdhcihecacfhadfgfejccibcjkfhbigbealjjkfldiecfdcafbamgfkbjlbifldghmiifkkglaflmjfmkfdjlbliijkgfdelklfnadbifgbmklfbqkhirhcadoadhmjrghlmelmjfpakqkdfcgqdkaeqpbcdoeqglqrarkipncckpfmajrqsfffldegbmahsfcqdfdqtrgrouqajgsojmmukptgerpanpcbejmergqtavwsvtveufdseuemwrhfmjqinxjodddnpcgqullrhmogflsxgsbapoghortiwcovejtinncozk\n",
"bcddcb\n",
"acd\n",
"abcdefghijklmnopqrstuvwxyz\n",
"ade\n",
"aaacb\n",
"abcccccccc\n",
"bc\n",
"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\n",
"acdef\n",
"aaaaaaaaaaa\n",
"b\n",
"abcdefghijklmnopqrstuvwxyzz\n",
"bcd\n",
"aaaaac\n",
"cde\n",
"fihyxmbnzq\n",
"a\n",
"aababbabbaabbbbbaabababaabbbaaaaabbabbabbaabbbbabaabbaaababbaaacbbabbbbbbcbcababbccaaacbaccaccaababbccaacccaabaaccaaabacacbaabacbaacbaaabcbbbcbbaacaabcbcbccbacabbcbabcaccaaaaaabcbacabcbabbbbbabccbbcacbaaabbccbbaaaaaaaaaaaadbbbabdacabdaddddbaabbddbdabbdacbacbacaaaabbacadbcddddadaddabbdccaddbaaacbceebbceadbeaadecddbbbcaaecbdeaebaddbbdebbcbaabcacbdcdc\n",
"bb\n",
"zx\n",
"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaabbbaabaabaababbbabbacacbbbacbbaaaabbccacbaabaaccbbbbbcbbbacabbccaaabbaaacabcbacbcabbbbecbecadcbacbaadeeadabeacdebccdbbcaecdbeeebbebcaaaeacdcbdeccdbbdcdebdcbdacebcecbacddeeaebcedffedfggbeedceacaecagdfedfabcfchffceachgcbicbcffeeebgcgiefcafhibhceiedgbfebbccegbehhibhhfedbaeedbghggffehggaeaidifhdhaggdjcfjhiaieaichjacedchejg\n",
"aabbbd\n",
"x\n",
"abcdeghijklmnopqrstuvwxyz\n",
"abcb\n",
"aba\n",
"abcdefghijklmnopqrstuvwxy\n",
"ca\n",
"aab\n",
"caa\n",
"aacc\n",
"darbbbcwynbbbbaacbkvbakavabbbabzajlbajryaabbbccxraakgniagbtsswcfbkubdmcasccepybkaefcfsbzdddxgcjadybcfjtmqbspflqrdghgfwnccfveogdmifkociqscahdejctacwzbkhihajfilrgcjiofwfklifobozikcmvcfeqlidrgsgdfxffaaebzjxngsjxiclyolhjokqpdbfffooticxsezpgqkhhzmbmqgskkqvefzyijrwhpftcmbedmaflapmeljaudllojfpgfkpvgylaglrhrslxlprbhgknrctilngqccbddvpamhifsbmyowohczizjcbleehfrecjbqtxertnpfmalejmbxkhkkbyopvwlhkxuqellsybgcndvniyyxfoufalstdsdfjoxlnmigkqwmgojsppaannfstxytelluvvkdcezlqfsperwyjsdsmkvgjdbksswamhmoukcawiigkggztr\n",
"bbba\n",
"bad\n",
"bca\n",
"bbbbbbbbcb\n",
"y\n",
"abcdefgsijklmnopqrhuvwxyz\n",
"zaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\n",
"cccccccccccbca\n",
"bcbcba\n",
"abac\n",
"bbbbbc\n",
"baa\n",
"aamlaswqzotaanasdhcvjoaiwdhctezzawagkdgfffeqkyrvbcrfqgkdsvximsnvmkmjyofswmtjdoxgwamsaatngenqvsvrvwlbzuoeaokfcnmdacrmdleafbsmerwmxzyylfhemnloayuhtpbikm\n",
"abcdwfghijklmnopqrsutvexyz\n",
"aaaaadaaaaaa\n",
"bba\n",
"abdefghijklmnopqrsttvwxyz\n",
"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaababaaababaabababccbabdbcbadccacdbdedabbeecbcabbdcaecdabbedddafeffaccgeacefbcahabfiiegecdbebabhhbdgfeghhbfahgagefbgghdbhadeicbdfgdchhefhigfcgdhcihecacfhadfgfejccibcjkfhbigbealjjkfldiecfdcafbamgfkbjlbifldghmiifkkglaflmjfmkfdjlbliijkgfdelklfnadbifgbmklfbqkhirhcadoadhmjrghlmelmjfpakqkdfcgqdkaeqpbcdoeqglqrarkipncckpfmajrqsfffldegbmahsfcqdfdqtrgrouqajhsojmmukptgerpanpcbejmergqtavwsvtveufdseuemwrhfmjqinxjodddnpcgqullrhmogflsxgsbapoghortiwcovejtinncozk\n",
"acddcb\n",
"bdc\n",
"abccefghijklmnopqrstuvwxyz\n",
"eda\n",
"aaabc\n",
"abbccccccc\n",
"bd\n",
"fedca\n",
"aabaaaaaaaa\n",
"d\n",
"zzyxwvutsrqponmlkjihgfedcba\n",
"bcc\n",
"bde\n",
"fyhixmbnzq\n",
"aababbabbaabbbbbaabababaabbbaaaaabbabbabbaabbbbabaabbaaababbaaacbbabbbbbbcbcababbccaaacbaccaccaababbccaacccaabaaccaaabacacbaabacbaacbaaabcbbbcbbaacaabcbcbccbacabbcbabcaccaaaaaabcbacabbbabbbbbabccbbcacbaaabbccbbaaaaaaaaaaaadbbbabdacabdaddddbaabbddbdabbdacbacbacaaaabbacadbcddddadaddabbdccaddbaaacbceebbceadbeaadecddbbbcaaecbdeaebaddbbdebbcbaabcacbdcdc\n",
"cb\n",
"xz\n",
"gjehcdecajhciaeiaihjfcjdggahdhfidiaeaggheffgghgbdeeabdefhhbihhebgeccbbefbgdeiechbihfacfeigcgbeeeffcbcibcghcaecffhcfcbafdefdgaceacaecdeebggfdeffdecbeaeeddcabcecbecadbcdbedcdbbdccedbcdcaeaaacbebbeeebdceacbbdccbedcaebadaeedaabcabcdacebcebbbbacbcabcbacaaabbaaaccbbacabbbcbbbbbccaabaabcaccbbaaaabbcabbbcacabbabbbabaabaabaabbbaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\n",
"baabbd\n",
"w\n",
"abcdegiijklmnopqrstuvwxyz\n",
"bcba\n",
"b`a\n",
"abcdefghijklmnopqqstuvwxy\n",
"jinptega\n",
"abcaaba\n",
"ba\n",
"aca\n",
"acca\n",
"darbbbcwynbbbbaacbkvbakavabbbabzajlbajryaabbbccxraakgniagbtsswcfbkubdmcasccepybkaefcfsbzdddxgcjadybcfjtmqbspflqrdghgfwnccfveogdmifkociqscahdejctacwzbkhihajfilrgcjiofefklifobozikcmvcfeqlidrgsgdfxffaaebzjxngsjxiclyolhjokqpdbfffooticxsezpgqkhhzmbmqgskkqvefzyijrwhpftcmbwdmaflapmeljaudllojfpgfkpvgylaglrhrslxlprbhgknrctilngqccbddvpamhifsbmyowohczizjcbleehfrecjbqtxertnpfmalejmbxkhkkbyopvwlhkxuqellsybgcndvniyyxfoufalstdsdfjoxlnmigkqwmgojsppaannfstxytelluvvkdcezlqfsperwyjsdsmkvgjdbksswamhmoukcawiigkggztr\n",
"baba\n",
"aad\n",
"bda\n",
"bcbbbbbbbb\n",
"v\n",
"aaa\n",
"zyxwvuhrqponmlkjisgfedcba\n",
"baaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaz\n",
"ccccdccccccbca\n",
"bdbcba\n",
"abab\n",
"babbbc\n",
"aamlaswqzotaanasdhcvjoaiwdhctezzawagkdgfffeqkyrvbcrfqgkdsvximsnvmkmjyofswmtjdoxgwamsaatngenqvsvrvwlbzuoeaokfcnmdacrmdleafbsmerwmxzyylfhemnloaxuhtpbikm\n",
"aaabadaaaaaa\n",
"bbc\n",
"abkefghijdlmnopqrsttvwxyz\n",
"accdcb\n",
"cdb\n",
"abccefghijklmnopqrstuvwyxz\n",
"dea\n",
"cccccccbba\n",
"db\n",
"ffdca\n",
"aabaabaaaaa\n",
"abcdefghijklmnopqrrtuvwxyzz\n",
"cbb\n",
"bce\n",
"qznbmxihyf\n",
"cdcdbcacbaabcbbedbbddabeaedbceaacbbbddcedaaebdaecbbeecbcaaabddaccdbbaddadaddddcbdacabbaaaacabcabcadbbadbddbbaabddddadbacadbabbbdaaaaaaaaaaaabbccbbaaabcacbbccbabbbbbabbbacabcbaaaaaaccacbabcbbacabccbcbcbaacaabbcbbbcbaaabcaabcabaabcacabaaaccaabaacccaaccbbabaaccaccabcaaaccbbabacbcbbbbbbabbcaaabbabaaabbaababbbbaabbabbabbaaaaabbbaabababaabbbbbaabbabbabaa\n",
"cc\n",
"xy\n",
"gjehcdecajhciaeiaihjfcjdggaadhfidiaeaggheffgghgbdeeabdefhhbihhebgeccbbefbgdeiechbihfacfeigcgbeeeffcbcibcghcaecffhcfcbafdefdgaceacaecdeebggfdeffdecbeaeeddcabcecbecadbcdbedcdbbdccedbcdcaeaaacbebbeeebdceacbbdccbedcaebadaeedaabcabcdacebcebbbbacbcabcbacaaabbaaaccbbacabbbcbbbbbccaabaabcaccbbaaaabbcabbbcacabbhbbbabaabaabaabbbaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\n",
"bbabbd\n",
"u\n",
"abcdegiijklmnooqrstuvwxyz\n",
"bbca\n",
"b`b\n"
],
"output": [
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"YES\n",
"NO\n",
"YES\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"YES\n",
"YES\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"YES\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Kostya likes Codeforces contests very much. However, he is very disappointed that his solutions are frequently hacked. That's why he decided to obfuscate (intentionally make less readable) his code before upcoming contest.
To obfuscate the code, Kostya first looks at the first variable name used in his program and replaces all its occurrences with a single symbol a, then he looks at the second variable name that has not been replaced yet, and replaces all its occurrences with b, and so on. Kostya is well-mannered, so he doesn't use any one-letter names before obfuscation. Moreover, there are at most 26 unique identifiers in his programs.
You are given a list of identifiers of some program with removed spaces and line breaks. Check if this program can be a result of Kostya's obfuscation.
Input
In the only line of input there is a string S of lowercase English letters (1 ≤ |S| ≤ 500) — the identifiers of a program with removed whitespace characters.
Output
If this program can be a result of Kostya's obfuscation, print "YES" (without quotes), otherwise print "NO".
Examples
Input
abacaba
Output
YES
Input
jinotega
Output
NO
Note
In the first sample case, one possible list of identifiers would be "number string number character number string number". Here how Kostya would obfuscate the program:
* replace all occurences of number with a, the result would be "a string a character a string a",
* replace all occurences of string with b, the result would be "a b a character a b a",
* replace all occurences of character with c, the result would be "a b a c a b a",
* all identifiers have been replaced, thus the obfuscation is finished.
### Input:
jinotega
### Output:
NO
### Input:
abacaba
### Output:
YES
### Code:
Alphabet = "abcdefghijklmnopqrstuvwxyz"
X = input()
Checked = []
i, Index = 0, 0
while i < len(X):
if X[i] not in Checked and X[i] == Alphabet[Index]:
Checked.append(Alphabet[Index])
Index += 1
elif X[i] not in Checked and X[i] != Alphabet[Index]:
print("NO")
exit()
i += 1
print("YES")
|
80_A. Panoramix's Prediction_10633
|
A prime number is a number which has exactly two distinct divisors: one and itself. For example, numbers 2, 7, 3 are prime, and 1, 6, 4 are not.
The next prime number after x is the smallest prime number greater than x. For example, the next prime number after 2 is 3, and the next prime number after 3 is 5. Note that there is exactly one next prime number after each number. So 5 is not the next prime number for 2.
One cold April morning Panoramix predicted that soon Kakofonix will break free from his straitjacket, and this will be a black day for the residents of the Gallic countryside.
Panoramix's prophecy tells that if some day Asterix and Obelix beat exactly x Roman soldiers, where x is a prime number, and next day they beat exactly y Roman soldiers, where y is the next prime number after x, then it's time to wait for Armageddon, for nothing can shut Kakofonix up while he sings his infernal song.
Yesterday the Gauls beat n Roman soldiers and it turned out that the number n was prime! Today their victims were a troop of m Romans (m > n). Determine whether the Gauls should wait for the black day after today's victory of Asterix and Obelix?
Input
The first and only input line contains two positive integers — n and m (2 ≤ n < m ≤ 50). It is guaranteed that n is prime.
Pretests contain all the cases with restrictions 2 ≤ n < m ≤ 4.
Output
Print YES, if m is the next prime number after n, or NO otherwise.
Examples
Input
3 5
Output
YES
Input
7 11
Output
YES
Input
7 9
Output
NO
|
from math import ceil, sqrt
def array(arr, struc):
return (list(map(struc, arr.split())))
def isPrime(x):
for i in range(2, ceil(sqrt(x))+1):
if x % i == 0:
return False
return True
arr = array(input(), int)
prime1 = arr[0]
prime2 = arr[1]
counter = 0
tmp = prime1 + 1
while tmp <= prime2:
if isPrime(tmp):
if tmp == prime2:
counter = 1
print('YES')
break
else:
break
tmp += 1
if counter == 0:
print('NO')
|
{
"input": [
"7 9\n",
"3 5\n",
"7 11\n",
"2 6\n",
"31 33\n",
"2 11\n",
"41 49\n",
"13 17\n",
"23 29\n",
"7 8\n",
"5 13\n",
"47 50\n",
"43 47\n",
"17 19\n",
"5 9\n",
"2 50\n",
"2 3\n",
"3 7\n",
"13 20\n",
"11 13\n",
"19 23\n",
"5 11\n",
"3 9\n",
"5 6\n",
"23 25\n",
"43 49\n",
"5 7\n",
"3 4\n",
"7 13\n",
"3 6\n",
"37 41\n",
"13 15\n",
"2 7\n",
"5 15\n",
"47 48\n",
"2 5\n",
"31 37\n",
"29 31\n",
"19 21\n",
"2 4\n",
"41 43\n",
"47 49\n",
"2 15\n",
"5 26\n",
"3 18\n",
"5 10\n",
"13 23\n",
"5 17\n",
"31 46\n",
"11 21\n",
"7 12\n",
"5 22\n",
"3 12\n",
"13 27\n",
"5 28\n",
"2 21\n",
"7 22\n",
"5 46\n",
"2 8\n",
"3 22\n",
"2 12\n",
"13 25\n",
"5 14\n",
"19 27\n",
"2 9\n",
"13 29\n",
"31 50\n",
"5 18\n",
"3 17\n",
"5 12\n",
"2 28\n",
"7 34\n",
"3 14\n",
"13 34\n",
"5 27\n",
"2 48\n",
"2 17\n",
"23 37\n",
"19 22\n",
"13 16\n",
"3 10\n",
"31 44\n",
"11 24\n",
"7 16\n",
"3 41\n",
"13 22\n",
"2 35\n",
"7 25\n",
"5 43\n",
"5 19\n",
"17 27\n",
"2 16\n",
"2 10\n",
"5 24\n",
"2 43\n",
"3 13\n",
"11 34\n",
"2 29\n",
"23 35\n",
"3 16\n",
"5 8\n",
"7 32\n",
"7 48\n",
"2 19\n",
"2 20\n",
"2 46\n",
"3 8\n",
"13 48\n",
"31 34\n",
"7 17\n",
"2 13\n",
"17 26\n",
"5 36\n",
"13 38\n",
"17 49\n",
"5 20\n",
"19 35\n"
],
"output": [
"NO\n",
"YES\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"YES\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"YES\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"YES\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
A prime number is a number which has exactly two distinct divisors: one and itself. For example, numbers 2, 7, 3 are prime, and 1, 6, 4 are not.
The next prime number after x is the smallest prime number greater than x. For example, the next prime number after 2 is 3, and the next prime number after 3 is 5. Note that there is exactly one next prime number after each number. So 5 is not the next prime number for 2.
One cold April morning Panoramix predicted that soon Kakofonix will break free from his straitjacket, and this will be a black day for the residents of the Gallic countryside.
Panoramix's prophecy tells that if some day Asterix and Obelix beat exactly x Roman soldiers, where x is a prime number, and next day they beat exactly y Roman soldiers, where y is the next prime number after x, then it's time to wait for Armageddon, for nothing can shut Kakofonix up while he sings his infernal song.
Yesterday the Gauls beat n Roman soldiers and it turned out that the number n was prime! Today their victims were a troop of m Romans (m > n). Determine whether the Gauls should wait for the black day after today's victory of Asterix and Obelix?
Input
The first and only input line contains two positive integers — n and m (2 ≤ n < m ≤ 50). It is guaranteed that n is prime.
Pretests contain all the cases with restrictions 2 ≤ n < m ≤ 4.
Output
Print YES, if m is the next prime number after n, or NO otherwise.
Examples
Input
3 5
Output
YES
Input
7 11
Output
YES
Input
7 9
Output
NO
### Input:
7 9
### Output:
NO
### Input:
3 5
### Output:
YES
### Code:
from math import ceil, sqrt
def array(arr, struc):
return (list(map(struc, arr.split())))
def isPrime(x):
for i in range(2, ceil(sqrt(x))+1):
if x % i == 0:
return False
return True
arr = array(input(), int)
prime1 = arr[0]
prime2 = arr[1]
counter = 0
tmp = prime1 + 1
while tmp <= prime2:
if isPrime(tmp):
if tmp == prime2:
counter = 1
print('YES')
break
else:
break
tmp += 1
if counter == 0:
print('NO')
|
855_B. Marvolo Gaunt's Ring_10640
|
Professor Dumbledore is helping Harry destroy the Horcruxes. He went to Gaunt Shack as he suspected a Horcrux to be present there. He saw Marvolo Gaunt's Ring and identified it as a Horcrux. Although he destroyed it, he is still affected by its curse. Professor Snape is helping Dumbledore remove the curse. For this, he wants to give Dumbledore exactly x drops of the potion he made.
Value of x is calculated as maximum of p·ai + q·aj + r·ak for given p, q, r and array a1, a2, ... an such that 1 ≤ i ≤ j ≤ k ≤ n. Help Snape find the value of x. Do note that the value of x may be negative.
Input
First line of input contains 4 integers n, p, q, r ( - 109 ≤ p, q, r ≤ 109, 1 ≤ n ≤ 105).
Next line of input contains n space separated integers a1, a2, ... an ( - 109 ≤ ai ≤ 109).
Output
Output a single integer the maximum value of p·ai + q·aj + r·ak that can be obtained provided 1 ≤ i ≤ j ≤ k ≤ n.
Examples
Input
5 1 2 3
1 2 3 4 5
Output
30
Input
5 1 2 -3
-1 -2 -3 -4 -5
Output
12
Note
In the first sample case, we can take i = j = k = 5, thus making the answer as 1·5 + 2·5 + 3·5 = 30.
In second sample case, selecting i = j = 1 and k = 5 gives the answer 12.
|
cin=lambda:map(int,input().split())
n,p,q,r=cin()
A=cin()
tp,tq,tr=-1e20,-1e20,-1e20
for a in A:
tp=max(tp,p*a)
tq=max(tq,tp+q*a)
tr=max(tr,tq+r*a)
print(tr)
# Made By Mostafa_Khaled
|
{
"input": [
"5 1 2 -3\n-1 -2 -3 -4 -5\n",
"5 1 2 3\n1 2 3 4 5\n",
"1 1000000000 1000000000 1000000000\n1000000000\n",
"1 -1000000000 -1000000000 -1000000000\n1000000000\n",
"1 999999999 999999999 999999999\n-999999999\n",
"1 1000000000 1000000000 1000000000\n-1000000000\n",
"3 -2 3 -2\n1 2 1\n",
"1 1 1 1\n-1\n",
"1 -1000000000 -1000000000 1000000000\n1000000000\n",
"1 -1 -1 -1\n1\n",
"3 1000000000 1000000000 1000000000\n-1000000000 -1000000000 -1000000000\n",
"2 -1000000000 -1000000000 -1000000000\n1000000000 1000000000\n",
"5 886327859 82309257 -68295239\n-731225382 354766539 -48222231 -474691998 360965777\n",
"43 959134961 -868367850 142426380\n921743429 63959718 -797293233 122041422 -407576197 700139744 299598010 168207043 362252658 591926075 941946099 812263640 -76679927 -824267725 89529990 -73303355 83596189 -982699817 -235197848 654773327 125211479 -497091570 -2301804 203486596 -126652024 309810546 -581289415 -740125230 64425927 -501018049 304730559 34930193 -762964086 723645139 -826821494 495947907 816331024 9932423 -876541603 -782692568 322360800 841436938 40787162\n",
"1 -1000000000 -1000000000 0\n1000000000\n",
"3 -1000000000 -1000000000 -1000000000\n1000000000 1000000000 1000000000\n",
"3 -1000000000 -1000000000 1\n1000000000 1000000000 1000000000\n",
"1 -100 -100 -100\n100\n",
"1 -1000000000 1 -1000000000\n1000000000\n",
"5 -1000000000 -1000000000 -1000000000\n1000000000 1000000000 1000000000 1000000000 1000000000\n",
"1 0 0 0\n0\n",
"3 1 1 1\n-1 -1 -1\n",
"1 1000000000 1000000000 -1000000000\n-1000000000\n",
"4 -96405765 -495906217 625385006\n-509961652 392159235 -577128498 -744548876\n",
"2 1 -1 1\n1 -1\n",
"1 1 2 3\n-1\n",
"1 -1000000000 0 0\n1000000000\n",
"1 1000000000 1000000000 1000010000\n1000000000\n",
"1 -1000000000 -1000000000 1000100000\n1000000000\n",
"1 -1 -1 0\n1\n",
"5 886327859 82309257 -52455744\n-731225382 354766539 -48222231 -474691998 360965777\n",
"3 -1000000000 -1000000000 2\n1000000000 1000000000 1000000000\n",
"1 -100 -100 -23\n100\n",
"1 0 0 0\n-1\n",
"4 -96405765 -495906217 625385006\n-509961652 392159235 -1028402579 -744548876\n",
"2 1 -1 2\n1 -1\n",
"1 2 2 3\n-1\n",
"1 -1000000000 0 1\n1000000000\n",
"5 1 2 -3\n-2 -2 -3 -4 -5\n",
"5 1 2 6\n1 2 3 4 5\n",
"1 1001000000 1000000000 1000010000\n1000000000\n",
"1 -1 0 0\n1\n",
"5 886327859 82309257 -52455744\n-731225382 354766539 -48222231 -474691998 611885880\n",
"3 -1000000000 -1000000000 2\n1000000000 1000000000 1010000000\n",
"1 -100 -100 -42\n100\n",
"1 0 -1 0\n-1\n",
"3 1 1 1\n-1 -1 1\n",
"4 -120766859 -495906217 625385006\n-509961652 392159235 -1028402579 -744548876\n",
"1 0 2 3\n-1\n",
"1 -879641637 0 1\n1000000000\n",
"5 1 2 -3\n-2 -2 -3 -4 -6\n",
"1 1001000000 1000000000 1010010000\n1000000000\n",
"3 -1000000000 -760174533 2\n1000000000 1000000000 1010000000\n",
"1 -100 -100 -56\n100\n",
"4 -143426208 -495906217 625385006\n-509961652 392159235 -1028402579 -744548876\n",
"1 0 2 3\n-2\n",
"3 -1000000000 -907115211 2\n1000000000 1000000000 1010000000\n",
"4 -198326037 -495906217 625385006\n-509961652 392159235 -1028402579 -744548876\n",
"1 0 4 3\n-2\n",
"5 1 2 6\n1 0 3 3 7\n",
"5 886327859 82309257 -64521244\n-731225382 336270522 -48222231 -474691998 611885880\n",
"4 -198326037 -237102669 625385006\n-509961652 392159235 -1028402579 -744548876\n",
"1 0 3 3\n-2\n",
"5 820732221 82309257 -64521244\n-731225382 336270522 -48222231 -474691998 611885880\n",
"4 -386394097 -237102669 625385006\n-509961652 392159235 -13316133 -744548876\n",
"5 1 2 11\n1 0 3 5 7\n",
"5 1159106736 82309257 -64521244\n-731225382 336270522 -7449814 -474691998 611885880\n",
"5 1 2 13\n1 0 3 5 7\n",
"4 -386394097 -237102669 625385006\n-509961652 521149045 -13316133 -1242508432\n",
"5 1159106736 82309257 -64521244\n-731225382 336270522 -2840438 -474691998 597955657\n",
"4 -386394097 -237102669 625385006\n-509961652 275901274 -13316133 -1242508432\n",
"5 1 2 13\n1 0 3 4 4\n",
"5 1159106736 82309257 -57396365\n-731225382 336270522 -2840438 -474691998 597955657\n",
"4 -655836964 -237102669 625385006\n-509961652 275901274 -13316133 -1242508432\n",
"5 1 2 8\n1 0 3 4 4\n",
"4 -655836964 -327236202 625385006\n-509961652 275901274 -13316133 -1242508432\n",
"5 1159106736 55594371 -57396365\n-731225382 336270522 -510102 -474691998 597955657\n",
"5 1 2 9\n1 0 3 1 4\n",
"5 1 2 9\n1 0 3 1 1\n",
"5 1 3 9\n1 0 3 1 1\n",
"5 2 3 9\n1 0 3 1 1\n",
"1 1100000000 1000000000 1000000000\n1000000000\n",
"3 0 3 -2\n1 2 1\n",
"1 1 1 1\n-2\n",
"1 -1000000000 -1000000000 1010000000\n1000000000\n",
"3 1 1 1\n-1 -1 0\n",
"2 2 -1 1\n1 -1\n",
"5 1 2 6\n1 0 3 4 5\n",
"1 -1 0 -1\n1\n",
"5 886327859 82309257 -52455744\n-731225382 494618017 -48222231 -474691998 611885880\n",
"1 0 -1 -1\n-1\n",
"3 1 1 0\n-1 -1 1\n",
"2 0 -1 1\n1 -1\n",
"5 1 2 6\n1 0 3 3 5\n",
"5 886327859 82309257 -52455744\n-731225382 336270522 -48222231 -474691998 611885880\n",
"1 0 0 -1\n-1\n",
"3 1 1 0\n-1 -1 0\n",
"2 0 -1 2\n1 -1\n",
"3 -1000000000 -907115211 2\n1000000000 1001000000 1010000000\n",
"1 0 1 -1\n-1\n",
"2 0 -1 2\n1 0\n",
"5 1 2 6\n1 0 3 5 7\n",
"1 0 1 -1\n0\n",
"4 -198326037 -237102669 625385006\n-509961652 392159235 -13316133 -744548876\n",
"2 -1 -1 2\n1 0\n",
"5 1 2 6\n1 -1 3 5 7\n",
"5 820732221 82309257 -64521244\n-731225382 336270522 -7449814 -474691998 611885880\n",
"1 -1 1 -1\n0\n",
"1 -1 1 -2\n0\n",
"4 -386394097 -237102669 625385006\n-509961652 392159235 -13316133 -1242508432\n",
"5 1159106736 82309257 -64521244\n-731225382 336270522 -2840438 -474691998 611885880\n",
"5 1 2 13\n1 0 3 4 7\n",
"5 1159106736 82309257 -57396365\n-731225382 336270522 -510102 -474691998 597955657\n",
"5 1 2 8\n1 0 3 1 4\n",
"5 4 3 9\n1 0 3 1 1\n"
],
"output": [
"12",
"30",
"3000000000000000000",
"-3000000000000000000",
"-2999999994000000003",
"-3000000000000000000",
"2",
"-3",
"-1000000000000000000",
"-3",
"-3000000000000000000",
"-3000000000000000000",
"376059240645059046",
"1876641179289775029",
"-2000000000000000000",
"-3000000000000000000",
"-1999999999000000000",
"-30000",
"-1999999999000000000",
"-3000000000000000000",
"0",
"-3",
"-1000000000000000000",
"547306902373544674",
"1",
"-6",
"-1000000000000000000",
"3000010000000000000\n",
"-999900000000000000\n",
"-2\n",
"368540359116198036\n",
"-1999999998000000000\n",
"-22300\n",
"0\n",
"547306902373544674\n",
"2\n",
"-7\n",
"-999999999000000000\n",
"9\n",
"45\n",
"3001010000000000000\n",
"-1\n",
"560598445045827360\n",
"-1999999997980000000\n",
"-24200\n",
"1\n",
"3\n",
"559730126114311962\n",
"-5\n",
"-879641636000000000\n",
"12\n",
"3011010000000000000\n",
"-1760174530980000000\n",
"-25600\n",
"571285525163596510\n",
"-10\n",
"-1907115208980000000\n",
"599282332654954018\n",
"-14\n",
"63\n",
"553215735960687360\n",
"467302447773412722\n",
"-12\n",
"513078691278895920\n",
"563209946339447842\n",
"98\n",
"720125279159244120\n",
"112\n",
"643878239440236702\n",
"703730872858145093\n",
"490503960701915076\n",
"64\n",
"707991234561635596\n",
"627909490276851360\n",
"44\n",
"673874135666127876\n",
"692016917351825494\n",
"48\n",
"36\n",
"39\n",
"42\n",
"3100000000000000000\n",
"4\n",
"-6\n",
"-990000000000000000\n",
"0\n",
"2\n",
"45\n",
"-2\n",
"560598445045827360\n",
"2\n",
"2\n",
"0\n",
"45\n",
"560598445045827360\n",
"1\n",
"0\n",
"1\n",
"-1907115208980000000\n",
"0\n",
"1\n",
"63\n",
"0\n",
"467302447773412722\n",
"0\n",
"63\n",
"513078691278895920\n",
"0\n",
"0\n",
"563209946339447842\n",
"720125279159244120\n",
"112\n",
"707991234561635596\n",
"44\n",
"48\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Professor Dumbledore is helping Harry destroy the Horcruxes. He went to Gaunt Shack as he suspected a Horcrux to be present there. He saw Marvolo Gaunt's Ring and identified it as a Horcrux. Although he destroyed it, he is still affected by its curse. Professor Snape is helping Dumbledore remove the curse. For this, he wants to give Dumbledore exactly x drops of the potion he made.
Value of x is calculated as maximum of p·ai + q·aj + r·ak for given p, q, r and array a1, a2, ... an such that 1 ≤ i ≤ j ≤ k ≤ n. Help Snape find the value of x. Do note that the value of x may be negative.
Input
First line of input contains 4 integers n, p, q, r ( - 109 ≤ p, q, r ≤ 109, 1 ≤ n ≤ 105).
Next line of input contains n space separated integers a1, a2, ... an ( - 109 ≤ ai ≤ 109).
Output
Output a single integer the maximum value of p·ai + q·aj + r·ak that can be obtained provided 1 ≤ i ≤ j ≤ k ≤ n.
Examples
Input
5 1 2 3
1 2 3 4 5
Output
30
Input
5 1 2 -3
-1 -2 -3 -4 -5
Output
12
Note
In the first sample case, we can take i = j = k = 5, thus making the answer as 1·5 + 2·5 + 3·5 = 30.
In second sample case, selecting i = j = 1 and k = 5 gives the answer 12.
### Input:
5 1 2 -3
-1 -2 -3 -4 -5
### Output:
12
### Input:
5 1 2 3
1 2 3 4 5
### Output:
30
### Code:
cin=lambda:map(int,input().split())
n,p,q,r=cin()
A=cin()
tp,tq,tr=-1e20,-1e20,-1e20
for a in A:
tp=max(tp,p*a)
tq=max(tq,tp+q*a)
tr=max(tr,tq+r*a)
print(tr)
# Made By Mostafa_Khaled
|
903_B. The Modcrab_10646
|
Vova is again playing some computer game, now an RPG. In the game Vova's character received a quest: to slay the fearsome monster called Modcrab.
After two hours of playing the game Vova has tracked the monster and analyzed its tactics. The Modcrab has h2 health points and an attack power of a2. Knowing that, Vova has decided to buy a lot of strong healing potions and to prepare for battle.
Vova's character has h1 health points and an attack power of a1. Also he has a large supply of healing potions, each of which increases his current amount of health points by c1 when Vova drinks a potion. All potions are identical to each other. It is guaranteed that c1 > a2.
The battle consists of multiple phases. In the beginning of each phase, Vova can either attack the monster (thus reducing its health by a1) or drink a healing potion (it increases Vova's health by c1; Vova's health can exceed h1). Then, if the battle is not over yet, the Modcrab attacks Vova, reducing his health by a2. The battle ends when Vova's (or Modcrab's) health drops to 0 or lower. It is possible that the battle ends in a middle of a phase after Vova's attack.
Of course, Vova wants to win the fight. But also he wants to do it as fast as possible. So he wants to make up a strategy that will allow him to win the fight after the minimum possible number of phases.
Help Vova to make up a strategy! You may assume that Vova never runs out of healing potions, and that he can always win.
Input
The first line contains three integers h1, a1, c1 (1 ≤ h1, a1 ≤ 100, 2 ≤ c1 ≤ 100) — Vova's health, Vova's attack power and the healing power of a potion.
The second line contains two integers h2, a2 (1 ≤ h2 ≤ 100, 1 ≤ a2 < c1) — the Modcrab's health and his attack power.
Output
In the first line print one integer n denoting the minimum number of phases required to win the battle.
Then print n lines. i-th line must be equal to HEAL if Vova drinks a potion in i-th phase, or STRIKE if he attacks the Modcrab.
The strategy must be valid: Vova's character must not be defeated before slaying the Modcrab, and the monster's health must be 0 or lower after Vova's last action.
If there are multiple optimal solutions, print any of them.
Examples
Input
10 6 100
17 5
Output
4
STRIKE
HEAL
STRIKE
STRIKE
Input
11 6 100
12 5
Output
2
STRIKE
STRIKE
Note
In the first example Vova's character must heal before or after his first attack. Otherwise his health will drop to zero in 2 phases while he needs 3 strikes to win.
In the second example no healing needed, two strikes are enough to get monster to zero health and win with 6 health left.
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class Character:
def __init__(self, hPoints, attPoints, healPoints):
self.hPoints = hPoints
self.attPoints = attPoints
self.healPoints = healPoints
def attack(self, boss):
boss.setHP(boss.getHP() - self.attPoints)
def recAttack(self, boss):
self.hPoints -= boss.getAP()
def heal(self):
self.hPoints += self.healPoints
def getHP(self):
return self.hPoints
def getAP(self):
return self.attPoints
def getHLP(self):
return self.healPoints
class Boss:
def __init__(self, hPoints, attPoints):
self.hPoints = hPoints
self.attPoints = attPoints
def setHP(self, nextHP):
self.hPoints = nextHP
def getAP(self):
return self.attPoints
def getHP(self):
return self.hPoints
def game(vova, modcrab):
numTurns = 0
vovaHP = vova.getHP()
vovaAP = vova.getAP()
vovaHeal = vova.getHLP()
mcHP = modcrab.getHP()
mcAP = modcrab.getAP()
while mcHP > 0:
if vovaHP - mcAP > 0 or vovaAP >= mcHP:
mcHP -= vovaAP
vovaHP -= mcAP
else:
vovaHP += vovaHeal
vovaHP -= mcAP
numTurns += 1
print(numTurns)
while modcrab.getHP() > 0:
if vova.getHP() - modcrab.getAP() > 0 or vova.getAP() >= modcrab.getHP():
vova.attack(modcrab)
vova.recAttack(modcrab)
print('STRIKE')
else:
vova.heal()
vova.recAttack(modcrab)
print('HEAL')
return
vStats = input().split()
mStats = input().split()
vova = Character(int(vStats[0]),int(vStats[1]), int(vStats[2]))
modcrab = Boss(int(mStats[0]),int(mStats[1]))
game(vova, modcrab)
|
{
"input": [
"10 6 100\n17 5\n",
"11 6 100\n12 5\n",
"6 6 100\n12 5\n",
"79 4 68\n9 65\n",
"50 1 2\n70 1\n",
"1 1 100\n100 99\n",
"12 12 19\n83 8\n",
"5 12 11\n4 2\n",
"25 27 91\n10 87\n",
"9 76 78\n86 69\n",
"1 1 2\n3 1\n",
"9 1 20\n4 19\n",
"14 5 2\n99 1\n",
"62 21 10\n47 2\n",
"20 1 5\n8 4\n",
"34 14 18\n74 14\n",
"4 1 2\n10 1\n",
"6 6 100\n17 5\n",
"50 1 3\n70 1\n",
"1 2 100\n100 99\n",
"12 12 19\n78 8\n",
"5 12 11\n4 1\n",
"9 76 78\n139 69\n",
"1 1 3\n3 1\n",
"8 5 2\n99 1\n",
"98 21 10\n47 2\n",
"20 2 5\n8 4\n",
"25 14 18\n74 14\n",
"4 1 2\n2 1\n",
"50 1 4\n70 1\n",
"1 4 100\n100 99\n",
"12 12 37\n78 8\n",
"9 10 78\n139 69\n",
"25 6 18\n74 14\n",
"50 1 4\n94 1\n",
"1 4 101\n100 99\n",
"12 12 17\n78 8\n",
"9 10 78\n189 69\n",
"25 6 18\n88 14\n",
"50 1 2\n94 1\n",
"1 4 101\n100 12\n",
"12 12 17\n78 11\n",
"22 6 18\n88 14\n",
"50 2 2\n94 1\n",
"12 24 17\n78 11\n",
"17 14 78\n189 69\n",
"1 4 100\n100 1\n",
"17 9 78\n189 69\n",
"55 3 2\n94 1\n",
"2 4 100\n100 1\n",
"13 24 14\n78 11\n",
"55 3 3\n164 1\n",
"55 3 6\n311 1\n",
"32 3 6\n311 1\n",
"20 3 6\n311 1\n",
"20 6 6\n311 1\n",
"20 6 2\n311 1\n",
"20 6 2\n366 1\n",
"20 9 2\n366 1\n",
"20 12 2\n366 1\n",
"17 12 2\n366 1\n",
"11 12 2\n366 1\n",
"2 6 100\n12 5\n",
"1 1 100\n100 90\n",
"12 24 19\n83 8\n",
"9 29 78\n86 69\n",
"8 1 20\n4 19\n",
"14 5 2\n191 1\n",
"34 20 18\n74 14\n",
"10 2 100\n17 5\n",
"6 6 100\n34 5\n",
"50 1 3\n130 1\n",
"1 2 100\n100 67\n",
"12 1 19\n78 8\n",
"14 1 2\n99 1\n",
"20 2 5\n14 4\n",
"38 14 18\n74 14\n",
"29 1 4\n70 1\n",
"1 4 100\n110 99\n",
"12 7 37\n78 8\n",
"9 10 78\n255 69\n",
"25 6 18\n74 13\n",
"50 1 4\n185 1\n",
"1 4 101\n110 99\n",
"12 12 33\n78 8\n",
"9 10 78\n304 69\n",
"1 6 18\n88 14\n",
"25 1 2\n94 1\n",
"1 4 101\n101 12\n",
"12 18 17\n78 11\n",
"5 14 78\n189 69\n",
"22 9 18\n88 14\n",
"1 4 100\n100 16\n",
"17 14 133\n189 69\n",
"35 2 2\n94 1\n",
"2 4 100\n110 1\n",
"13 24 17\n128 11\n",
"17 9 78\n297 69\n",
"13 24 14\n110 11\n",
"55 3 3\n143 1\n",
"55 3 3\n106 1\n",
"53 3 6\n311 1\n",
"20 3 8\n311 1\n",
"11 6 100\n14 5\n",
"9 6 100\n17 5\n",
"5 12 9\n4 1\n",
"98 21 10\n47 1\n",
"4 1 4\n2 1\n",
"11 6 100\n14 9\n",
"9 12 9\n4 1\n",
"11 6 100\n8 9\n",
"9 12 9\n6 1\n",
"9 14 78\n189 69\n",
"1 4 100\n100 12\n",
"9 24 9\n6 1\n",
"55 2 2\n94 1\n",
"13 24 17\n78 11\n"
],
"output": [
"4\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\n",
"2\nSTRIKE\nSTRIKE\n",
"2\nSTRIKE\nSTRIKE\n",
"21\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nSTRIKE\n",
"90\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\n",
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"11\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\n",
"1\nSTRIKE\n",
"1\nSTRIKE\n",
"9\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nSTRIKE\n",
"5\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\n",
"53\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nSTRIKE\n",
"26\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\n",
"3\nSTRIKE\nSTRIKE\nSTRIKE\n",
"17\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nSTRIKE\n",
"16\nSTRIKE\nSTRIKE\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nSTRIKE\n",
"16\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\n",
"4\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\n",
"80\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\n",
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"11\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\n",
"1\nSTRIKE\n",
"9\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nSTRIKE\n",
"4\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\n",
"32\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\n",
"3\nSTRIKE\nSTRIKE\nSTRIKE\n",
"4\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\n",
"18\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nSTRIKE\n",
"2\nSTRIKE\nSTRIKE\n",
"77\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\n",
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EAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nSTRIKE\n",
"9\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\n",
"113\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nSTRIKE\n",
"49\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nSTRIKE\nSTRIKE\n",
"109\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\n",
"1213\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nSTRIKE\n",
"12\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\n",
"157\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nSTRIKE\n",
"58\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nSTRIKE\nSTRIKE\n",
"138\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\n",
"29\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\n",
"17\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nSTRIKE\n",
"59\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nSTRIKE\nSTRIKE\n",
"47\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\n",
"8\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nSTRIKE\n",
"112\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nSTRIKE\n",
"26\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\n",
"173\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nSTRIKE\n",
"32\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\n",
"26\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\n",
"11\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nSTRIKE\nSTRIKE\n",
"55\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\n",
"114\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\n",
"119\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\n",
"121\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\n",
"59\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\n",
"84\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\n",
"102\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\n",
"62\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\n",
"42\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\n",
"45\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\n",
"51\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\n",
"3\nHEAL\nSTRIKE\nSTRIKE\n",
"991\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nSTRIKE\n",
"6\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\n",
"18\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nSTRIKE\n",
"54\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nSTRIKE\n",
"64\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\n",
"7\nSTRIKE\nSTRIKE\nHEAL\nHEAL\nHEAL\nSTRIKE\nSTRIKE\n",
"10\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\n",
"7\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\n",
"170\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\n",
"150\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nSTRIKE\n",
"133\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\n",
"184\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\n",
"12\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nSTRIKE\n",
"15\nSTRIKE\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nSTRIKE\n",
"84\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\n",
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nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nSTRIKE\n",
"15\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\n",
"217\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nSTRIKE\n",
"40\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nSTRIKE\nSTRIKE\n",
"230\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\n",
"1365\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nSTRIKE\n",
"9\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\n",
"261\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nSTRIKE\n",
"64\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nSTRIKE\nSTRIKE\n",
"163\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\n",
"30\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\n",
"11\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nSTRIKE\n",
"114\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nSTRIKE\n",
"37\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nSTRIKE\n",
"30\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\n",
"28\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\n",
"59\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\n",
"29\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\n",
"14\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nSTRIKE\n",
"277\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nSTRIKE\n",
"16\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nSTRIKE\n",
"48\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\n",
"36\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\n",
"115\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\n",
"116\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\n",
"3\nSTRIKE\nSTRIKE\nSTRIKE\n",
"4\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\n",
"1\nSTRIKE\n",
"3\nSTRIKE\nSTRIKE\nSTRIKE\n",
"2\nSTRIKE\nSTRIKE\n",
"4\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\n",
"1\nSTRIKE\n",
"2\nSTRIKE\nSTRIKE\n",
"1\nSTRIKE\n",
"113\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nHEAL\nSTRIKE\nSTRIKE\n",
"29\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nHEAL\nSTRIKE\nSTRIKE\nSTRIKE\n",
"1\nSTRIKE\n",
"47\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\nSTRIKE\n",
"8\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nHEAL\nHEAL\nSTRIKE\nSTRIKE\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Vova is again playing some computer game, now an RPG. In the game Vova's character received a quest: to slay the fearsome monster called Modcrab.
After two hours of playing the game Vova has tracked the monster and analyzed its tactics. The Modcrab has h2 health points and an attack power of a2. Knowing that, Vova has decided to buy a lot of strong healing potions and to prepare for battle.
Vova's character has h1 health points and an attack power of a1. Also he has a large supply of healing potions, each of which increases his current amount of health points by c1 when Vova drinks a potion. All potions are identical to each other. It is guaranteed that c1 > a2.
The battle consists of multiple phases. In the beginning of each phase, Vova can either attack the monster (thus reducing its health by a1) or drink a healing potion (it increases Vova's health by c1; Vova's health can exceed h1). Then, if the battle is not over yet, the Modcrab attacks Vova, reducing his health by a2. The battle ends when Vova's (or Modcrab's) health drops to 0 or lower. It is possible that the battle ends in a middle of a phase after Vova's attack.
Of course, Vova wants to win the fight. But also he wants to do it as fast as possible. So he wants to make up a strategy that will allow him to win the fight after the minimum possible number of phases.
Help Vova to make up a strategy! You may assume that Vova never runs out of healing potions, and that he can always win.
Input
The first line contains three integers h1, a1, c1 (1 ≤ h1, a1 ≤ 100, 2 ≤ c1 ≤ 100) — Vova's health, Vova's attack power and the healing power of a potion.
The second line contains two integers h2, a2 (1 ≤ h2 ≤ 100, 1 ≤ a2 < c1) — the Modcrab's health and his attack power.
Output
In the first line print one integer n denoting the minimum number of phases required to win the battle.
Then print n lines. i-th line must be equal to HEAL if Vova drinks a potion in i-th phase, or STRIKE if he attacks the Modcrab.
The strategy must be valid: Vova's character must not be defeated before slaying the Modcrab, and the monster's health must be 0 or lower after Vova's last action.
If there are multiple optimal solutions, print any of them.
Examples
Input
10 6 100
17 5
Output
4
STRIKE
HEAL
STRIKE
STRIKE
Input
11 6 100
12 5
Output
2
STRIKE
STRIKE
Note
In the first example Vova's character must heal before or after his first attack. Otherwise his health will drop to zero in 2 phases while he needs 3 strikes to win.
In the second example no healing needed, two strikes are enough to get monster to zero health and win with 6 health left.
### Input:
10 6 100
17 5
### Output:
4
STRIKE
HEAL
STRIKE
STRIKE
### Input:
11 6 100
12 5
### Output:
2
STRIKE
STRIKE
### Code:
class Character:
def __init__(self, hPoints, attPoints, healPoints):
self.hPoints = hPoints
self.attPoints = attPoints
self.healPoints = healPoints
def attack(self, boss):
boss.setHP(boss.getHP() - self.attPoints)
def recAttack(self, boss):
self.hPoints -= boss.getAP()
def heal(self):
self.hPoints += self.healPoints
def getHP(self):
return self.hPoints
def getAP(self):
return self.attPoints
def getHLP(self):
return self.healPoints
class Boss:
def __init__(self, hPoints, attPoints):
self.hPoints = hPoints
self.attPoints = attPoints
def setHP(self, nextHP):
self.hPoints = nextHP
def getAP(self):
return self.attPoints
def getHP(self):
return self.hPoints
def game(vova, modcrab):
numTurns = 0
vovaHP = vova.getHP()
vovaAP = vova.getAP()
vovaHeal = vova.getHLP()
mcHP = modcrab.getHP()
mcAP = modcrab.getAP()
while mcHP > 0:
if vovaHP - mcAP > 0 or vovaAP >= mcHP:
mcHP -= vovaAP
vovaHP -= mcAP
else:
vovaHP += vovaHeal
vovaHP -= mcAP
numTurns += 1
print(numTurns)
while modcrab.getHP() > 0:
if vova.getHP() - modcrab.getAP() > 0 or vova.getAP() >= modcrab.getHP():
vova.attack(modcrab)
vova.recAttack(modcrab)
print('STRIKE')
else:
vova.heal()
vova.recAttack(modcrab)
print('HEAL')
return
vStats = input().split()
mStats = input().split()
vova = Character(int(vStats[0]),int(vStats[1]), int(vStats[2]))
modcrab = Boss(int(mStats[0]),int(mStats[1]))
game(vova, modcrab)
|
925_C. Big Secret_10650
|
Vitya has learned that the answer for The Ultimate Question of Life, the Universe, and Everything is not the integer 54 42, but an increasing integer sequence a_1, …, a_n. In order to not reveal the secret earlier than needed, Vitya encrypted the answer and obtained the sequence b_1, …, b_n using the following rules:
* b_1 = a_1;
* b_i = a_i ⊕ a_{i - 1} for all i from 2 to n, where x ⊕ y is the [bitwise XOR](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) of x and y.
It is easy to see that the original sequence can be obtained using the rule a_i = b_1 ⊕ … ⊕ b_i.
However, some time later Vitya discovered that the integers b_i in the cypher got shuffled, and it can happen that when decrypted using the rule mentioned above, it can produce a sequence that is not increasing. In order to save his reputation in the scientific community, Vasya decided to find some permutation of integers b_i so that the sequence a_i = b_1 ⊕ … ⊕ b_i is strictly increasing. Help him find such a permutation or determine that it is impossible.
Input
The first line contains a single integer n (1 ≤ n ≤ 10^5).
The second line contains n integers b_1, …, b_n (1 ≤ b_i < 2^{60}).
Output
If there are no valid permutations, print a single line containing "No".
Otherwise in the first line print the word "Yes", and in the second line print integers b'_1, …, b'_n — a valid permutation of integers b_i. The unordered multisets \\{b_1, …, b_n\} and \\{b'_1, …, b'_n\} should be equal, i. e. for each integer x the number of occurrences of x in the first multiset should be equal to the number of occurrences of x in the second multiset. Apart from this, the sequence a_i = b'_1 ⊕ … ⊕ b'_i should be strictly increasing.
If there are multiple answers, print any of them.
Examples
Input
3
1 2 3
Output
No
Input
6
4 7 7 12 31 61
Output
Yes
4 12 7 31 7 61
Note
In the first example no permutation is valid.
In the second example the given answer lead to the sequence a_1 = 4, a_2 = 8, a_3 = 15, a_4 = 16, a_5 = 23, a_6 = 42.
|
n=int(input())
s=[[] for i in range(60)]
for b in list(map(int,input().split())):
for i in range(59,-1,-1):
if b>>i&1:
s[i].append(b)
break
ans=[]
cur=0
for i in range(n):
fl=False
for j in range(60):
if s[j]!=[] and cur>>j&1==0:
ans.append(s[j][-1])
cur^=s[j][-1]
s[j].pop()
fl=True
break
if not fl:
print('No')
exit()
print('Yes')
print(' '.join(str(i) for i in ans))
|
{
"input": [
"3\n1 2 3\n",
"6\n4 7 7 12 31 61\n",
"1\n4\n",
"5\n3 1 1 7 1\n",
"2\n531 108\n",
"10\n10 1 1 1 1 1 3 6 7 3\n",
"31\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 3 3 7 7 7 7 15 15 31\n",
"1\n3\n",
"5\n3 1 1 6 1\n",
"2\n610 108\n",
"1\n6\n",
"2\n610 14\n",
"2\n610 16\n",
"3\n1 1 3\n",
"2\n915 16\n",
"2\n915 31\n",
"2\n915 57\n",
"2\n915 3\n",
"2\n915 4\n",
"2\n915 8\n",
"2\n321 8\n",
"2\n321 2\n",
"2\n516 2\n",
"2\n516 3\n",
"2\n516 4\n",
"2\n689 4\n",
"2\n588 4\n",
"2\n588 6\n",
"2\n588 2\n",
"2\n799 2\n",
"2\n1463 2\n",
"2\n1546 2\n",
"2\n1546 3\n",
"2\n1956 3\n",
"2\n2678 3\n",
"2\n2111 3\n",
"2\n3643 3\n",
"2\n1572 3\n",
"2\n1572 1\n",
"2\n1646 1\n",
"2\n1449 1\n",
"2\n561 1\n",
"2\n561 2\n",
"2\n317 2\n",
"2\n180 2\n",
"2\n180 1\n",
"2\n104 2\n",
"2\n126 2\n",
"2\n153 2\n",
"2\n253 2\n",
"2\n253 3\n",
"2\n253 5\n",
"31\n1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 5 3 3 3 3 7 7 7 7 15 15 31\n",
"3\n2 2 3\n",
"6\n4 7 7 12 50 61\n",
"5\n4 1 1 6 1\n",
"3\n4 2 3\n",
"6\n4 7 7 7 50 61\n",
"5\n2 1 1 6 1\n",
"6\n4 7 7 7 50 47\n",
"5\n1 1 1 6 1\n",
"6\n5 7 7 7 50 47\n",
"5\n1 2 1 6 1\n",
"6\n5 7 7 7 61 47\n",
"6\n5 7 4 7 61 47\n",
"6\n5 7 4 4 61 47\n",
"6\n5 7 4 4 61 86\n",
"6\n5 7 4 4 29 86\n"
],
"output": [
"No\n",
"Yes\n4 12 7 31 7 61 ",
"Yes\n4 ",
"Yes\n1 3 1 7 1 ",
"Yes\n108 531 ",
"No\n",
"Yes\n1 3 1 7 1 3 1 15 1 3 1 7 1 3 1 31 1 3 1 7 1 3 1 15 1 3 1 7 1 3 1 ",
"Yes\n3 ",
"No\n",
"Yes\n108 610 ",
"Yes\n6 ",
"Yes\n14 610 ",
"Yes\n16 610 ",
"Yes\n1 3 1 ",
"Yes\n16 915 ",
"Yes\n31 915 ",
"Yes\n57 915 ",
"Yes\n3 915 ",
"Yes\n4 915 ",
"Yes\n8 915 ",
"Yes\n8 321 ",
"Yes\n2 321 ",
"Yes\n2 516 ",
"Yes\n3 516 ",
"Yes\n4 516 ",
"Yes\n4 689 ",
"Yes\n4 588 ",
"Yes\n6 588 ",
"Yes\n2 588 ",
"Yes\n2 799 ",
"Yes\n2 1463 ",
"Yes\n2 1546 ",
"Yes\n3 1546 ",
"Yes\n3 1956 ",
"Yes\n3 2678 ",
"Yes\n3 2111 ",
"Yes\n3 3643 ",
"Yes\n3 1572 ",
"Yes\n1 1572 ",
"Yes\n1 1646 ",
"Yes\n1 1449 ",
"Yes\n1 561 ",
"Yes\n2 561 ",
"Yes\n2 317 ",
"Yes\n2 180 ",
"Yes\n1 180 ",
"Yes\n2 104 ",
"Yes\n2 126 ",
"Yes\n2 153 ",
"Yes\n2 253 ",
"Yes\n3 253 ",
"Yes\n5 253 ",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Vitya has learned that the answer for The Ultimate Question of Life, the Universe, and Everything is not the integer 54 42, but an increasing integer sequence a_1, …, a_n. In order to not reveal the secret earlier than needed, Vitya encrypted the answer and obtained the sequence b_1, …, b_n using the following rules:
* b_1 = a_1;
* b_i = a_i ⊕ a_{i - 1} for all i from 2 to n, where x ⊕ y is the [bitwise XOR](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) of x and y.
It is easy to see that the original sequence can be obtained using the rule a_i = b_1 ⊕ … ⊕ b_i.
However, some time later Vitya discovered that the integers b_i in the cypher got shuffled, and it can happen that when decrypted using the rule mentioned above, it can produce a sequence that is not increasing. In order to save his reputation in the scientific community, Vasya decided to find some permutation of integers b_i so that the sequence a_i = b_1 ⊕ … ⊕ b_i is strictly increasing. Help him find such a permutation or determine that it is impossible.
Input
The first line contains a single integer n (1 ≤ n ≤ 10^5).
The second line contains n integers b_1, …, b_n (1 ≤ b_i < 2^{60}).
Output
If there are no valid permutations, print a single line containing "No".
Otherwise in the first line print the word "Yes", and in the second line print integers b'_1, …, b'_n — a valid permutation of integers b_i. The unordered multisets \\{b_1, …, b_n\} and \\{b'_1, …, b'_n\} should be equal, i. e. for each integer x the number of occurrences of x in the first multiset should be equal to the number of occurrences of x in the second multiset. Apart from this, the sequence a_i = b'_1 ⊕ … ⊕ b'_i should be strictly increasing.
If there are multiple answers, print any of them.
Examples
Input
3
1 2 3
Output
No
Input
6
4 7 7 12 31 61
Output
Yes
4 12 7 31 7 61
Note
In the first example no permutation is valid.
In the second example the given answer lead to the sequence a_1 = 4, a_2 = 8, a_3 = 15, a_4 = 16, a_5 = 23, a_6 = 42.
### Input:
3
1 2 3
### Output:
No
### Input:
6
4 7 7 12 31 61
### Output:
Yes
4 12 7 31 7 61
### Code:
n=int(input())
s=[[] for i in range(60)]
for b in list(map(int,input().split())):
for i in range(59,-1,-1):
if b>>i&1:
s[i].append(b)
break
ans=[]
cur=0
for i in range(n):
fl=False
for j in range(60):
if s[j]!=[] and cur>>j&1==0:
ans.append(s[j][-1])
cur^=s[j][-1]
s[j].pop()
fl=True
break
if not fl:
print('No')
exit()
print('Yes')
print(' '.join(str(i) for i in ans))
|
954_D. Fight Against Traffic_10654
|
Little town Nsk consists of n junctions connected by m bidirectional roads. Each road connects two distinct junctions and no two roads connect the same pair of junctions. It is possible to get from any junction to any other junction by these roads. The distance between two junctions is equal to the minimum possible number of roads on a path between them.
In order to improve the transportation system, the city council asks mayor to build one new road. The problem is that the mayor has just bought a wonderful new car and he really enjoys a ride from his home, located near junction s to work located near junction t. Thus, he wants to build a new road in such a way that the distance between these two junctions won't decrease.
You are assigned a task to compute the number of pairs of junctions that are not connected by the road, such that if the new road between these two junctions is built the distance between s and t won't decrease.
Input
The firt line of the input contains integers n, m, s and t (2 ≤ n ≤ 1000, 1 ≤ m ≤ 1000, 1 ≤ s, t ≤ n, s ≠ t) — the number of junctions and the number of roads in Nsk, as well as the indices of junctions where mayors home and work are located respectively. The i-th of the following m lines contains two integers ui and vi (1 ≤ ui, vi ≤ n, ui ≠ vi), meaning that this road connects junctions ui and vi directly. It is guaranteed that there is a path between any two junctions and no two roads connect the same pair of junctions.
Output
Print one integer — the number of pairs of junctions not connected by a direct road, such that building a road between these two junctions won't decrease the distance between junctions s and t.
Examples
Input
5 4 1 5
1 2
2 3
3 4
4 5
Output
0
Input
5 4 3 5
1 2
2 3
3 4
4 5
Output
5
Input
5 6 1 5
1 2
1 3
1 4
4 5
3 5
2 5
Output
3
|
from collections import deque
def bfs(s, graph):
q = deque()
d = [0] * len(graph)
used = [False] * len(graph)
used[s] = True
q.append(s)
while len(q):
cur = q[0]
q.popleft()
for to in graph[cur]:
if not used[to]:
used[to] = True
d[to] = d[cur] + 1
q.append(to)
return d
n, m, s, t = map(int, input().split())
graph = [set() for _ in range(n + 1)]
for i in range(m):
u, v = map(int, input().split())
graph[u].add(v)
graph[v].add(u)
ds = bfs(s, graph)
dt = bfs(t, graph)
ans = 0
for u in range(1, n + 1):
for v in range(u + 1, n + 1):
if v not in graph[u] and min(ds[u] + dt[v], dt[u] + ds[v]) + 1 >= ds[t]:
ans += 1
print(ans)
|
{
"input": [
"5 4 3 5\n1 2\n2 3\n3 4\n4 5\n",
"5 6 1 5\n1 2\n1 3\n1 4\n4 5\n3 5\n2 5\n",
"5 4 1 5\n1 2\n2 3\n3 4\n4 5\n",
"3 3 2 3\n1 2\n2 3\n1 3\n",
"2 1 2 1\n1 2\n",
"3 2 2 3\n1 2\n2 3\n",
"3 2 1 3\n1 2\n2 3\n",
"3 2 1 1\n1 2\n2 3\n",
"3 3 3 3\n1 2\n2 3\n1 3\n",
"5 4 3 5\n1 4\n2 3\n3 4\n4 5\n",
"5 6 1 5\n1 2\n1 3\n1 4\n4 5\n3 5\n1 5\n",
"5 6 1 5\n1 2\n1 3\n2 4\n4 5\n3 5\n2 5\n",
"5 4 4 5\n1 2\n2 3\n1 4\n4 5\n",
"5 4 4 5\n1 4\n2 3\n2 4\n3 5\n",
"3 2 1 1\n1 3\n2 3\n",
"3 2 2 3\n1 3\n2 3\n",
"5 6 1 5\n1 2\n1 3\n1 4\n1 5\n3 5\n2 5\n",
"3 3 1 3\n1 2\n2 3\n1 3\n",
"5 4 3 5\n1 2\n2 3\n1 4\n4 5\n",
"5 6 1 5\n1 2\n1 5\n1 4\n4 5\n3 5\n2 5\n",
"3 2 1 1\n1 3\n2 1\n",
"5 6 1 5\n1 2\n1 5\n1 4\n4 3\n3 5\n2 5\n",
"3 2 2 3\n1 2\n1 3\n",
"3 2 1 2\n1 2\n2 3\n",
"5 6 1 5\n1 2\n1 3\n1 4\n1 5\n3 2\n2 5\n",
"5 4 3 5\n1 5\n2 3\n3 4\n4 5\n",
"5 6 1 5\n1 2\n1 3\n1 4\n1 5\n3 4\n2 5\n",
"3 3 2 1\n1 2\n2 3\n1 3\n",
"5 4 1 5\n1 2\n2 5\n3 4\n4 5\n",
"5 6 1 2\n1 2\n1 3\n1 4\n4 5\n3 5\n1 5\n",
"5 4 3 5\n1 3\n2 3\n3 4\n4 5\n",
"5 6 1 5\n1 2\n1 3\n1 4\n1 5\n5 4\n2 5\n",
"5 4 1 5\n1 3\n2 3\n3 4\n4 5\n",
"5 6 2 5\n1 2\n1 3\n1 4\n4 5\n3 5\n1 5\n",
"5 4 1 2\n1 3\n2 3\n3 4\n4 5\n",
"2 1 2 2\n1 2\n",
"5 6 2 5\n1 2\n1 3\n1 4\n4 5\n3 5\n2 5\n",
"5 4 1 1\n1 2\n2 3\n3 4\n4 5\n",
"5 6 1 5\n1 2\n1 3\n2 4\n4 5\n1 5\n2 5\n",
"5 6 1 3\n1 2\n1 3\n1 4\n1 5\n3 5\n2 5\n",
"3 2 1 2\n1 3\n2 1\n",
"3 2 2 2\n1 2\n2 3\n",
"5 4 4 5\n1 3\n2 3\n3 4\n4 5\n",
"2 1 1 2\n1 2\n",
"3 2 2 2\n1 2\n1 3\n",
"5 6 1 5\n1 2\n1 3\n1 4\n4 5\n1 5\n2 5\n",
"5 6 1 2\n1 2\n1 3\n1 4\n1 5\n3 4\n2 5\n",
"5 4 1 5\n1 2\n2 5\n3 4\n3 5\n",
"5 4 4 5\n1 2\n2 3\n2 4\n4 5\n",
"5 6 2 5\n1 2\n1 3\n1 4\n4 5\n2 5\n1 5\n",
"5 4 1 2\n1 3\n2 5\n3 4\n4 5\n",
"5 6 1 3\n1 2\n1 3\n2 4\n1 5\n3 5\n2 5\n",
"5 4 4 5\n1 3\n2 3\n2 4\n4 5\n",
"5 4 1 5\n1 2\n2 5\n2 4\n3 5\n",
"5 4 4 5\n1 4\n2 3\n2 4\n4 5\n",
"5 6 1 5\n1 2\n1 5\n2 4\n4 3\n3 5\n2 5\n",
"5 4 4 5\n1 3\n2 3\n1 4\n4 5\n",
"5 4 1 2\n1 3\n2 1\n3 4\n4 5\n",
"5 4 1 1\n1 2\n2 3\n3 4\n3 5\n",
"5 6 1 5\n1 2\n1 3\n2 3\n4 5\n1 5\n2 5\n",
"5 6 1 2\n1 2\n1 3\n2 4\n1 5\n3 5\n2 5\n",
"5 6 1 5\n1 2\n1 5\n1 4\n4 2\n3 5\n2 5\n",
"5 4 1 5\n1 2\n1 5\n3 4\n4 5\n",
"5 6 1 3\n1 2\n1 3\n1 4\n1 5\n3 5\n4 5\n",
"5 4 4 5\n1 2\n1 3\n2 4\n4 5\n",
"5 6 2 5\n1 2\n2 3\n1 4\n4 5\n2 5\n1 5\n",
"5 4 4 1\n1 4\n2 3\n2 4\n4 5\n",
"5 6 2 5\n1 2\n1 5\n2 4\n4 3\n3 5\n2 5\n",
"5 4 1 5\n1 3\n2 3\n1 4\n4 5\n",
"5 4 1 2\n2 3\n2 1\n3 4\n4 5\n",
"5 4 1 1\n1 2\n2 3\n3 4\n1 5\n",
"5 4 1 1\n1 4\n2 3\n2 4\n4 5\n",
"5 4 1 3\n2 3\n2 1\n3 4\n4 5\n"
],
"output": [
"5\n",
"3\n",
"0\n",
"0\n",
"0\n",
"1\n",
"0\n",
"1\n",
"0\n",
"5\n",
"4\n",
"3\n",
"6\n",
"2\n",
"1\n",
"1\n",
"4\n",
"0\n",
"0\n",
"4\n",
"1\n",
"4\n",
"0\n",
"1\n",
"4\n",
"5\n",
"4\n",
"0\n",
"5\n",
"4\n",
"5\n",
"4\n",
"3\n",
"3\n",
"5\n",
"0\n",
"4\n",
"6\n",
"4\n",
"4\n",
"1\n",
"1\n",
"6\n",
"0\n",
"1\n",
"4\n",
"4\n",
"5\n",
"6\n",
"4\n",
"0\n",
"4\n",
"6\n",
"5\n",
"6\n",
"4\n",
"6\n",
"6\n",
"6\n",
"4\n",
"4\n",
"4\n",
"6\n",
"4\n",
"6\n",
"4\n",
"6\n",
"4\n",
"5\n",
"6\n",
"6\n",
"6\n",
"5\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Little town Nsk consists of n junctions connected by m bidirectional roads. Each road connects two distinct junctions and no two roads connect the same pair of junctions. It is possible to get from any junction to any other junction by these roads. The distance between two junctions is equal to the minimum possible number of roads on a path between them.
In order to improve the transportation system, the city council asks mayor to build one new road. The problem is that the mayor has just bought a wonderful new car and he really enjoys a ride from his home, located near junction s to work located near junction t. Thus, he wants to build a new road in such a way that the distance between these two junctions won't decrease.
You are assigned a task to compute the number of pairs of junctions that are not connected by the road, such that if the new road between these two junctions is built the distance between s and t won't decrease.
Input
The firt line of the input contains integers n, m, s and t (2 ≤ n ≤ 1000, 1 ≤ m ≤ 1000, 1 ≤ s, t ≤ n, s ≠ t) — the number of junctions and the number of roads in Nsk, as well as the indices of junctions where mayors home and work are located respectively. The i-th of the following m lines contains two integers ui and vi (1 ≤ ui, vi ≤ n, ui ≠ vi), meaning that this road connects junctions ui and vi directly. It is guaranteed that there is a path between any two junctions and no two roads connect the same pair of junctions.
Output
Print one integer — the number of pairs of junctions not connected by a direct road, such that building a road between these two junctions won't decrease the distance between junctions s and t.
Examples
Input
5 4 1 5
1 2
2 3
3 4
4 5
Output
0
Input
5 4 3 5
1 2
2 3
3 4
4 5
Output
5
Input
5 6 1 5
1 2
1 3
1 4
4 5
3 5
2 5
Output
3
### Input:
5 4 3 5
1 2
2 3
3 4
4 5
### Output:
5
### Input:
5 6 1 5
1 2
1 3
1 4
4 5
3 5
2 5
### Output:
3
### Code:
from collections import deque
def bfs(s, graph):
q = deque()
d = [0] * len(graph)
used = [False] * len(graph)
used[s] = True
q.append(s)
while len(q):
cur = q[0]
q.popleft()
for to in graph[cur]:
if not used[to]:
used[to] = True
d[to] = d[cur] + 1
q.append(to)
return d
n, m, s, t = map(int, input().split())
graph = [set() for _ in range(n + 1)]
for i in range(m):
u, v = map(int, input().split())
graph[u].add(v)
graph[v].add(u)
ds = bfs(s, graph)
dt = bfs(t, graph)
ans = 0
for u in range(1, n + 1):
for v in range(u + 1, n + 1):
if v not in graph[u] and min(ds[u] + dt[v], dt[u] + ds[v]) + 1 >= ds[t]:
ans += 1
print(ans)
|
980_C. Posterized_10658
|
Professor Ibrahim has prepared the final homework for his algorithm’s class. He asked his students to implement the Posterization Image Filter.
Their algorithm will be tested on an array of integers, where the i-th integer represents the color of the i-th pixel in the image. The image is in black and white, therefore the color of each pixel will be an integer between 0 and 255 (inclusive).
To implement the filter, students are required to divide the black and white color range [0, 255] into groups of consecutive colors, and select one color in each group to be the group’s key. In order to preserve image details, the size of a group must not be greater than k, and each color should belong to exactly one group.
Finally, the students will replace the color of each pixel in the array with that color’s assigned group key.
To better understand the effect, here is an image of a basking turtle where the Posterization Filter was applied with increasing k to the right.
<image>
To make the process of checking the final answer easier, Professor Ibrahim wants students to divide the groups and assign the keys in a way that produces the lexicographically smallest possible array.
Input
The first line of input contains two integers n and k (1 ≤ n ≤ 10^5, 1 ≤ k ≤ 256), the number of pixels in the image, and the maximum size of a group, respectively.
The second line contains n integers p_1, p_2, ..., p_n (0 ≤ p_i ≤ 255), where p_i is the color of the i-th pixel.
Output
Print n space-separated integers; the lexicographically smallest possible array that represents the image after applying the Posterization filter.
Examples
Input
4 3
2 14 3 4
Output
0 12 3 3
Input
5 2
0 2 1 255 254
Output
0 1 1 254 254
Note
One possible way to group colors and assign keys for the first sample:
Color 2 belongs to the group [0,2], with group key 0.
Color 14 belongs to the group [12,14], with group key 12.
Colors 3 and 4 belong to group [3, 5], with group key 3.
Other groups won't affect the result so they are not listed here.
|
R = lambda: map(int, input().split())
n, k = R()
a = list(range(0, 257)); v = [1]*257
for p in R():
if v[p]:
t = p
while t >= 0 and p-a[t]<=k-1: t -= 1
t += 1
for i in range(t, p+1): a[i] = a[t]; v[i] = 0
print(a[p], end=' ')
|
{
"input": [
"5 2\n0 2 1 255 254\n",
"4 3\n2 14 3 4\n",
"10 3\n112 184 161 156 118 231 191 128 91 229\n",
"9 3\n174 149 118 124 166 146 219 233 107\n",
"1 4\n51\n",
"8 4\n180 195 13 195 61 24 132 160\n",
"4 2\n122 108 224 154\n",
"3 3\n212 167 3\n",
"2 4\n218 213\n",
"100 7\n39 242 238 155 95 30 129 132 72 59 22 61 133 113 99 81 253 204 160 109 92 187 11 227 145 148 100 42 78 14 113 91 140 197 123 182 4 185 208 27 182 207 63 146 102 79 159 195 26 100 72 127 157 159 152 53 0 117 111 125 19 188 179 145 240 50 205 207 113 246 42 56 181 13 188 244 159 222 119 204 87 182 212 175 199 69 81 45 30 32 238 255 81 61 177 125 149 121 35 38\n",
"10 3\n112 184 75 156 118 231 191 128 91 229\n",
"8 4\n180 18 13 195 61 24 132 160\n",
"2 5\n218 213\n",
"100 7\n39 242 238 155 95 30 129 132 72 59 22 91 133 113 99 81 253 204 160 109 92 187 11 227 145 148 100 42 78 14 113 91 140 197 123 182 4 185 208 27 182 207 63 146 102 79 159 195 26 100 72 127 157 159 152 53 0 117 111 125 19 188 179 145 240 50 205 207 113 246 42 56 181 13 188 244 159 222 119 204 87 182 212 175 199 69 81 45 30 32 238 255 81 61 177 125 149 121 35 38\n",
"5 2\n0 2 1 142 254\n",
"10 3\n112 214 75 156 118 231 191 128 91 229\n",
"2 5\n209 213\n",
"100 7\n39 242 238 155 95 30 129 132 72 59 22 91 133 113 99 81 253 204 160 109 92 187 11 227 145 148 100 42 78 14 113 91 140 197 123 182 4 185 208 27 182 207 63 146 102 79 159 195 26 100 72 127 157 159 152 53 0 117 111 125 19 188 179 145 240 50 205 207 113 246 42 56 161 13 188 244 159 222 119 204 87 182 212 175 199 69 81 45 30 32 238 255 81 61 177 125 149 121 35 38\n",
"10 3\n112 214 75 7 118 231 191 128 91 229\n",
"100 7\n39 242 238 155 95 30 129 132 72 59 22 91 133 113 99 81 253 204 160 109 92 187 11 227 145 148 100 42 78 14 113 91 140 197 123 182 4 185 208 27 182 207 63 146 102 39 159 195 26 100 72 127 157 159 152 53 0 117 111 125 19 188 179 145 240 50 205 207 113 246 42 56 161 13 188 244 159 222 119 204 87 182 212 175 199 69 81 45 30 32 238 255 81 61 177 125 149 121 35 38\n",
"10 3\n112 214 75 7 118 231 191 79 91 229\n",
"100 7\n39 242 238 155 95 19 129 132 72 59 22 91 133 113 99 81 253 204 160 109 92 187 11 227 145 148 100 42 78 14 113 91 140 197 123 182 4 185 208 27 182 207 63 146 102 39 159 195 26 100 72 127 157 159 152 53 0 117 111 125 19 188 179 145 240 50 205 207 113 246 42 56 161 13 188 244 159 222 119 204 87 182 212 175 199 69 81 45 30 32 238 255 81 61 177 125 149 121 35 38\n",
"10 3\n56 214 75 7 118 231 191 79 91 229\n",
"10 3\n56 214 75 7 118 232 191 79 91 229\n",
"10 3\n56 214 75 7 118 232 191 79 91 25\n",
"9 3\n174 149 118 124 242 146 219 233 107\n",
"8 4\n180 195 7 195 61 24 132 160\n",
"3 3\n212 167 0\n",
"2 4\n62 213\n",
"5 2\n0 0 1 255 254\n",
"4 3\n2 14 3 3\n",
"10 3\n112 72 75 156 118 231 191 128 91 229\n",
"8 4\n180 18 13 195 61 24 132 69\n",
"10 3\n112 214 75 156 147 231 191 128 91 229\n",
"2 3\n209 213\n",
"100 7\n39 242 238 155 95 30 129 132 72 59 22 91 133 113 99 81 253 204 160 109 92 187 11 227 145 148 100 42 78 14 113 91 140 197 156 182 4 185 208 27 182 207 63 146 102 79 159 195 26 100 72 127 157 159 152 53 0 117 111 125 19 188 179 145 240 50 205 207 113 246 42 56 161 13 188 244 159 222 119 204 87 182 212 175 199 69 81 45 30 32 238 255 81 61 177 125 149 121 35 38\n",
"10 3\n112 239 75 7 118 231 191 128 91 229\n",
"100 7\n39 242 238 155 95 30 129 132 72 59 22 91 203 113 99 81 253 204 160 109 92 187 11 227 145 148 100 42 78 14 113 91 140 197 123 182 4 185 208 27 182 207 63 146 102 39 159 195 26 100 72 127 157 159 152 53 0 117 111 125 19 188 179 145 240 50 205 207 113 246 42 56 161 13 188 244 159 222 119 204 87 182 212 175 199 69 81 45 30 32 238 255 81 61 177 125 149 121 35 38\n",
"10 3\n167 214 75 7 118 231 191 79 91 229\n",
"100 7\n39 242 238 155 95 19 129 132 72 59 22 91 133 113 99 81 253 204 160 109 83 187 11 227 145 148 100 42 78 14 113 91 140 197 123 182 4 185 208 27 182 207 63 146 102 39 159 195 26 100 72 127 157 159 152 53 0 117 111 125 19 188 179 145 240 50 205 207 113 246 42 56 161 13 188 244 159 222 119 204 87 182 212 175 199 69 81 45 30 32 238 255 81 61 177 125 149 121 35 38\n",
"10 3\n81 214 75 7 118 231 191 79 91 229\n",
"10 3\n56 214 75 4 118 232 191 79 91 25\n",
"9 3\n86 149 118 124 242 146 219 233 107\n",
"5 2\n0 0 2 255 254\n",
"4 3\n2 14 2 3\n",
"10 3\n112 138 75 156 118 231 191 128 91 229\n",
"8 4\n180 18 13 195 61 14 132 69\n",
"10 3\n112 214 75 156 147 231 34 128 91 229\n",
"2 4\n209 213\n",
"100 7\n39 242 238 155 95 30 129 132 72 59 22 91 133 113 99 81 253 204 160 109 92 187 11 227 145 148 100 42 78 14 113 91 140 197 156 182 4 185 208 27 182 207 63 146 102 79 159 195 26 100 72 127 157 159 152 53 0 117 111 125 19 188 179 145 240 50 205 207 113 246 42 56 161 13 188 244 159 222 119 204 87 182 212 175 199 69 81 45 30 32 238 255 81 61 177 125 111 121 35 38\n",
"100 7\n39 242 238 155 95 30 129 132 72 59 22 91 203 113 99 81 253 204 160 109 92 187 11 227 145 211 100 42 78 14 113 91 140 197 123 182 4 185 208 27 182 207 63 146 102 39 159 195 26 100 72 127 157 159 152 53 0 117 111 125 19 188 179 145 240 50 205 207 113 246 42 56 161 13 188 244 159 222 119 204 87 182 212 175 199 69 81 45 30 32 238 255 81 61 177 125 149 121 35 38\n",
"10 3\n167 214 75 7 118 231 191 58 91 229\n",
"100 7\n39 242 238 155 95 19 129 132 72 59 22 91 133 113 99 81 253 204 160 109 83 187 11 227 145 148 100 42 78 14 113 91 140 197 123 182 4 185 208 27 182 207 63 146 102 39 159 195 26 100 72 127 157 159 152 53 0 117 111 125 19 188 179 145 240 50 205 207 113 246 42 56 161 13 188 244 159 222 119 204 87 182 212 175 199 69 81 45 30 32 238 255 81 61 177 125 149 121 7 38\n",
"10 6\n81 214 75 7 118 231 191 79 91 229\n",
"10 3\n56 214 75 4 118 232 240 79 91 25\n",
"8 4\n180 18 13 195 61 14 132 129\n",
"10 3\n112 214 75 156 147 70 34 128 91 229\n",
"100 7\n39 242 238 155 95 30 129 132 72 59 22 91 203 113 99 81 253 204 160 109 92 187 11 227 145 211 100 42 78 14 113 91 140 197 123 182 4 185 208 27 182 207 63 146 102 39 159 195 26 100 72 127 157 159 152 53 0 117 111 125 19 188 179 145 240 50 205 207 113 246 42 56 161 13 188 244 159 222 119 204 26 182 212 175 199 69 81 45 30 32 238 255 81 61 177 125 149 121 35 38\n",
"10 3\n167 214 109 7 118 231 191 58 91 229\n",
"100 7\n39 242 238 155 95 19 129 132 72 59 22 91 133 113 99 81 253 204 160 109 83 187 11 227 145 148 100 42 78 14 113 91 140 197 123 182 4 185 208 27 182 207 63 146 102 39 159 195 26 100 72 127 157 159 152 53 0 117 111 125 19 188 179 145 240 50 205 207 113 246 42 56 161 13 188 244 159 222 119 204 87 182 212 175 199 25 81 45 30 32 238 255 81 61 177 125 149 121 7 38\n",
"10 6\n142 214 75 7 118 231 191 79 91 229\n",
"8 4\n180 12 13 195 61 14 132 129\n",
"10 3\n112 214 75 156 147 113 34 128 91 229\n",
"100 7\n39 242 238 155 95 30 129 132 72 59 22 91 203 113 99 81 253 204 160 109 92 187 11 227 145 211 100 42 78 14 113 91 140 197 123 182 4 185 208 27 182 207 63 146 102 39 159 195 26 100 72 127 157 159 152 53 0 117 111 125 19 188 179 145 240 50 205 207 113 246 42 56 161 13 188 244 159 222 119 204 26 182 212 175 199 69 81 45 30 32 238 255 81 61 177 150 149 121 35 38\n",
"100 7\n39 242 238 155 95 19 129 132 72 59 22 91 133 113 99 81 253 204 160 109 83 187 11 227 145 148 100 42 78 14 113 91 140 197 123 182 4 185 208 27 182 207 63 146 102 39 159 195 26 100 72 127 157 159 152 53 0 117 111 125 19 188 179 145 240 50 205 207 113 246 42 56 161 13 188 244 159 222 119 204 87 182 212 175 199 31 81 45 30 32 238 255 81 61 177 125 149 121 7 38\n",
"10 6\n142 214 75 7 118 231 191 112 91 229\n",
"8 4\n180 19 13 195 61 14 132 129\n",
"10 3\n112 139 75 156 147 113 34 128 91 229\n",
"100 7\n39 242 238 155 95 30 129 132 72 59 22 91 203 113 99 81 253 204 160 109 92 187 11 227 145 211 100 42 78 14 113 91 140 197 123 182 4 185 208 27 182 207 63 146 102 39 159 195 26 100 72 127 157 159 152 53 0 117 101 125 19 188 179 145 240 50 205 207 113 246 42 56 161 13 188 244 159 222 119 204 26 182 212 175 199 69 81 45 30 32 238 255 81 61 177 150 149 121 35 38\n",
"100 7\n39 242 238 155 95 19 129 132 72 59 22 91 133 113 99 81 253 204 160 109 83 187 11 227 145 148 100 42 78 14 113 91 140 197 123 182 4 185 208 27 182 207 63 146 102 39 159 195 20 100 72 127 157 159 152 53 0 117 111 125 19 188 179 145 240 50 205 207 113 246 42 56 161 13 188 244 159 222 119 204 87 182 212 175 199 31 81 45 30 32 238 255 81 61 177 125 149 121 7 38\n",
"10 6\n142 214 75 7 118 231 249 112 91 229\n",
"10 3\n112 139 75 156 15 113 34 128 91 229\n",
"100 7\n39 242 238 155 95 30 129 132 72 59 22 91 203 113 99 81 253 204 160 109 92 187 11 227 145 211 100 42 78 14 113 91 140 197 123 182 4 185 208 27 182 207 63 146 102 39 159 195 26 100 72 127 157 159 152 53 0 117 101 125 19 188 179 145 240 50 205 207 113 246 42 56 161 13 188 244 159 222 119 204 26 182 212 175 199 69 81 45 30 32 238 255 142 61 177 150 149 121 35 38\n",
"100 7\n39 242 238 155 95 19 129 3 72 59 22 91 133 113 99 81 253 204 160 109 83 187 11 227 145 148 100 42 78 14 113 91 140 197 123 182 4 185 208 27 182 207 63 146 102 39 159 195 20 100 72 127 157 159 152 53 0 117 111 125 19 188 179 145 240 50 205 207 113 246 42 56 161 13 188 244 159 222 119 204 87 182 212 175 199 31 81 45 30 32 238 255 81 61 177 125 149 121 7 38\n",
"10 6\n142 214 75 7 118 247 249 112 91 229\n",
"10 3\n112 139 75 156 15 113 34 164 91 229\n",
"100 7\n39 242 238 155 95 30 129 132 72 59 22 91 203 113 99 81 253 204 160 109 92 187 11 227 145 211 100 42 78 14 113 91 140 197 123 182 4 185 208 27 182 207 63 146 102 39 159 195 26 100 72 127 157 159 152 53 0 117 101 125 19 188 179 145 240 50 205 207 113 246 42 56 161 13 188 244 159 222 119 204 26 182 212 175 199 69 81 45 30 64 238 255 142 61 177 150 149 121 35 38\n",
"100 7\n39 242 238 155 95 19 129 3 72 59 22 91 133 113 99 81 253 204 160 109 83 187 11 227 145 148 100 42 78 14 113 91 140 33 123 182 4 185 208 27 182 207 63 146 102 39 159 195 20 100 72 127 157 159 152 53 0 117 111 125 19 188 179 145 240 50 205 207 113 246 42 56 161 13 188 244 159 222 119 204 87 182 212 175 199 31 81 45 30 32 238 255 81 61 177 125 149 121 7 38\n",
"10 6\n142 118 75 7 118 247 249 112 91 229\n",
"100 10\n39 242 238 155 95 30 129 132 72 59 22 91 203 113 99 81 253 204 160 109 92 187 11 227 145 211 100 42 78 14 113 91 140 197 123 182 4 185 208 27 182 207 63 146 102 39 159 195 26 100 72 127 157 159 152 53 0 117 101 125 19 188 179 145 240 50 205 207 113 246 42 56 161 13 188 244 159 222 119 204 26 182 212 175 199 69 81 45 30 64 238 255 142 61 177 150 149 121 35 38\n",
"100 7\n39 242 238 155 95 19 129 3 72 59 22 91 133 113 99 81 253 204 174 109 83 187 11 227 145 148 100 42 78 14 113 91 140 33 123 182 4 185 208 27 182 207 63 146 102 39 159 195 20 100 72 127 157 159 152 53 0 117 111 125 19 188 179 145 240 50 205 207 113 246 42 56 161 13 188 244 159 222 119 204 87 182 212 175 199 31 81 45 30 32 238 255 81 61 177 125 149 121 7 38\n",
"100 10\n39 242 238 155 95 30 129 132 72 59 22 91 203 113 99 81 253 204 160 109 92 187 11 227 145 211 100 42 12 14 113 91 140 197 123 182 4 185 208 27 182 207 63 146 102 39 159 195 26 100 72 127 157 159 152 53 0 117 101 125 19 188 179 145 240 50 205 207 113 246 42 56 161 13 188 244 159 222 119 204 26 182 212 175 199 69 81 45 30 64 238 255 142 61 177 150 149 121 35 38\n",
"100 7\n39 242 238 155 95 19 129 3 72 59 22 91 133 113 99 81 253 204 174 109 83 187 11 227 145 148 100 42 78 14 113 91 140 33 123 182 4 185 208 27 182 207 63 146 189 39 159 195 20 100 72 127 157 159 152 53 0 117 111 125 19 188 179 145 240 50 205 207 113 246 42 56 161 13 188 244 159 222 119 204 87 182 212 175 199 31 81 45 30 32 238 255 81 61 177 125 149 121 7 38\n",
"100 7\n39 242 238 155 95 19 129 3 72 59 22 91 133 113 196 81 253 204 174 109 83 187 11 227 145 148 100 42 78 14 113 91 140 33 123 182 4 185 208 27 182 207 63 146 189 39 159 195 20 100 72 127 157 159 152 53 0 117 111 125 19 188 179 145 240 50 205 207 113 246 42 56 161 13 188 244 159 222 119 204 87 182 212 175 199 31 81 45 30 32 238 255 81 61 177 125 149 121 7 38\n",
"100 7\n39 242 238 152 95 19 129 3 72 59 22 91 133 113 196 81 253 204 174 109 83 187 11 227 145 148 100 42 78 14 113 91 140 33 123 182 4 185 208 27 182 207 63 146 189 39 159 195 20 100 72 127 157 159 152 53 0 117 111 125 19 188 179 145 240 50 205 207 113 246 42 56 161 13 188 244 159 222 119 204 87 182 212 175 199 31 81 45 30 32 238 255 81 61 177 125 149 121 7 38\n",
"100 7\n39 242 238 152 95 19 129 3 72 59 22 91 133 113 196 81 253 204 174 109 83 187 11 227 145 148 100 42 78 14 113 91 140 33 123 182 4 185 208 27 182 207 63 146 189 39 159 195 20 100 72 127 157 159 152 53 0 117 111 125 19 83 179 145 240 50 205 207 113 246 42 56 161 13 188 244 159 222 119 204 87 182 212 175 199 31 81 45 30 32 238 255 81 61 177 125 149 121 7 38\n",
"9 3\n174 149 118 124 166 146 219 210 107\n",
"2 4\n218 106\n",
"100 7\n39 242 238 155 95 30 129 132 72 59 22 61 133 113 99 81 253 204 160 109 92 187 11 227 145 148 100 42 78 14 113 91 140 197 123 182 4 185 208 27 182 207 63 146 102 79 159 195 26 100 72 127 157 159 152 53 0 117 111 125 30 188 179 145 240 50 205 207 113 246 42 56 181 13 188 244 159 222 119 204 87 182 212 175 199 69 81 45 30 32 238 255 81 61 177 125 149 121 35 38\n",
"4 3\n0 14 3 4\n",
"10 6\n112 184 75 156 118 231 191 128 91 229\n",
"100 7\n39 242 238 155 95 30 129 132 72 59 22 91 133 113 99 81 253 204 160 109 92 187 11 227 145 148 100 42 78 14 113 91 140 197 123 182 4 185 208 27 182 207 63 146 102 79 159 195 26 100 72 127 157 159 152 53 0 117 111 125 19 188 179 145 240 50 205 207 113 246 33 56 181 13 188 244 159 222 119 204 87 182 212 175 199 69 81 45 30 32 238 255 81 61 177 125 149 121 35 38\n",
"5 2\n0 2 1 142 246\n",
"10 3\n112 214 75 156 43 231 191 128 91 229\n",
"100 7\n39 242 238 155 95 30 129 132 72 59 22 91 133 113 99 81 253 204 160 109 92 187 11 227 145 148 100 42 78 14 113 91 140 197 123 182 4 185 208 27 182 207 63 146 102 79 159 195 26 100 72 127 157 159 152 53 0 117 111 125 19 11 179 145 240 50 205 207 113 246 42 56 161 13 188 244 159 222 119 204 87 182 212 175 199 69 81 45 30 32 238 255 81 61 177 125 149 121 35 38\n",
"10 3\n112 214 75 7 118 231 191 128 178 229\n",
"100 7\n39 242 238 155 95 30 129 132 72 59 22 91 133 113 99 81 253 204 160 109 92 187 11 227 145 148 100 42 78 14 113 91 140 197 123 182 4 185 208 27 182 207 63 146 102 39 159 195 26 100 72 127 157 159 152 53 0 117 111 125 19 188 179 145 240 50 79 207 113 246 42 56 161 13 188 244 159 222 119 204 87 182 212 175 199 69 81 45 30 32 238 255 81 61 177 125 149 121 35 38\n",
"100 7\n39 242 238 155 95 19 129 132 72 59 22 91 133 113 99 81 253 204 160 109 92 187 11 227 145 148 100 42 78 14 113 91 140 197 123 182 4 185 208 27 182 207 63 146 102 39 159 97 26 100 72 127 157 159 152 53 0 117 111 125 19 188 179 145 240 50 205 207 113 246 42 56 161 13 188 244 159 222 119 204 87 182 212 175 199 69 81 45 30 32 238 255 81 61 177 125 149 121 35 38\n",
"10 3\n56 214 75 7 118 232 191 79 153 229\n",
"10 3\n56 214 75 7 118 232 191 79 160 25\n",
"9 3\n174 149 118 124 175 146 219 233 107\n",
"8 4\n180 195 7 195 61 12 132 160\n",
"10 2\n112 72 75 156 118 231 191 128 91 229\n",
"8 4\n180 18 13 195 61 24 132 48\n",
"10 3\n112 214 75 69 147 231 191 128 91 229\n",
"2 3\n245 213\n",
"100 7\n39 242 238 155 95 30 129 132 72 59 22 91 133 113 99 81 253 204 160 109 92 187 11 227 145 148 100 42 78 14 113 91 140 197 156 182 4 185 208 27 182 207 63 146 102 79 159 195 26 100 72 127 157 159 152 53 0 117 111 125 19 188 179 145 240 50 205 207 113 246 42 56 161 13 188 244 159 222 119 204 87 182 212 175 199 69 81 45 30 32 238 255 81 61 177 190 149 121 35 38\n",
"10 3\n112 239 75 7 145 231 191 128 91 229\n",
"3 3\n212 167 2\n",
"5 2\n0 1 1 255 254\n"
],
"output": [
"0 1 1 254 254 \n",
"0 12 3 3 \n",
"110 182 159 154 116 229 189 126 89 229 \n",
"172 147 116 122 164 144 217 231 105 \n",
"48 \n",
"177 192 10 192 58 21 129 157 \n",
"121 107 223 153 \n",
"210 165 1 \n",
"215 210 \n",
"33 236 236 149 89 24 123 130 66 53 16 60 130 107 96 75 247 198 156 107 89 181 5 221 139 146 96 40 75 12 107 89 139 191 123 181 0 181 205 24 181 205 60 146 96 75 156 191 24 96 66 123 156 156 149 53 0 114 107 123 16 188 173 139 236 44 205 205 107 243 40 53 181 12 188 243 156 221 114 198 82 181 209 173 198 66 75 44 24 31 236 254 75 60 173 123 149 120 33 33 \n",
"110 182 73 154 116 229 189 126 89 229\n",
"177 15 10 192 58 21 129 157\n",
"214 209\n",
"33 236 236 149 89 24 123 130 66 53 16 89 130 107 96 75 247 198 156 107 89 181 5 221 139 146 96 40 75 12 107 89 139 191 123 181 0 181 205 24 181 205 60 146 96 75 156 191 24 96 66 123 156 156 149 53 0 114 107 123 16 188 173 139 236 44 205 205 107 243 40 53 181 12 188 243 156 221 114 198 82 181 209 173 198 66 75 44 24 31 236 254 75 60 173 123 149 120 33 33\n",
"0 1 1 141 253\n",
"110 212 73 154 116 229 189 126 89 229\n",
"205 210\n",
"33 236 236 149 89 24 123 130 66 53 16 89 130 107 96 75 247 198 156 107 89 181 5 221 139 146 96 40 75 12 107 89 139 191 123 181 0 181 205 24 181 205 60 146 96 75 156 191 24 96 66 123 156 156 149 53 0 114 107 123 16 188 173 139 236 44 205 205 107 243 40 53 156 12 188 243 156 221 114 198 82 181 209 173 198 66 75 44 24 31 236 254 75 60 173 123 149 120 33 33\n",
"110 212 73 5 116 229 189 126 89 229\n",
"33 236 236 149 89 24 123 130 66 53 16 89 130 107 96 75 247 198 156 107 89 181 5 221 139 146 96 40 75 12 107 89 139 191 123 181 0 181 205 24 181 205 60 146 96 33 156 191 24 96 66 123 156 156 149 53 0 114 107 123 16 188 173 139 236 44 205 205 107 243 40 53 156 12 188 243 156 221 114 198 82 181 209 173 198 66 75 44 24 31 236 254 75 60 173 123 149 120 33 33\n",
"110 212 73 5 116 229 189 77 89 229\n",
"33 236 236 149 89 13 123 130 66 53 20 89 130 107 96 75 247 198 156 107 89 181 5 221 139 146 96 40 75 13 107 89 139 191 123 181 0 181 205 23 181 205 60 146 96 33 156 191 23 96 66 123 156 156 149 53 0 114 107 123 13 188 173 139 236 44 205 205 107 243 40 53 156 13 188 243 156 221 114 198 82 181 209 173 198 66 75 44 28 28 236 254 75 60 173 123 149 120 33 33\n",
"54 212 73 5 116 229 189 77 89 229\n",
"54 212 73 5 116 230 189 77 89 227\n",
"54 212 73 5 116 230 189 77 89 23\n",
"172 147 116 122 240 144 217 231 105\n",
"177 192 4 192 58 21 129 157\n",
"210 165 0\n",
"59 210\n",
"0 0 0 254 254\n",
"0 12 3 3\n",
"110 70 73 154 116 229 189 126 89 229\n",
"177 15 10 192 58 21 129 66\n",
"110 212 73 154 145 229 189 126 89 229\n",
"207 211\n",
"33 236 236 149 89 24 123 130 66 53 16 89 130 107 96 75 247 198 156 107 89 181 5 221 139 146 96 40 75 12 107 89 139 191 156 181 0 181 205 24 181 205 60 146 96 75 156 191 24 96 66 123 156 156 149 53 0 114 107 123 16 188 173 139 236 44 205 205 107 243 40 53 156 12 188 243 156 221 114 198 82 181 209 173 198 66 75 44 24 31 236 254 75 60 173 123 149 120 33 33\n",
"110 237 73 5 116 229 189 126 89 229\n",
"33 236 236 149 89 24 123 130 66 53 16 89 197 107 96 75 247 204 156 107 89 181 5 221 139 146 96 40 75 12 107 89 139 197 123 181 0 181 204 24 181 204 60 146 96 33 156 189 24 96 66 123 156 156 149 53 0 114 107 123 16 188 173 139 236 44 204 204 107 243 40 53 156 12 188 243 156 221 114 204 82 181 209 173 197 66 75 44 24 31 236 254 75 60 173 123 149 120 33 33\n",
"165 212 73 5 116 229 189 77 89 229\n",
"33 236 236 149 89 13 123 130 66 53 20 89 130 107 96 75 247 198 156 107 82 181 5 221 139 146 96 40 75 13 107 89 139 191 123 181 0 181 205 23 181 205 60 146 96 33 156 191 23 96 66 123 156 156 149 53 0 114 107 123 13 188 173 139 236 44 205 205 107 243 40 53 156 13 188 243 156 221 114 198 82 181 209 173 198 66 75 44 28 28 236 254 75 60 173 123 149 120 33 33\n",
"79 212 73 5 116 229 189 79 89 229\n",
"54 212 73 2 116 230 189 77 89 23\n",
"84 147 116 122 240 144 217 231 105\n",
"0 0 1 254 254\n",
"0 12 0 3\n",
"110 136 73 154 116 229 189 126 89 229\n",
"177 15 10 192 58 14 129 66\n",
"110 212 73 154 145 229 32 126 89 229\n",
"206 210\n",
"33 236 236 149 89 24 123 130 66 53 16 89 130 107 96 75 247 198 156 107 89 181 5 221 139 146 96 40 75 12 107 89 139 191 156 181 0 181 205 24 181 205 60 146 96 75 156 191 24 96 66 123 156 156 149 53 0 114 107 123 16 188 173 139 236 44 205 205 107 243 40 53 156 12 188 243 156 221 114 198 82 181 209 173 198 66 75 44 24 31 236 254 75 60 173 123 107 120 33 33\n",
"33 236 236 149 89 24 123 130 66 53 16 89 197 107 96 75 247 204 156 107 89 181 5 221 139 205 96 40 75 12 107 89 139 197 123 181 0 181 205 24 181 205 60 146 96 33 156 189 24 96 66 123 156 156 149 53 0 114 107 123 16 188 173 139 236 44 205 205 107 243 40 53 156 12 188 243 156 221 114 204 82 181 212 173 197 66 75 44 24 31 236 254 75 60 173 123 149 120 33 33\n",
"165 212 73 5 116 229 189 56 89 229\n",
"33 236 236 149 89 13 123 130 66 53 20 89 130 107 96 75 247 198 156 107 82 181 5 221 139 146 96 40 75 13 107 89 139 191 123 181 0 181 205 23 181 205 60 146 96 33 156 191 23 96 66 123 156 156 149 53 0 114 107 123 13 188 173 139 236 44 205 205 107 243 40 53 156 13 188 243 156 221 114 198 82 181 209 173 198 66 75 44 28 28 236 254 75 60 173 123 149 120 5 33\n",
"76 209 70 2 113 226 186 76 86 226\n",
"54 212 73 2 116 230 238 77 89 23\n",
"177 15 10 192 58 14 129 129\n",
"110 212 73 154 145 68 32 126 89 227\n",
"33 236 236 149 89 24 123 130 66 53 16 89 197 107 96 75 247 204 156 107 89 181 5 221 139 205 96 40 75 12 107 89 139 197 123 181 0 181 205 24 181 205 60 146 96 33 156 189 24 96 66 123 156 156 149 53 0 114 107 123 16 188 173 139 236 44 205 205 107 243 40 53 156 12 188 243 156 221 114 204 24 181 212 173 197 66 75 44 24 31 236 254 75 60 173 123 149 120 33 33\n",
"165 212 107 5 116 229 189 56 89 229\n",
"33 236 236 149 89 13 123 130 66 53 20 89 130 107 96 75 247 198 156 107 82 181 5 221 139 146 96 40 75 13 107 89 139 191 123 181 0 181 205 23 181 205 60 146 96 33 156 191 23 96 66 123 156 156 149 53 0 114 107 123 13 188 173 139 236 44 205 205 107 243 40 53 156 13 188 243 156 221 114 198 82 181 209 173 198 23 75 44 28 28 236 254 75 60 173 123 149 120 5 33\n",
"137 209 70 2 113 226 186 76 86 226\n",
"177 9 13 192 58 13 129 129\n",
"110 212 73 154 145 113 32 126 89 227\n",
"33 236 236 149 89 24 123 130 66 53 16 89 197 107 96 75 247 204 156 107 89 181 5 221 139 205 96 40 75 12 107 89 139 197 123 181 0 181 205 24 181 205 60 146 96 33 156 189 24 96 66 123 156 156 149 53 0 114 107 123 16 188 173 139 236 44 205 205 107 243 40 53 156 12 188 243 156 221 114 204 24 181 212 173 197 66 75 44 24 31 236 254 75 60 173 149 149 120 33 33\n",
"33 236 236 149 89 13 123 130 66 53 20 89 130 107 96 75 247 198 156 107 82 181 5 221 139 146 96 40 75 13 107 89 139 191 123 181 0 181 205 23 181 205 60 146 96 33 156 191 23 96 66 123 156 156 149 53 0 114 107 123 13 188 173 139 236 44 205 205 107 243 40 53 156 13 188 243 156 221 114 198 82 181 209 173 198 28 75 44 28 28 236 254 75 60 173 123 149 120 5 33\n",
"137 209 70 2 113 226 186 107 86 226\n",
"177 16 10 192 58 14 129 129\n",
"110 137 73 154 145 113 32 126 89 227\n",
"33 236 236 149 89 24 123 130 66 53 16 89 197 107 96 75 247 204 156 107 89 181 5 221 139 205 96 40 75 12 107 89 139 197 123 181 0 181 205 24 181 205 60 146 96 33 156 189 24 96 66 123 156 156 149 53 0 114 96 123 16 188 173 139 236 44 205 205 107 243 40 53 156 12 188 243 156 221 114 204 24 181 212 173 197 66 75 44 24 31 236 254 75 60 173 149 149 120 33 33\n",
"33 236 236 149 89 13 123 130 66 53 20 89 130 107 96 75 247 198 156 107 82 181 5 221 139 146 96 40 75 13 107 89 139 191 123 181 0 181 205 23 181 205 60 146 96 33 156 191 20 96 66 123 156 156 149 53 0 114 107 123 13 188 173 139 236 44 205 205 107 243 40 53 156 13 188 243 156 221 114 198 82 181 209 173 198 28 75 44 28 28 236 254 75 60 173 123 149 120 5 33\n",
"137 209 70 2 113 226 244 107 86 226\n",
"110 137 73 154 13 113 32 126 89 227\n",
"33 236 236 149 89 24 123 130 66 53 16 89 197 107 96 75 247 204 156 107 89 181 5 221 139 205 96 40 75 12 107 89 139 197 123 181 0 181 205 24 181 205 60 146 96 33 156 189 24 96 66 123 156 156 149 53 0 114 96 123 16 188 173 139 236 44 205 205 107 243 40 53 156 12 188 243 156 221 114 204 24 181 212 173 197 66 75 44 24 31 236 254 139 60 173 149 149 120 33 33\n",
"33 236 236 149 89 13 123 0 66 53 20 89 130 107 96 75 247 198 156 107 82 181 5 221 139 146 96 40 75 13 107 89 139 191 123 181 0 181 205 23 181 205 60 146 96 33 156 191 20 96 66 123 156 156 149 53 0 114 107 123 13 188 173 139 236 44 205 205 107 243 40 53 156 13 188 243 156 221 114 198 82 181 209 173 198 28 75 44 28 28 236 254 75 60 173 123 149 120 5 33\n",
"137 209 70 2 113 242 248 107 86 224\n",
"110 137 73 154 13 113 32 162 89 227\n",
"33 236 236 149 89 24 123 130 66 53 16 89 197 107 96 75 247 204 156 107 89 181 5 221 139 205 96 40 75 12 107 89 139 197 123 181 0 181 205 24 181 205 60 146 96 33 156 189 24 96 66 123 156 156 149 53 0 114 96 123 16 188 173 139 236 44 205 205 107 243 40 53 156 12 188 243 156 221 114 204 24 181 212 173 197 66 75 44 24 60 236 254 139 60 173 149 149 120 33 33\n",
"33 236 236 149 89 13 123 0 66 53 20 89 130 107 96 75 247 198 156 107 82 181 5 221 139 146 96 40 75 13 107 89 139 33 123 181 0 181 205 23 181 205 60 146 96 33 156 189 20 96 66 123 156 156 149 53 0 114 107 123 13 188 173 139 236 44 205 205 107 243 40 53 156 13 188 243 156 221 114 198 82 181 209 173 198 28 75 44 28 28 236 254 75 60 173 123 149 120 5 33\n",
"137 113 70 2 113 242 248 107 86 224\n",
"30 233 233 146 86 30 120 130 63 50 13 86 194 104 96 73 244 204 156 104 86 178 2 218 136 204 96 40 73 13 104 86 136 194 120 178 2 178 204 23 178 204 63 146 96 30 156 194 23 96 63 120 156 156 146 50 0 114 96 120 13 188 178 136 233 50 204 204 104 244 40 50 156 13 188 244 156 218 114 204 23 178 204 166 194 63 73 40 30 63 233 254 136 60 176 146 146 120 30 30\n",
"33 236 236 149 89 13 123 0 66 53 20 89 130 107 96 75 247 198 168 107 82 181 5 221 139 146 96 40 75 13 107 89 139 33 123 181 0 181 205 23 181 205 60 146 96 33 156 189 20 96 66 123 156 156 149 53 0 114 107 123 13 188 175 139 236 44 205 205 107 243 40 53 156 13 188 243 156 221 114 198 82 181 209 175 198 28 75 44 28 28 236 254 75 60 175 123 149 120 5 33\n",
"30 233 233 146 86 30 120 130 63 50 13 86 194 104 96 73 244 204 156 104 86 178 2 218 136 204 96 40 12 13 104 86 136 194 120 178 2 178 204 23 178 204 63 146 96 30 156 194 23 96 63 120 156 156 146 50 0 114 96 120 13 188 178 136 233 50 204 204 104 244 40 50 156 13 188 244 156 218 114 204 23 178 204 166 194 63 73 40 30 63 233 254 136 60 176 146 146 120 30 30\n",
"33 236 236 149 89 13 123 0 66 53 20 89 130 107 96 75 247 198 168 107 82 181 5 221 139 146 96 40 75 13 107 89 139 33 123 181 0 181 205 23 181 205 60 146 188 33 156 190 20 96 66 123 156 156 149 53 0 114 107 123 13 188 175 139 236 44 205 205 107 243 40 53 156 13 188 243 156 221 114 198 82 181 209 175 198 28 75 44 28 28 236 254 75 60 175 123 149 120 5 33\n",
"33 236 236 149 89 13 123 0 66 53 20 89 130 107 190 75 247 198 168 107 82 181 5 221 139 146 96 40 75 13 107 89 139 33 123 181 0 181 205 23 181 205 60 146 188 33 156 190 20 96 66 123 156 156 149 53 0 114 107 123 13 188 175 139 236 44 205 205 107 243 40 53 156 13 188 243 156 221 114 198 82 181 209 175 198 28 75 44 28 28 236 254 75 60 175 123 149 120 5 33\n",
"33 236 236 146 89 13 123 0 66 53 20 89 130 107 190 75 247 198 168 107 82 181 5 221 139 146 96 40 75 13 107 89 139 33 123 181 0 181 205 23 181 205 60 146 188 33 153 190 20 96 66 123 153 153 146 53 0 114 107 123 13 188 175 139 236 44 205 205 107 243 40 53 160 13 188 243 153 221 114 198 82 181 209 175 198 28 75 44 28 28 236 254 75 60 175 123 146 120 5 33\n",
"33 236 236 146 89 13 123 0 66 53 20 89 130 107 190 75 247 198 168 107 82 181 5 221 139 146 96 40 75 13 107 89 139 33 123 181 0 181 205 23 181 205 60 146 188 33 153 190 20 96 66 123 153 153 146 53 0 114 107 123 13 82 175 139 236 44 205 205 107 243 40 53 160 13 188 243 153 221 114 198 82 181 209 175 198 28 75 44 28 28 236 254 75 60 175 123 146 120 5 33\n",
"172 147 116 122 164 144 217 208 105\n",
"215 103\n",
"33 236 236 149 89 24 123 130 66 53 16 60 130 107 96 75 247 198 156 107 89 181 5 221 139 146 96 40 75 12 107 89 139 191 123 181 0 181 205 24 181 205 60 146 96 75 156 191 24 96 66 123 156 156 149 53 0 114 107 123 24 188 173 139 236 44 205 205 107 243 40 53 181 12 188 243 156 221 114 198 82 181 209 173 198 66 75 44 24 31 236 254 75 60 173 123 149 120 33 33\n",
"0 12 1 4\n",
"107 179 70 151 113 226 186 123 86 226\n",
"33 236 236 149 89 24 123 130 66 53 16 89 130 107 96 75 247 198 156 107 89 181 5 221 139 146 96 40 75 12 107 89 139 191 123 181 0 181 205 24 181 205 60 146 96 75 156 191 24 96 66 123 156 156 149 53 0 114 107 123 16 188 173 139 236 44 205 205 107 243 33 53 181 12 188 243 156 221 114 198 82 181 209 173 198 66 75 44 24 31 236 254 75 60 173 123 149 120 33 33\n",
"0 1 1 141 245\n",
"110 212 73 154 41 229 189 126 89 229\n",
"33 236 236 149 89 24 123 130 66 53 16 89 130 107 96 75 247 198 156 107 89 181 5 221 139 146 96 40 75 12 107 89 139 191 123 181 0 181 205 24 181 205 60 146 96 75 156 191 24 96 66 123 156 156 149 53 0 114 107 123 16 5 173 139 236 44 205 205 107 243 40 53 156 12 188 243 156 221 114 198 82 181 209 173 198 66 75 44 24 31 236 254 75 60 173 123 149 120 33 33\n",
"110 212 73 5 116 229 189 126 176 229\n",
"33 236 236 149 89 24 123 130 66 53 16 89 130 107 96 75 247 198 156 107 89 181 5 221 139 146 96 40 75 12 107 89 139 191 123 181 0 181 205 24 181 205 60 146 96 33 156 191 24 96 66 123 156 156 149 53 0 114 107 123 16 188 173 139 236 44 75 205 107 243 40 53 156 12 188 243 156 221 114 198 82 181 209 173 198 66 75 44 24 31 236 254 75 60 173 123 149 120 33 33\n",
"33 236 236 149 89 13 123 130 66 53 20 89 130 107 96 75 247 198 156 107 89 181 5 221 139 146 96 40 75 13 107 89 139 191 123 181 0 181 205 23 181 205 60 146 96 33 156 96 23 96 66 123 156 156 149 53 0 114 107 123 13 188 173 139 236 44 205 205 107 243 40 53 156 13 188 243 156 221 114 198 82 181 209 173 198 66 75 44 28 28 236 254 75 60 173 123 149 120 33 33\n",
"54 212 73 5 116 230 189 77 151 227\n",
"54 212 73 5 116 230 189 77 158 23\n",
"172 147 116 122 175 144 217 231 105\n",
"177 192 4 192 58 9 129 157\n",
"111 71 74 155 117 230 190 127 90 228\n",
"177 15 10 192 58 21 129 45\n",
"110 212 73 67 145 229 189 126 89 229\n",
"243 211\n",
"33 236 236 149 89 24 123 130 66 53 16 89 130 107 96 75 247 198 156 107 89 181 5 221 139 146 96 40 75 12 107 89 139 191 156 181 0 181 205 24 181 205 60 146 96 75 156 191 24 96 66 123 156 156 149 53 0 114 107 123 16 188 173 139 236 44 205 205 107 243 40 53 156 12 188 243 156 221 114 198 82 181 209 173 198 66 75 44 24 31 236 254 75 60 173 188 149 120 33 33\n",
"110 237 73 5 143 229 189 126 89 229\n",
"210 165 0\n",
"0 0 0 254 254\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Professor Ibrahim has prepared the final homework for his algorithm’s class. He asked his students to implement the Posterization Image Filter.
Their algorithm will be tested on an array of integers, where the i-th integer represents the color of the i-th pixel in the image. The image is in black and white, therefore the color of each pixel will be an integer between 0 and 255 (inclusive).
To implement the filter, students are required to divide the black and white color range [0, 255] into groups of consecutive colors, and select one color in each group to be the group’s key. In order to preserve image details, the size of a group must not be greater than k, and each color should belong to exactly one group.
Finally, the students will replace the color of each pixel in the array with that color’s assigned group key.
To better understand the effect, here is an image of a basking turtle where the Posterization Filter was applied with increasing k to the right.
<image>
To make the process of checking the final answer easier, Professor Ibrahim wants students to divide the groups and assign the keys in a way that produces the lexicographically smallest possible array.
Input
The first line of input contains two integers n and k (1 ≤ n ≤ 10^5, 1 ≤ k ≤ 256), the number of pixels in the image, and the maximum size of a group, respectively.
The second line contains n integers p_1, p_2, ..., p_n (0 ≤ p_i ≤ 255), where p_i is the color of the i-th pixel.
Output
Print n space-separated integers; the lexicographically smallest possible array that represents the image after applying the Posterization filter.
Examples
Input
4 3
2 14 3 4
Output
0 12 3 3
Input
5 2
0 2 1 255 254
Output
0 1 1 254 254
Note
One possible way to group colors and assign keys for the first sample:
Color 2 belongs to the group [0,2], with group key 0.
Color 14 belongs to the group [12,14], with group key 12.
Colors 3 and 4 belong to group [3, 5], with group key 3.
Other groups won't affect the result so they are not listed here.
### Input:
5 2
0 2 1 255 254
### Output:
0 1 1 254 254
### Input:
4 3
2 14 3 4
### Output:
0 12 3 3
### Code:
R = lambda: map(int, input().split())
n, k = R()
a = list(range(0, 257)); v = [1]*257
for p in R():
if v[p]:
t = p
while t >= 0 and p-a[t]<=k-1: t -= 1
t += 1
for i in range(t, p+1): a[i] = a[t]; v[i] = 0
print(a[p], end=' ')
|
9_C. Hexadecimal's Numbers_10662
|
One beautiful July morning a terrible thing happened in Mainframe: a mean virus Megabyte somehow got access to the memory of his not less mean sister Hexadecimal. He loaded there a huge amount of n different natural numbers from 1 to n to obtain total control over her energy.
But his plan failed. The reason for this was very simple: Hexadecimal didn't perceive any information, apart from numbers written in binary format. This means that if a number in a decimal representation contained characters apart from 0 and 1, it was not stored in the memory. Now Megabyte wants to know, how many numbers were loaded successfully.
Input
Input data contains the only number n (1 ≤ n ≤ 109).
Output
Output the only number — answer to the problem.
Examples
Input
10
Output
2
Note
For n = 10 the answer includes numbers 1 and 10.
|
n=int(input())
a=[]
c=int
for i in range(515):
a.append(c(bin(i)[2:]))
a.remove(0)
ans=0
for i in a:
if i<=n:
ans+=1
print(ans)
|
{
"input": [
"10\n",
"100\n",
"1010011\n",
"1\n",
"999999999\n",
"112\n",
"101\n",
"121212121\n",
"99\n",
"101010101\n",
"901556123\n",
"2\n",
"312410141\n",
"1000000000\n",
"100100\n",
"111111111\n",
"100111001\n",
"745\n",
"7\n",
"832513432\n",
"12\n",
"111100100\n",
"732875234\n",
"23536\n",
"13\n",
"9\n",
"102\n",
"106341103\n",
"11\n",
"3\n",
"72\n",
"101020101\n",
"110100102\n",
"20\n",
"110110101\n",
"111\n",
"1110011\n",
"486798001\n",
"14\n",
"101010001\n",
"21719102\n",
"4\n",
"110100\n",
"101111111\n",
"100101001\n",
"1028\n",
"111110100\n",
"40491\n",
"10559444\n",
"137\n",
"110110111\n",
"1110010\n",
"111010101\n",
"110101\n",
"101110111\n",
"101101001\n",
"101100100\n",
"111110111\n",
"1110110\n",
"105\n",
"110010101\n",
"1126899\n",
"111101\n",
"101110101\n",
"101100000\n",
"1111110\n",
"100309918\n",
"110010001\n",
"581628\n",
"111100\n",
"101100001\n",
"1101110\n",
"110010000\n",
"225990745\n",
"57\n",
"150276991\n",
"623742682\n",
"25\n",
"69435180\n",
"16\n",
"40\n",
"6\n",
"92825478\n",
"176158344\n",
"8\n",
"15\n",
"275596937\n",
"17\n",
"255003163\n",
"55\n",
"17732733\n",
"5\n",
"248425899\n",
"390\n",
"593041336\n",
"49\n",
"52751111\n",
"70376\n",
"23\n",
"13636042\n",
"32\n",
"29\n",
"51083193\n",
"230519282\n",
"22\n",
"42439572\n",
"34\n",
"152692306\n",
"491642854\n",
"24\n",
"485340199\n",
"38\n",
"76549978\n",
"60146\n",
"8025558\n",
"44\n",
"46495238\n",
"194955954\n",
"30\n",
"45014542\n",
"51\n",
"147\n",
"225390655\n",
"45\n",
"782722370\n",
"109\n",
"92197783\n",
"99110\n",
"14888380\n",
"26\n",
"47118972\n",
"377477752\n",
"18\n",
"89468833\n",
"41\n",
"120690970\n"
],
"output": [
"2\n",
"4\n",
"83\n",
"1\n",
"511\n",
"7\n",
"5\n",
"511\n",
"3\n",
"341\n",
"511\n",
"1\n",
"511\n",
"512\n",
"36\n",
"511\n",
"313\n",
"7\n",
"1\n",
"511\n",
"3\n",
"484\n",
"511\n",
"31\n",
"3\n",
"1\n",
"5\n",
"383\n",
"3\n",
"1\n",
"3\n",
"351\n",
"421\n",
"3\n",
"437\n",
"7\n",
"115\n",
"511\n",
"3\n",
"337\n",
"255\n",
"1\n",
"52\n",
"383\n",
"297\n",
"11\n",
"500\n",
"31\n",
"191\n",
"7\n",
"439\n",
"114\n",
"469\n",
"53\n",
"375\n",
"361\n",
"356\n",
"503\n",
"118\n",
"5\n",
"405\n",
"127\n",
"61\n",
"373\n",
"352\n",
"126\n",
"319\n",
"401\n",
"63\n",
"60\n",
"353\n",
"110\n",
"400\n",
"511\n",
"3\n",
"511\n",
"511\n",
"3\n",
"255\n",
"3\n",
"3\n",
"1\n",
"255\n",
"511\n",
"1\n",
"3\n",
"511\n",
"3\n",
"511\n",
"3\n",
"255\n",
"1\n",
"511\n",
"7\n",
"511\n",
"3\n",
"255\n",
"31\n",
"3\n",
"255\n",
"3\n",
"3\n",
"255\n",
"511\n",
"3\n",
"255\n",
"3\n",
"511\n",
"511\n",
"3\n",
"511\n",
"3\n",
"255\n",
"31\n",
"127\n",
"3\n",
"255\n",
"511\n",
"3\n",
"255\n",
"3\n",
"7\n",
"511\n",
"3\n",
"511\n",
"5\n",
"255\n",
"31\n",
"255\n",
"3\n",
"255\n",
"511\n",
"3\n",
"255\n",
"3\n",
"511\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
One beautiful July morning a terrible thing happened in Mainframe: a mean virus Megabyte somehow got access to the memory of his not less mean sister Hexadecimal. He loaded there a huge amount of n different natural numbers from 1 to n to obtain total control over her energy.
But his plan failed. The reason for this was very simple: Hexadecimal didn't perceive any information, apart from numbers written in binary format. This means that if a number in a decimal representation contained characters apart from 0 and 1, it was not stored in the memory. Now Megabyte wants to know, how many numbers were loaded successfully.
Input
Input data contains the only number n (1 ≤ n ≤ 109).
Output
Output the only number — answer to the problem.
Examples
Input
10
Output
2
Note
For n = 10 the answer includes numbers 1 and 10.
### Input:
10
### Output:
2
### Input:
100
### Output:
4
### Code:
n=int(input())
a=[]
c=int
for i in range(515):
a.append(c(bin(i)[2:]))
a.remove(0)
ans=0
for i in a:
if i<=n:
ans+=1
print(ans)
|
p02546 AtCoder Beginner Contest 179 - Plural Form_10675
|
In the Kingdom of AtCoder, people use a language called Taknese, which uses lowercase English letters.
In Taknese, the plural form of a noun is spelled based on the following rules:
* If a noun's singular form does not end with `s`, append `s` to the end of the singular form.
* If a noun's singular form ends with `s`, append `es` to the end of the singular form.
You are given the singular form S of a Taknese noun. Output its plural form.
Constraints
* S is a string of length 1 between 1000, inclusive.
* S contains only lowercase English letters.
Input
Input is given from Standard Input in the following format:
S
Output
Print the plural form of the given Taknese word.
Examples
Input
apple
Output
apples
Input
bus
Output
buses
Input
box
Output
boxs
|
n=input()
if( n[-1]=='s'):
n+='es'
else:
n+='s'
print(n)
|
{
"input": [
"box",
"bus",
"apple",
"aox",
"bsu",
"aeplp",
"xoa",
"bsv",
"eaplp",
"xo`",
"csv",
"daplp",
"xp`",
"crv",
"d`plp",
"px`",
"vrc",
"c`plp",
"xn`",
"vsc",
"c_plp",
"`nx",
"urc",
"plp_c",
"`mx",
"usc",
"c_plq",
"xm`",
"utc",
"p_clq",
"`ox",
"ctu",
"p_blq",
"`oy",
"ttc",
"p^blq",
"`yo",
"ctt",
"qlb^p",
"_yo",
"tct",
"qlb^q",
"oy`",
"tbt",
"qlb]q",
"ny`",
"ubt",
"qlbq]",
"ny_",
"ubu",
"lqbq]",
"oy_",
"ucu",
"lqbp]",
"o_y",
"uuc",
"lbqp]",
"_oy",
"uub",
"]pqbl",
"^oy",
"tbu",
"]pqbm",
"yo^",
"tbv",
"]pqcm",
"oy^",
"vbt",
"mbqp]",
"py^",
"btv",
"mbqo]",
"px^",
"ubv",
"mcqo]",
"xp^",
"buu",
"mcq]o",
"^px",
"btu",
"cmq]o",
"^pw",
"utb",
"bmq]o",
"wp^",
"tub",
"o]qmb",
"^ow",
"tua",
"o]qmc",
"^wo",
"tau",
"c]qmo",
"^wp",
"uat",
"b]qmo",
"pw^",
"tcu",
"b]qlo",
"pw_",
"uct",
"b]rlo",
"_wp"
],
"output": [
"boxs",
"buses",
"apples",
"aoxs\n",
"bsus\n",
"aeplps\n",
"xoas\n",
"bsvs\n",
"eaplps\n",
"xo`s\n",
"csvs\n",
"daplps\n",
"xp`s\n",
"crvs\n",
"d`plps\n",
"px`s\n",
"vrcs\n",
"c`plps\n",
"xn`s\n",
"vscs\n",
"c_plps\n",
"`nxs\n",
"urcs\n",
"plp_cs\n",
"`mxs\n",
"uscs\n",
"c_plqs\n",
"xm`s\n",
"utcs\n",
"p_clqs\n",
"`oxs\n",
"ctus\n",
"p_blqs\n",
"`oys\n",
"ttcs\n",
"p^blqs\n",
"`yos\n",
"ctts\n",
"qlb^ps\n",
"_yos\n",
"tcts\n",
"qlb^qs\n",
"oy`s\n",
"tbts\n",
"qlb]qs\n",
"ny`s\n",
"ubts\n",
"qlbq]s\n",
"ny_s\n",
"ubus\n",
"lqbq]s\n",
"oy_s\n",
"ucus\n",
"lqbp]s\n",
"o_ys\n",
"uucs\n",
"lbqp]s\n",
"_oys\n",
"uubs\n",
"]pqbls\n",
"^oys\n",
"tbus\n",
"]pqbms\n",
"yo^s\n",
"tbvs\n",
"]pqcms\n",
"oy^s\n",
"vbts\n",
"mbqp]s\n",
"py^s\n",
"btvs\n",
"mbqo]s\n",
"px^s\n",
"ubvs\n",
"mcqo]s\n",
"xp^s\n",
"buus\n",
"mcq]os\n",
"^pxs\n",
"btus\n",
"cmq]os\n",
"^pws\n",
"utbs\n",
"bmq]os\n",
"wp^s\n",
"tubs\n",
"o]qmbs\n",
"^ows\n",
"tuas\n",
"o]qmcs\n",
"^wos\n",
"taus\n",
"c]qmos\n",
"^wps\n",
"uats\n",
"b]qmos\n",
"pw^s\n",
"tcus\n",
"b]qlos\n",
"pw_s\n",
"ucts\n",
"b]rlos\n",
"_wps\n"
]
}
| 5ATCODER
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
In the Kingdom of AtCoder, people use a language called Taknese, which uses lowercase English letters.
In Taknese, the plural form of a noun is spelled based on the following rules:
* If a noun's singular form does not end with `s`, append `s` to the end of the singular form.
* If a noun's singular form ends with `s`, append `es` to the end of the singular form.
You are given the singular form S of a Taknese noun. Output its plural form.
Constraints
* S is a string of length 1 between 1000, inclusive.
* S contains only lowercase English letters.
Input
Input is given from Standard Input in the following format:
S
Output
Print the plural form of the given Taknese word.
Examples
Input
apple
Output
apples
Input
bus
Output
buses
Input
box
Output
boxs
### Input:
box
### Output:
boxs
### Input:
bus
### Output:
buses
### Code:
n=input()
if( n[-1]=='s'):
n+='es'
else:
n+='s'
print(n)
|
p02677 AtCoder Beginner Contest 168 - : (Colon)_10679
|
Consider an analog clock whose hour and minute hands are A and B centimeters long, respectively.
An endpoint of the hour hand and an endpoint of the minute hand are fixed at the same point, around which each hand rotates clockwise at constant angular velocity. It takes the hour and minute hands 12 hours and 1 hour to make one full rotation, respectively.
At 0 o'clock, the two hands overlap each other. H hours and M minutes later, what is the distance in centimeters between the unfixed endpoints of the hands?
Constraints
* All values in input are integers.
* 1 \leq A, B \leq 1000
* 0 \leq H \leq 11
* 0 \leq M \leq 59
Input
Input is given from Standard Input in the following format:
A B H M
Output
Print the answer without units. Your output will be accepted when its absolute or relative error from the correct value is at most 10^{-9}.
Examples
Input
3 4 9 0
Output
5.00000000000000000000
Input
3 4 10 40
Output
4.56425719433005567605
|
from math import *
a,b,h,m = map(int, input().split())
d = radians(fabs(((11*m)/2) - (30 * h)))
print(sqrt(a**2 + b**2 - 2*a*b*cos(d)))
|
{
"input": [
"3 4 9 0",
"3 4 10 40",
"3 4 13 0",
"3 1 10 40",
"3 4 17 0",
"3 1 10 59",
"6 4 17 0",
"3 2 10 59",
"9 4 17 0",
"3 2 10 89",
"9 4 21 0",
"3 2 1 89",
"9 4 21 1",
"3 3 1 89",
"5 4 21 1",
"3 6 1 89",
"5 4 16 1",
"3 6 1 158",
"5 4 8 1",
"1 6 1 158",
"2 4 8 1",
"1 6 1 235",
"3 4 8 1",
"1 6 2 235",
"3 3 8 1",
"2 6 2 235",
"2 3 8 1",
"2 8 2 235",
"2 3 8 2",
"3 8 2 235",
"2 0 8 2",
"2 8 2 269",
"4 8 2 269",
"4 8 1 269",
"2 1 13 2",
"4 4 1 269",
"4 4 0 269",
"4 4 0 312",
"8 4 0 312",
"8 1 0 312",
"0 0 3 4",
"8 1 -1 312",
"5 1 -1 312",
"0 -1 3 2",
"5 1 -2 312",
"3 1 -2 312",
"6 1 -2 312",
"6 1 -2 593",
"6 1 -2 284",
"1 -2 4 1",
"6 0 -2 284",
"1 -3 4 1",
"8 1 -2 284",
"1 -6 4 1",
"8 1 -2 52",
"1 -6 2 1",
"8 1 -4 52",
"1 -6 3 1",
"14 1 -4 52",
"1 -8 3 1",
"14 2 -4 52",
"1 -8 5 1",
"14 2 0 52",
"1 -8 5 0",
"14 3 0 52",
"0 -8 5 0",
"14 2 0 90",
"-1 -8 5 0",
"14 3 0 90",
"-1 -8 4 0",
"26 3 0 90",
"-1 -8 4 -1",
"26 3 0 158",
"-2 -8 4 -1",
"26 3 0 42",
"26 2 0 42",
"42 2 0 42",
"1 -8 4 0",
"47 2 0 42",
"2 -8 4 0",
"47 2 1 42",
"4 -8 4 0",
"47 2 1 1",
"4 -8 1 0",
"55 2 1 1",
"4 -8 1 1",
"55 2 2 1",
"4 -8 1 2",
"55 2 0 1",
"4 -5 1 1",
"55 2 0 0",
"4 -7 1 1",
"60 2 0 1",
"4 -7 1 2",
"116 2 0 1",
"6 -7 1 2",
"149 2 0 1",
"6 -7 0 2",
"105 2 0 1",
"7 -7 0 2",
"105 2 1 1",
"0 -7 0 2"
],
"output": [
"5.00000000000000000000",
"4.56425719433005567605",
"2.05314157066\n",
"2.99301034646\n",
"6.76643256752\n",
"2.130782104\n",
"9.67311838973\n",
"1.44238162408\n",
"12.6235426514\n",
"4.98351554813\n",
"9.8488578018\n",
"3.87047429527\n",
"10.1931788065\n",
"4.5793948187\n",
"6.69580690438\n",
"7.13734641243\n",
"7.58865796477\n",
"7.9027303085\n",
"8.0142447073\n",
"6.54352469568\n",
"5.41213888323\n",
"6.99918414238\n",
"6.23994158122\n",
"6.90247274519\n",
"5.33410284891\n",
"7.82868188115\n",
"4.4686055396\n",
"9.81755298747\n",
"4.56866592649\n",
"10.7506520729\n",
"2.0\n",
"6.16656224683\n",
"4.47805536903\n",
"4.10825041856\n",
"1.10359670967\n",
"0.662465660098\n",
"2.70333374403\n",
"5.35304485087\n",
"8.56213631933\n",
"7.95786055342\n",
"0.0\n",
"7.45623470415\n",
"4.48577167019\n",
"1.0\n",
"4.10664649362\n",
"2.12572981683\n",
"5.10269090856\n",
"5.9351737183\n",
"6.99947783225\n",
"1.82790235772\n",
"6.0\n",
"2.74077371267\n",
"8.99945849662\n",
"5.65894699464\n",
"7.03386582041\n",
"6.63086988777\n",
"7.34067204503\n",
"6.17658069082\n",
"13.3247726295\n",
"8.15680893734\n",
"12.692483258\n",
"7.20931007145\n",
"13.5854447139\n",
"7.15147492056\n",
"13.4850458698\n",
"8.0\n",
"15.4789527988\n",
"8.88011297566\n",
"16.2602881161\n",
"8.54400374532\n",
"28.2012173118\n",
"8.6192370481\n",
"28.613250408\n",
"9.30497149822\n",
"27.9852457735\n",
"27.302917805\n",
"43.2865547913\n",
"7.54983443527\n",
"48.2836642511\n",
"7.21110255093\n",
"48.8724167622\n",
"6.92820323028\n",
"45.1876894859\n",
"11.6372516447\n",
"53.1865445428\n",
"11.7574453576\n",
"53.8632096123\n",
"11.8538259156\n",
"53.0095541988\n",
"8.79763893525\n",
"53.0\n",
"10.7683717975\n",
"58.0095243248\n",
"10.8604346245\n",
"114.009368755\n",
"12.8227750643\n",
"147.009332581\n",
"12.9405055315\n",
"103.009385964\n",
"13.9355467771\n",
"103.183410809\n",
"7.0\n"
]
}
| 5ATCODER
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Consider an analog clock whose hour and minute hands are A and B centimeters long, respectively.
An endpoint of the hour hand and an endpoint of the minute hand are fixed at the same point, around which each hand rotates clockwise at constant angular velocity. It takes the hour and minute hands 12 hours and 1 hour to make one full rotation, respectively.
At 0 o'clock, the two hands overlap each other. H hours and M minutes later, what is the distance in centimeters between the unfixed endpoints of the hands?
Constraints
* All values in input are integers.
* 1 \leq A, B \leq 1000
* 0 \leq H \leq 11
* 0 \leq M \leq 59
Input
Input is given from Standard Input in the following format:
A B H M
Output
Print the answer without units. Your output will be accepted when its absolute or relative error from the correct value is at most 10^{-9}.
Examples
Input
3 4 9 0
Output
5.00000000000000000000
Input
3 4 10 40
Output
4.56425719433005567605
### Input:
3 4 9 0
### Output:
5.00000000000000000000
### Input:
3 4 10 40
### Output:
4.56425719433005567605
### Code:
from math import *
a,b,h,m = map(int, input().split())
d = radians(fabs(((11*m)/2) - (30 * h)))
print(sqrt(a**2 + b**2 - 2*a*b*cos(d)))
|
p02805 AtCoder Beginner Contest 151 - Enclose All_10683
|
Given are N points (x_i, y_i) in a two-dimensional plane.
Find the minimum radius of a circle such that all the points are inside or on it.
Constraints
* 2 \leq N \leq 50
* 0 \leq x_i \leq 1000
* 0 \leq y_i \leq 1000
* The given N points are all different.
* The values in input are all integers.
Input
Input is given from Standard Input in the following format:
N
x_1 y_1
:
x_N y_N
Output
Print the minimum radius of a circle such that all the N points are inside or on it.
Your output will be considered correct if the absolute or relative error from our answer is at most 10^{-6}.
Examples
Input
2
0 0
1 0
Output
0.500000000000000000
Input
3
0 0
0 1
1 0
Output
0.707106781186497524
Input
10
10 9
5 9
2 0
0 0
2 7
3 3
2 5
10 0
3 7
1 9
Output
6.726812023536805158
|
n = int(input())
xy=[list(map(int,input().split())) for i in range(n)]
import math
def calc(x1, y1, x2, y2, x3, y3):
try:
d = 2 * ((y1 - y3) * (x1 - x2) - (y1 - y2) * (x1 - x3))
x = ((y1 - y3) * (y1 ** 2 - y2 ** 2 + x1 ** 2 - x2 ** 2) - (y1 - y2) * (y1 ** 2 - y3 ** 2 + x1 ** 2 - x3 ** 2)) / d
y = ((x1 - x3) * (x1 ** 2 - x2 ** 2 + y1 ** 2 - y2 ** 2) - (x1 - x2) * (x1 ** 2 - x3 ** 2 + y1 ** 2 - y3 ** 2)) / -d
r2 = (x - x1) ** 2 + (y - y1) ** 2
except:
return 0,0,-1
else:
return x,y,r2
def check(cx,cy,r2):
for tmp in xy:
x,y=tmp
if (x-cx)**2 + (y-cy)**2 > r2:
return False
return True
ans=float("inf")
eps=10**(-5)
for i in range(n):
for j in range(i+1,n):
x1,y1=xy[i]
x2,y2=xy[j]
cx=(x1+x2)/2
cy=(y1+y2)/2
r2=(cx-x1)**2+(cy-y1)**2
if check(cx,cy,r2+eps):
ans=min(ans,math.sqrt(r2))
for i in range(n):
for j in range(i+1,n):
for k in range(j+1,n):
x1,y1=xy[i]
x2,y2=xy[j]
x3,y3=xy[k]
cx,cy,r2=calc(x1, y1, x2, y2, x3, y3)
if 0 < r2 and check(cx,cy,r2+eps):
ans=min(ans,math.sqrt(r2))
print(ans)
|
{
"input": [
"3\n0 0\n0 1\n1 0",
"2\n0 0\n1 0",
"10\n10 9\n5 9\n2 0\n0 0\n2 7\n3 3\n2 5\n10 0\n3 7\n1 9",
"3\n0 0\n1 1\n1 0",
"10\n10 9\n5 9\n2 0\n0 0\n2 7\n3 3\n2 5\n10 0\n5 7\n1 9",
"2\n0 1\n2 0",
"2\n0 2\n2 0",
"3\n0 1\n0 1\n3 0",
"3\n0 1\n0 2\n3 0",
"2\n-1 2\n2 2",
"2\n-1 2\n4 4",
"2\n-1 2\n7 4",
"3\n0 1\n0 0\n6 0",
"2\n-1 2\n7 3",
"3\n1 1\n0 0\n6 0",
"2\n-1 4\n7 1",
"2\n-1 4\n7 0",
"10\n10 9\n5 10\n0 0\n0 0\n3 7\n3 1\n1 5\n14 1\n5 7\n1 4",
"3\n1 2\n-1 0\n6 1",
"2\n0 4\n7 1",
"3\n1 4\n-1 0\n6 1",
"2\n1 4\n7 1",
"3\n1 4\n0 0\n6 1",
"2\n1 4\n12 1",
"3\n1 4\n0 0\n6 2",
"2\n1 4\n12 0",
"10\n10 9\n5 10\n0 0\n0 0\n3 7\n3 2\n0 8\n14 1\n5 7\n2 4",
"3\n1 4\n0 1\n6 2",
"2\n1 0\n12 0",
"10\n18 9\n5 10\n0 0\n0 0\n3 7\n3 2\n0 8\n14 1\n5 7\n2 4",
"3\n1 4\n1 1\n6 2",
"2\n0 0\n12 0",
"3\n1 4\n1 1\n6 1",
"2\n0 0\n21 0",
"2\n-1 0\n21 0",
"10\n18 9\n5 10\n0 0\n-1 0\n0 7\n3 2\n0 8\n14 1\n5 7\n2 8",
"2\n-1 0\n21 -1",
"2\n-1 1\n21 -1",
"2\n-1 2\n21 -1",
"10\n21 9\n10 10\n0 0\n-1 0\n0 7\n3 2\n0 8\n14 1\n5 7\n3 8",
"3\n1 4\n1 1\n0 0",
"2\n-2 2\n7 -1",
"2\n-3 2\n7 -1",
"10\n21 2\n10 7\n-1 0\n-1 0\n0 7\n3 2\n0 8\n14 1\n5 7\n3 8",
"3\n1 4\n1 0\n0 -1",
"2\n-3 2\n7 -2",
"10\n21 2\n10 7\n-1 0\n-2 0\n0 7\n3 2\n0 8\n20 1\n5 7\n3 8",
"3\n1 4\n1 1\n1 -1",
"2\n-4 4\n7 -2",
"2\n-4 4\n7 -3",
"10\n21 2\n10 7\n-1 0\n-2 0\n0 7\n3 2\n0 14\n20 1\n5 7\n3 5",
"2\n-4 4\n2 -3",
"3\n1 4\n1 1\n0 -7",
"2\n-4 7\n2 -3",
"10\n21 2\n10 7\n-1 0\n-2 0\n0 7\n3 2\n1 14\n20 1\n5 7\n4 5",
"3\n1 8\n1 1\n0 -7",
"2\n-4 7\n3 -3",
"3\n0 8\n1 1\n0 -7",
"2\n-4 5\n3 -3",
"3\n0 10\n1 1\n0 -7",
"3\n0 13\n1 1\n0 -7",
"2\n-1 5\n3 -4",
"10\n21 2\n10 7\n-1 0\n-2 0\n1 10\n3 2\n1 4\n20 1\n6 7\n4 5",
"3\n0 13\n1 1\n0 0",
"2\n-1 12\n3 -4",
"2\n-1 23\n3 -4",
"10\n21 1\n10 7\n-1 -1\n-2 0\n1 10\n3 3\n1 4\n20 1\n6 7\n4 5",
"3\n0 13\n2 1\n0 -1",
"2\n-1 7\n3 -8",
"2\n-1 7\n3 -10",
"2\n-1 7\n5 -10",
"2\n-1 7\n8 -10",
"10\n21 1\n9 7\n1 -1\n-2 0\n1 0\n2 3\n1 4\n20 1\n6 7\n4 5",
"2\n-1 7\n14 -10",
"2\n-1 7\n14 -15",
"10\n21 1\n9 7\n1 -1\n-2 1\n1 0\n2 3\n1 4\n20 1\n6 7\n2 5",
"3\n0 20\n4 2\n1 0",
"2\n-1 7\n14 -30",
"2\n-1 7\n9 -30",
"3\n0 11\n8 2\n1 0",
"2\n-2 7\n9 -30",
"3\n0 11\n9 2\n1 0",
"2\n-2 5\n9 -30",
"2\n-4 5\n9 -30",
"3\n0 11\n2 2\n1 -1",
"2\n-4 5\n5 -30",
"2\n-4 5\n5 -42",
"10\n21 1\n9 7\n1 -1\n-2 3\n1 1\n2 3\n1 0\n20 1\n6 7\n0 5",
"3\n0 13\n2 0\n1 -1",
"2\n-6 5\n5 -42",
"3\n0 13\n2 0\n1 0",
"2\n-6 5\n5 -12",
"3\n0 13\n2 -1\n1 0",
"2\n-6 5\n5 -4",
"10\n6 1\n9 7\n1 -1\n-2 3\n1 1\n2 0\n1 0\n25 1\n6 7\n0 5",
"3\n0 13\n3 -1\n1 0",
"2\n-6 5\n8 -4",
"2\n-5 5\n8 -4",
"2\n-5 0\n8 -4",
"2\n-5 1\n8 -4",
"2\n-10 1\n8 -4",
"3\n0 13\n2 -1\n4 -1",
"2\n-10 1\n11 -8"
],
"output": [
"0.707106781186497524",
"0.500000000000000000",
"6.726812023536805158",
"0.707106762032\n",
"6.72681205183\n",
"1.1180339432\n",
"1.41421357958\n",
"1.58113883097\n",
"1.80277565098\n",
"1.49999995758\n",
"2.69258243479\n",
"4.12310557918\n",
"3.04138131346\n",
"4.03112881964\n",
"2.99999997067\n",
"4.27200191888\n",
"4.47213593935\n",
"7.39744704381\n",
"3.53553392118\n",
"3.80788650611\n",
"3.54597867736\n",
"3.35410194063\n",
"3.17912024483\n",
"5.70087715923\n",
"3.19154352946\n",
"5.85234999351\n",
"7.84617742999\n",
"3.04663866357\n",
"5.49999995547\n",
"10.0623059329\n",
"2.74590600258\n",
"5.99999999684\n",
"2.91547591624\n",
"10.5000000361\n",
"10.9999999665\n",
"10.5118980742\n",
"11.01135777\n",
"11.0453610147\n",
"11.1018016447\n",
"11.8848643704\n",
"2.06155276183\n",
"4.74341649292\n",
"5.2201532541\n",
"11.1775478318\n",
"2.54950976997\n",
"5.38516481408\n",
"11.5498076103\n",
"2.50000004032\n",
"6.26498203316\n",
"6.51920245565\n",
"12.4165064341\n",
"4.60977217509\n",
"5.5226804796\n",
"5.830951888\n",
"12.1989627844\n",
"7.51664813725\n",
"6.10327782757\n",
"7.50000000993\n",
"5.31507288182\n",
"8.49999998165\n",
"9.99999999474\n",
"4.92442892019\n",
"11.589316673\n",
"6.50000003821\n",
"8.24621121387\n",
"13.6473440882\n",
"11.6109530324\n",
"6.99999996856\n",
"7.76208736175\n",
"8.73212463448\n",
"9.01387814389\n",
"9.61769203167\n",
"11.5108644283\n",
"11.3357840337\n",
"13.3135270031\n",
"11.5000000078\n",
"10.0124922242\n",
"19.9624647368\n",
"19.1637678504\n",
"6.12836698055\n",
"19.3002591131\n",
"6.44049685805\n",
"18.3439363144\n",
"18.6681547443\n",
"6.02079724965\n",
"18.0693109919\n",
"23.9269722369\n",
"11.5433964054\n",
"7.01783436918\n",
"24.1350368024\n",
"6.57647319935\n",
"10.1242284001\n",
"7.07106778686\n",
"7.10633524248\n",
"13.5369863652\n",
"7.15891051994\n",
"8.32165852893\n",
"7.90569415487\n",
"6.80073525272\n",
"6.96419416579\n",
"9.340770879\n",
"7.28010990381\n",
"11.4236596294\n"
]
}
| 5ATCODER
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Given are N points (x_i, y_i) in a two-dimensional plane.
Find the minimum radius of a circle such that all the points are inside or on it.
Constraints
* 2 \leq N \leq 50
* 0 \leq x_i \leq 1000
* 0 \leq y_i \leq 1000
* The given N points are all different.
* The values in input are all integers.
Input
Input is given from Standard Input in the following format:
N
x_1 y_1
:
x_N y_N
Output
Print the minimum radius of a circle such that all the N points are inside or on it.
Your output will be considered correct if the absolute or relative error from our answer is at most 10^{-6}.
Examples
Input
2
0 0
1 0
Output
0.500000000000000000
Input
3
0 0
0 1
1 0
Output
0.707106781186497524
Input
10
10 9
5 9
2 0
0 0
2 7
3 3
2 5
10 0
3 7
1 9
Output
6.726812023536805158
### Input:
3
0 0
0 1
1 0
### Output:
0.707106781186497524
### Input:
2
0 0
1 0
### Output:
0.500000000000000000
### Code:
n = int(input())
xy=[list(map(int,input().split())) for i in range(n)]
import math
def calc(x1, y1, x2, y2, x3, y3):
try:
d = 2 * ((y1 - y3) * (x1 - x2) - (y1 - y2) * (x1 - x3))
x = ((y1 - y3) * (y1 ** 2 - y2 ** 2 + x1 ** 2 - x2 ** 2) - (y1 - y2) * (y1 ** 2 - y3 ** 2 + x1 ** 2 - x3 ** 2)) / d
y = ((x1 - x3) * (x1 ** 2 - x2 ** 2 + y1 ** 2 - y2 ** 2) - (x1 - x2) * (x1 ** 2 - x3 ** 2 + y1 ** 2 - y3 ** 2)) / -d
r2 = (x - x1) ** 2 + (y - y1) ** 2
except:
return 0,0,-1
else:
return x,y,r2
def check(cx,cy,r2):
for tmp in xy:
x,y=tmp
if (x-cx)**2 + (y-cy)**2 > r2:
return False
return True
ans=float("inf")
eps=10**(-5)
for i in range(n):
for j in range(i+1,n):
x1,y1=xy[i]
x2,y2=xy[j]
cx=(x1+x2)/2
cy=(y1+y2)/2
r2=(cx-x1)**2+(cy-y1)**2
if check(cx,cy,r2+eps):
ans=min(ans,math.sqrt(r2))
for i in range(n):
for j in range(i+1,n):
for k in range(j+1,n):
x1,y1=xy[i]
x2,y2=xy[j]
x3,y3=xy[k]
cx,cy,r2=calc(x1, y1, x2, y2, x3, y3)
if 0 < r2 and check(cx,cy,r2+eps):
ans=min(ans,math.sqrt(r2))
print(ans)
|
p02941 AtCoder Grand Contest 037 - Numbers on a Circle_10687
|
There are N positive integers arranged in a circle.
Now, the i-th number is A_i. Takahashi wants the i-th number to be B_i. For this objective, he will repeatedly perform the following operation:
* Choose an integer i such that 1 \leq i \leq N.
* Let a, b, c be the (i-1)-th, i-th, and (i+1)-th numbers, respectively. Replace the i-th number with a+b+c.
Here the 0-th number is the N-th number, and the (N+1)-th number is the 1-st number.
Determine if Takahashi can achieve his objective. If the answer is yes, find the minimum number of operations required.
Constraints
* 3 \leq N \leq 2 \times 10^5
* 1 \leq A_i, B_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
B_1 B_2 ... B_N
Output
Print the minimum number of operations required, or `-1` if the objective cannot be achieved.
Examples
Input
3
1 1 1
13 5 7
Output
4
Input
4
1 2 3 4
2 3 4 5
Output
-1
Input
5
5 6 5 2 1
9817 1108 6890 4343 8704
Output
25
|
n,*t=map(int,open(0).read().split());A=t[:n];B=t[n:];r=0
while 1:
c=0
for i in range(n):
b=B[~-i%n]+B[-~i%n]
if A[i]<B[i]>b:t=(B[i]-A[i])//b;c+=t;B[i]-=t*b
r+=c
if c==0:break
print([-1,r][A==B])
|
{
"input": [
"5\n5 6 5 2 1\n9817 1108 6890 4343 8704",
"4\n1 2 3 4\n2 3 4 5",
"3\n1 1 1\n13 5 7",
"5\n5 6 5 2 1\n9053 1108 6890 4343 8704",
"3\n1 1 1\n13 1 7",
"4\n0 2 3 4\n2 3 4 5",
"3\n2 1 1\n13 5 7",
"5\n5 6 5 2 1\n9053 1108 6890 4343 13928",
"4\n0 2 3 4\n2 2 4 5",
"3\n2 1 1\n13 1 7",
"5\n5 6 5 2 1\n9053 1108 6890 4343 12481",
"4\n0 2 3 4\n2 0 4 5",
"3\n2 1 1\n13 2 7",
"5\n5 6 5 2 2\n9053 1108 6890 4343 12481",
"4\n0 2 3 4\n2 0 2 5",
"3\n2 1 1\n13 2 0",
"5\n9 6 5 2 2\n9053 1108 6890 4343 12481",
"4\n0 2 3 4\n2 0 2 4",
"3\n1 1 1\n13 2 0",
"5\n9 6 5 2 2\n9053 1108 2114 4343 12481",
"4\n0 3 3 4\n2 0 2 4",
"3\n1 1 1\n13 3 0",
"5\n9 6 5 2 2\n9053 1108 2114 4343 2135",
"4\n0 3 3 4\n2 1 2 4",
"3\n1 1 1\n13 4 0",
"5\n9 6 5 4 2\n9053 1108 2114 4343 2135",
"4\n0 0 3 4\n2 1 2 4",
"5\n10 6 5 4 2\n9053 1108 2114 4343 2135",
"4\n0 0 3 4\n2 1 2 8",
"5\n10 8 5 4 2\n9053 1108 2114 4343 2135",
"4\n1 0 3 4\n2 1 2 8",
"5\n10 8 5 4 2\n9053 1859 2114 4343 2135",
"4\n1 0 3 5\n2 1 2 8",
"5\n10 8 5 4 2\n9053 1859 2048 4343 2135",
"4\n0 0 3 5\n2 1 2 8",
"5\n10 4 5 4 2\n9053 1859 2048 4343 2135",
"4\n0 0 5 5\n2 1 2 8",
"5\n10 4 5 4 2\n12280 1859 2048 4343 2135",
"4\n0 0 2 5\n2 1 2 8",
"5\n10 4 5 4 2\n12280 1859 2048 4227 2135",
"4\n0 0 4 5\n2 1 2 8",
"5\n10 4 5 4 2\n6426 1859 2048 4227 2135",
"4\n0 0 4 5\n4 1 2 8",
"5\n10 4 1 4 2\n6426 1859 2048 4227 2135",
"4\n0 -1 4 5\n4 1 2 8",
"5\n10 5 1 4 2\n6426 1859 2048 4227 2135",
"4\n0 -1 4 5\n4 1 1 8",
"5\n10 5 1 4 2\n10833 1859 2048 4227 2135",
"4\n0 -1 4 4\n4 1 1 8",
"5\n10 1 1 4 2\n10833 1859 2048 4227 2135",
"4\n0 -1 4 4\n3 1 1 8",
"5\n10 1 1 4 2\n10833 3397 2048 4227 2135",
"4\n0 -1 4 4\n3 1 1 16",
"5\n10 1 1 4 2\n10833 3397 2048 4170 2135",
"4\n0 -1 4 4\n3 1 2 16",
"5\n17 1 1 4 2\n10833 3397 2048 4170 2135",
"4\n0 -1 4 4\n3 1 2 4",
"5\n17 1 1 4 2\n10833 3397 2048 4170 1630",
"4\n1 -1 4 4\n3 1 2 4",
"5\n15 1 1 4 2\n10833 3397 2048 4170 1630",
"4\n1 -1 4 4\n3 1 0 4",
"5\n15 1 1 4 2\n10833 3397 2048 4170 2680",
"4\n1 -1 4 4\n4 1 0 4",
"5\n15 1 1 4 2\n10833 359 2048 4170 2680",
"4\n1 -1 4 4\n4 1 -1 4",
"5\n15 1 2 4 2\n10833 359 2048 4170 2680",
"4\n1 -1 4 4\n4 2 -1 4",
"5\n15 1 2 4 4\n10833 359 2048 4170 2680",
"4\n1 -1 4 4\n4 2 0 4",
"5\n15 1 2 4 5\n10833 359 2048 4170 2680",
"4\n1 -1 4 4\n4 2 1 4",
"5\n15 1 2 4 5\n10833 41 2048 4170 2680",
"4\n1 -1 4 4\n4 2 1 0",
"5\n15 1 2 4 5\n10833 41 2048 4170 1021",
"4\n1 -2 4 4\n4 2 1 0",
"5\n15 1 2 4 10\n10833 41 2048 4170 1021",
"4\n2 -2 4 4\n4 2 1 0",
"5\n15 1 2 4 10\n14435 41 2048 4170 1021",
"4\n2 -2 4 4\n4 3 1 0",
"5\n15 1 2 4 2\n14435 41 2048 4170 1021",
"4\n2 -2 4 4\n4 3 0 0",
"5\n15 1 2 4 2\n14435 41 2048 7434 1021",
"5\n15 1 2 4 4\n14435 41 2048 7434 1021",
"5\n15 1 2 4 4\n814 41 2048 7434 1021",
"5\n15 1 2 4 4\n814 15 2048 7434 1021",
"5\n15 1 2 4 4\n814 15 1962 7434 1021",
"5\n15 0 2 4 4\n814 15 1962 7434 1021",
"5\n15 0 2 4 4\n814 15 1962 8255 1021",
"5\n15 0 2 4 4\n814 17 1962 8255 1021",
"5\n15 1 2 4 4\n814 17 1962 8255 1021",
"5\n15 1 2 4 4\n814 17 1962 8255 1606",
"5\n15 1 2 4 4\n814 17 1962 4699 1606",
"5\n15 1 2 4 4\n814 17 3683 4699 1606",
"5\n15 1 2 4 4\n814 17 3683 4699 1671",
"5\n15 1 2 4 4\n814 17 3683 540 1671",
"5\n15 1 2 4 4\n274 17 3683 540 1671",
"5\n15 1 2 4 4\n274 17 3549 540 1671",
"5\n15 1 2 4 4\n263 17 3549 540 1671",
"5\n15 1 2 4 4\n263 8 3549 540 1671",
"5\n15 0 2 4 4\n263 8 3549 540 1671",
"5\n15 1 2 4 4\n263 14 3549 540 1671",
"5\n15 1 2 2 4\n263 14 3549 540 1671",
"5\n15 2 2 2 4\n263 14 3549 540 1671"
],
"output": [
"25",
"-1",
"4",
"-1\n",
"4\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n",
"-1\n"
]
}
| 5ATCODER
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
There are N positive integers arranged in a circle.
Now, the i-th number is A_i. Takahashi wants the i-th number to be B_i. For this objective, he will repeatedly perform the following operation:
* Choose an integer i such that 1 \leq i \leq N.
* Let a, b, c be the (i-1)-th, i-th, and (i+1)-th numbers, respectively. Replace the i-th number with a+b+c.
Here the 0-th number is the N-th number, and the (N+1)-th number is the 1-st number.
Determine if Takahashi can achieve his objective. If the answer is yes, find the minimum number of operations required.
Constraints
* 3 \leq N \leq 2 \times 10^5
* 1 \leq A_i, B_i \leq 10^9
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N
A_1 A_2 ... A_N
B_1 B_2 ... B_N
Output
Print the minimum number of operations required, or `-1` if the objective cannot be achieved.
Examples
Input
3
1 1 1
13 5 7
Output
4
Input
4
1 2 3 4
2 3 4 5
Output
-1
Input
5
5 6 5 2 1
9817 1108 6890 4343 8704
Output
25
### Input:
5
5 6 5 2 1
9817 1108 6890 4343 8704
### Output:
25
### Input:
4
1 2 3 4
2 3 4 5
### Output:
-1
### Code:
n,*t=map(int,open(0).read().split());A=t[:n];B=t[n:];r=0
while 1:
c=0
for i in range(n):
b=B[~-i%n]+B[-~i%n]
if A[i]<B[i]>b:t=(B[i]-A[i])//b;c+=t;B[i]-=t*b
r+=c
if c==0:break
print([-1,r][A==B])
|
p03078 AtCoder Beginner Contest 123 - Cake 123_10691
|
The Patisserie AtCoder sells cakes with number-shaped candles. There are X, Y and Z kinds of cakes with 1-shaped, 2-shaped and 3-shaped candles, respectively. Each cake has an integer value called deliciousness, as follows:
* The deliciousness of the cakes with 1-shaped candles are A_1, A_2, ..., A_X.
* The deliciousness of the cakes with 2-shaped candles are B_1, B_2, ..., B_Y.
* The deliciousness of the cakes with 3-shaped candles are C_1, C_2, ..., C_Z.
Takahashi decides to buy three cakes, one for each of the three shapes of the candles, to celebrate ABC 123.
There are X \times Y \times Z such ways to choose three cakes.
We will arrange these X \times Y \times Z ways in descending order of the sum of the deliciousness of the cakes.
Print the sums of the deliciousness of the cakes for the first, second, ..., K-th ways in this list.
Constraints
* 1 \leq X \leq 1 \ 000
* 1 \leq Y \leq 1 \ 000
* 1 \leq Z \leq 1 \ 000
* 1 \leq K \leq \min(3 \ 000, X \times Y \times Z)
* 1 \leq A_i \leq 10 \ 000 \ 000 \ 000
* 1 \leq B_i \leq 10 \ 000 \ 000 \ 000
* 1 \leq C_i \leq 10 \ 000 \ 000 \ 000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
X Y Z K
A_1 \ A_2 \ A_3 \ ... \ A_X
B_1 \ B_2 \ B_3 \ ... \ B_Y
C_1 \ C_2 \ C_3 \ ... \ C_Z
Output
Print K lines. The i-th line should contain the i-th value stated in the problem statement.
Examples
Input
2 2 2 8
4 6
1 5
3 8
Output
19
17
15
14
13
12
10
8
Input
3 3 3 5
1 10 100
2 20 200
1 10 100
Output
400
310
310
301
301
Input
10 10 10 20
7467038376 5724769290 292794712 2843504496 3381970101 8402252870 249131806 6310293640 6690322794 6082257488
1873977926 2576529623 1144842195 1379118507 6003234687 4925540914 3902539811 3326692703 484657758 2877436338
4975681328 8974383988 2882263257 7690203955 514305523 6679823484 4263279310 585966808 3752282379 620585736
Output
23379871545
22444657051
22302177772
22095691512
21667941469
21366963278
21287912315
21279176669
21160477018
21085311041
21059876163
21017997739
20703329561
20702387965
20590247696
20383761436
20343962175
20254073196
20210218542
20150096547
|
from heapq import nlargest
x,y,z,k=map(int,input().split())
a=list(map(int,input().split()))
b=list(map(int,input().split()))
c=list(map(int,input().split()))
ab=nlargest(k,(x+y for x in a for y in b))
abc=nlargest(k,(xy+z for xy in ab for z in c))
for i in abc:
print(i)
|
{
"input": [
"2 2 2 8\n4 6\n1 5\n3 8",
"10 10 10 20\n7467038376 5724769290 292794712 2843504496 3381970101 8402252870 249131806 6310293640 6690322794 6082257488\n1873977926 2576529623 1144842195 1379118507 6003234687 4925540914 3902539811 3326692703 484657758 2877436338\n4975681328 8974383988 2882263257 7690203955 514305523 6679823484 4263279310 585966808 3752282379 620585736",
"3 3 3 5\n1 10 100\n2 20 200\n1 10 100",
"2 2 2 1\n4 6\n1 5\n3 8",
"10 10 10 20\n7467038376 5724769290 292794712 2843504496 3381970101 8402252870 249131806 6310293640 6690322794 6082257488\n1873977926 2576529623 1144842195 1379118507 6003234687 4925540914 3902539811 3326692703 484657758 2877436338\n4975681328 8974383988 2882263257 6426500770 514305523 6679823484 4263279310 585966808 3752282379 620585736",
"10 10 10 20\n7467038376 5724769290 292794712 2843504496 3381970101 8402252870 249131806 6310293640 6690322794 6082257488\n1873977926 2576529623 1144842195 1379118507 6003234687 4925540914 3902539811 3326692703 484657758 2877436338\n4975681328 8974383988 2882263257 4734915691 514305523 6679823484 4263279310 585966808 3752282379 620585736",
"10 10 10 20\n7467038376 5724769290 292794712 2843504496 3381970101 14107954240 249131806 6310293640 6690322794 6082257488\n1873977926 2576529623 1144842195 1379118507 6003234687 4925540914 3902539811 3326692703 484657758 2877436338\n4975681328 8974383988 2882263257 4734915691 514305523 6679823484 3306606453 585966808 3752282379 620585736",
"10 10 10 20\n7467038376 5724769290 292794712 2843504496 3381970101 14107954240 249131806 11770255275 6690322794 6082257488\n1873977926 2576529623 1144842195 1379118507 6003234687 4925540914 3902539811 3326692703 484657758 2877436338\n4975681328 8974383988 2882263257 4734915691 514305523 6679823484 3306606453 585966808 3752282379 620585736",
"10 10 10 20\n7467038376 5724769290 292794712 2843504496 3381970101 14107954240 249131806 11770255275 6690322794 6082257488\n1873977926 4407421270 1144842195 1379118507 6003234687 4925540914 3902539811 3326692703 484657758 2877436338\n4975681328 8974383988 2882263257 4734915691 514305523 6679823484 3306606453 585966808 3752282379 620585736",
"10 10 10 22\n7467038376 5724769290 292794712 2843504496 3381970101 14107954240 249131806 11770255275 6690322794 6082257488\n1873977926 4407421270 1144842195 1379118507 6003234687 4925540914 3902539811 3326692703 484657758 2877436338\n4975681328 8974383988 2882263257 4734915691 514305523 6679823484 3306606453 585966808 3752282379 620585736",
"10 10 10 22\n7467038376 5724769290 480936 2843504496 3381970101 14107954240 249131806 11770255275 6690322794 6082257488\n1873977926 4407421270 1144842195 1379118507 7229165398 4925540914 3902539811 3326692703 484657758 2877436338\n4975681328 8974383988 2882263257 4734915691 514305523 6679823484 3306606453 585966808 3752282379 620585736",
"10 10 10 22\n7467038376 5724769290 480936 2843504496 3381970101 14107954240 249131806 14297961023 6690322794 6082257488\n1873977926 4407421270 1144842195 1379118507 7229165398 4925540914 3902539811 3326692703 484657758 2877436338\n4975681328 8974383988 2882263257 4734915691 514305523 6679823484 3306606453 585966808 3752282379 620585736",
"10 10 10 22\n7467038376 5724769290 480936 2843504496 3381970101 14107954240 249131806 14297961023 11861432929 6082257488\n1873977926 4407421270 1144842195 1379118507 7229165398 4925540914 3902539811 3326692703 484657758 2877436338\n4975681328 8974383988 2882263257 4734915691 514305523 6679823484 3306606453 585966808 3752282379 620585736",
"10 10 10 22\n7467038376 5724769290 480936 2843504496 3381970101 14107954240 249131806 14297961023 14218869544 6082257488\n1873977926 4407421270 1144842195 1379118507 7229165398 4925540914 3902539811 3326692703 484657758 2877436338\n4975681328 8974383988 2882263257 4734915691 514305523 6679823484 3306606453 585966808 3752282379 620585736",
"10 10 10 20\n7467038376 5724769290 292794712 2843504496 3834869267 8402252870 249131806 6310293640 6690322794 6082257488\n1873977926 2576529623 1144842195 1379118507 6003234687 4925540914 3902539811 3326692703 484657758 2877436338\n4975681328 8974383988 2882263257 7690203955 514305523 6679823484 4263279310 585966808 3752282379 620585736",
"10 10 10 20\n7467038376 5724769290 292794712 2843504496 3381970101 14107954240 249131806 6310293640 6690322794 6082257488\n1873977926 2576529623 1144842195 1379118507 6003234687 4925540914 3902539811 3326692703 484657758 2877436338\n4975681328 8974383988 2882263257 6801655704 514305523 6679823484 3306606453 585966808 3752282379 620585736",
"10 10 10 20\n7467038376 5724769290 292794712 2843504496 3381970101 14107954240 249131806 11770255275 6690322794 6082257488\n1873977926 4407421270 1144842195 1379118507 6003234687 4925540914 3902539811 3326692703 484657758 2877436338\n4975681328 5274071675 2882263257 4734915691 514305523 6679823484 3306606453 585966808 3752282379 620585736",
"10 10 10 22\n7467038376 5724769290 480936 2843504496 3381970101 14107954240 249131806 14297961023 11861432929 6082257488\n1873977926 4407421270 1144842195 1379118507 7229165398 4925540914 3902539811 3326692703 484657758 2877436338\n4975681328 8974383988 2882263257 4734915691 514305523 6679823484 5231244603 585966808 3752282379 620585736",
"10 10 10 20\n7467038376 5724769290 292794712 2843504496 3834869267 8402252870 249131806 6310293640 6690322794 6082257488\n1873977926 2576529623 1144842195 1379118507 6003234687 4925540914 3902539811 3326692703 484657758 2877436338\n4975681328 8974383988 2882263257 7690203955 514305523 2128918965 4263279310 585966808 3752282379 620585736",
"10 10 10 20\n7467038376 5724769290 292794712 2843504496 3381970101 8402252870 249131806 1526300067 6690322794 6082257488\n1873977926 2576529623 606195516 1379118507 6003234687 4925540914 3902539811 3326692703 484657758 2877436338\n4975681328 8974383988 2882263257 4734915691 514305523 6679823484 4263279310 585966808 3752282379 620585736",
"10 10 10 20\n7467038376 5724769290 292794712 2843504496 3381970101 14107954240 249131806 6310293640 6690322794 6082257488\n1873977926 2576529623 1144842195 1379118507 2045525737 4925540914 3902539811 3326692703 484657758 2877436338\n4975681328 8974383988 2882263257 6801655704 514305523 6679823484 3306606453 585966808 3752282379 620585736",
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"10 10 10 22\n7467038376 5724769290 309564 2843504496 3023742294 498870719 249131806 14297961023 14218869544 2469507727\n1862193477 4407421270 658617344 1379118507 7229165398 467268175 2582425414 5893361582 484657758 2877436338\n5627410812 8974383988 2882263257 4734915691 514305523 1792630495 1473857612 585966808 5022505692 808178650",
"10 10 10 42\n3471439818 7125082499 52097 2843504496 3381970101 14107954240 249131806 9465078905 6690322794 2898542789\n1873977926 4407421270 764181049 1379118507 9014541718 4925540914 3902539811 5851891101 178325203 2877436338\n8482502021 8974383988 2882263257 7655946647 95905874 8599494163 3306606453 188606520 9711411241 876155962",
"10 10 10 22\n7467038376 5724769290 309564 2843504496 3023742294 498870719 249131806 14297961023 2985137660 2469507727\n1862193477 4407421270 658617344 1379118507 7229165398 467268175 2582425414 5893361582 484657758 2877436338\n5627410812 8974383988 2882263257 4734915691 514305523 1792630495 2274572613 585966808 5022505692 808178650",
"10 10 10 29\n7467038376 2043183524 309564 2843504496 3023742294 498870719 249131806 14297961023 2985137660 2469507727\n1862193477 4407421270 658617344 1379118507 7229165398 467268175 2582425414 5893361582 484657758 2877436338\n5627410812 8974383988 2882263257 4734915691 514305523 1792630495 2274572613 585966808 5022505692 808178650",
"10 10 10 29\n7467038376 2043183524 309564 2843504496 3023742294 498870719 249131806 14297961023 2985137660 2469507727\n1862193477 4407421270 658617344 1379118507 7229165398 467268175 2582425414 5893361582 484657758 2877436338\n3679621223 8974383988 2882263257 4734915691 514305523 1792630495 2274572613 585966808 5022505692 808178650",
"10 10 10 29\n7467038376 2043183524 309564 2843504496 3023742294 165580015 249131806 14297961023 2985137660 2469507727\n1862193477 4407421270 658617344 388592354 7229165398 467268175 2582425414 5893361582 484657758 2877436338\n3679621223 8974383988 2882263257 4734915691 514305523 1792630495 2274572613 585966808 5022505692 808178650",
"2 2 2 6\n4 6\n1 5\n3 8",
"3 3 3 5\n1 10 101\n2 20 200\n1 10 100",
"10 10 10 20\n7467038376 5724769290 292794712 2843504496 3381970101 8402252870 249131806 6310293640 6690322794 6082257488\n1873977926 2576529623 1144842195 1379118507 1616641807 4925540914 3902539811 3326692703 484657758 2877436338\n4975681328 8974383988 2882263257 6426500770 514305523 6679823484 4263279310 585966808 3752282379 620585736",
"10 10 10 20\n7467038376 5724769290 292794712 2843504496 3381970101 8402252870 249131806 6310293640 4547469684 6082257488\n1873977926 2576529623 1144842195 1379118507 6003234687 4925540914 3902539811 3326692703 484657758 2877436338\n4975681328 8974383988 2882263257 4734915691 514305523 6679823484 4263279310 585966808 3752282379 620585736",
"10 10 10 20\n7467038376 5724769290 292794712 2843504496 3381970101 8402252870 249131806 6310293640 6690322794 6082257488\n1873977926 2576529623 1144842195 1379118507 6003234687 4925540914 3902539811 3326692703 484657758 2877436338\n4975681328 17135590902 2882263257 4734915691 514305523 6679823484 3306606453 585966808 3752282379 620585736",
"10 10 10 16\n7467038376 5724769290 480936 2843504496 3381970101 14107954240 249131806 11770255275 6690322794 6082257488\n1873977926 4407421270 1144842195 1379118507 6003234687 4925540914 3902539811 3326692703 484657758 2877436338\n4975681328 8974383988 2882263257 4734915691 514305523 6679823484 3306606453 585966808 3752282379 620585736",
"10 10 10 22\n7467038376 5724769290 480936 2843504496 3381970101 14107954240 249131806 14297961023 11861432929 6082257488\n1873977926 1654566501 1144842195 1379118507 7229165398 4925540914 3902539811 3326692703 484657758 2877436338\n4975681328 8974383988 2882263257 4734915691 514305523 6679823484 3306606453 585966808 3752282379 620585736",
"10 10 10 22\n7467038376 5724769290 480936 2843504496 3381970101 14107954240 249131806 14297961023 14218869544 6082257488\n1873977926 4407421270 1144842195 1379118507 7229165398 4925540914 3902539811 2166815882 484657758 2877436338\n4975681328 8974383988 2882263257 4734915691 514305523 6679823484 3306606453 585966808 3752282379 620585736",
"10 10 10 20\n7467038376 5724769290 292794712 2843504496 3834869267 495515942 249131806 6310293640 6690322794 6082257488\n1873977926 2576529623 1144842195 1379118507 6003234687 4925540914 3902539811 3326692703 484657758 2877436338\n4975681328 8974383988 2882263257 7690203955 514305523 6679823484 4263279310 585966808 3752282379 620585736",
"10 10 10 20\n7467038376 5724769290 292794712 2843504496 3381970101 8402252870 249131806 6310293640 6690322794 5112756826\n1873977926 2576529623 606195516 1379118507 6003234687 4925540914 3902539811 3326692703 484657758 2877436338\n4975681328 8974383988 2882263257 4734915691 514305523 6679823484 4263279310 585966808 3752282379 620585736",
"10 10 10 22\n7467038376 5724769290 480936 2843504496 3381970101 14107954240 249131806 894879326 6690322794 6082257488\n1873977926 4407421270 1144842195 1379118507 6003234687 4925540914 3902539811 3326692703 871804439 2877436338\n4975681328 8974383988 2882263257 4734915691 514305523 6679823484 3306606453 585966808 3752282379 620585736",
"10 10 10 22\n7467038376 5724769290 52097 2843504496 3381970101 14107954240 249131806 11770255275 6690322794 6082257488\n1873977926 4407421270 1144842195 121085442 7229165398 4925540914 3902539811 3326692703 484657758 2877436338\n4975681328 8974383988 2882263257 4734915691 514305523 6679823484 3306606453 585966808 3752282379 620585736",
"10 10 10 20\n7467038376 5724769290 292794712 2843504496 6266807579 8402252870 249131806 6310293640 6690322794 6082257488\n1873977926 2576529623 1144842195 1379118507 6003234687 4925540914 3902539811 3326692703 484657758 2877436338\n4975681328 8974383988 2882263257 7690203955 514305523 2128918965 4263279310 585966808 3752282379 620585736",
"10 10 10 20\n7467038376 5724769290 292794712 2843504496 3381970101 8402252870 249131806 1526300067 6690322794 6783872709\n1873977926 2576529623 606195516 1379118507 6003234687 4925540914 3902539811 3326692703 484657758 2877436338\n4975681328 8974383988 2882263257 4734915691 514305523 6679823484 4263279310 585966808 3752282379 620585736",
"10 10 10 20\n7467038376 5724769290 148301192 2843504496 3381970101 8402252870 249131806 7536802306 6690322794 6082257488\n1873977926 2576529623 1144842195 1379118507 6003234687 4925540914 3902539811 3326692703 484657758 2877436338\n4975681328 8974383988 2882263257 4734915691 514305523 6679823484 1097173209 585966808 3752282379 620585736",
"10 10 10 20\n7467038376 5724769290 292794712 2843504496 3381970101 14107954240 249131806 6310293640 6690322794 6082257488\n1873977926 2576529623 1144842195 1379118507 2045525737 4925540914 3902539811 3326692703 563433980 2877436338\n4975681328 8974383988 2882263257 6801655704 514305523 6679823484 3306606453 585966808 3752282379 620585736",
"10 10 10 22\n7467038376 5724769290 292794712 2843504496 3381970101 17758351638 249131806 11770255275 6690322794 6082257488\n1873977926 4407421270 1144842195 1379118507 6003234687 4925540914 3902539811 4159176501 528020791 2877436338\n4975681328 8974383988 2882263257 4734915691 514305523 6679823484 3306606453 585966808 3752282379 620585736",
"10 10 10 22\n11432277847 5724769290 480936 2843504496 3381970101 14107954240 249131806 14297961023 11861432929 6082257488\n1873977926 4407421270 1144842195 1379118507 7229165398 4925540914 3902539811 3326692703 484657758 2877436338\n4975681328 8974383988 2882263257 4734915691 514305523 6679823484 7848263435 585966808 3752282379 620585736",
"10 10 10 22\n7467038376 5724769290 309564 2843504496 3381970101 24362601688 249131806 14297961023 14218869544 6082257488\n1873977926 4407421270 1372462105 1379118507 7229165398 4925540914 3902539811 3326692703 484657758 2877436338\n4975681328 8974383988 2882263257 4734915691 514305523 6679823484 3306606453 585966808 3752282379 620585736",
"10 10 10 20\n7467038376 5724769290 148301192 2843504496 3381970101 8402252870 249131806 6310293640 6690322794 10610013270\n1873977926 2576529623 1144842195 1379118507 6003234687 4925540914 3902539811 3326692703 484657758 2877436338\n4975681328 8974383988 2882263257 4734915691 514305523 6679823484 837560161 585966808 3752282379 620585736",
"10 10 10 20\n7467038376 5724769290 292794712 2843504496 3381970101 14107954240 249131806 11770255275 2323224880 6082257488\n1873977926 2576529623 1479553652 1379118507 6003234687 4925540914 3902539811 3326692703 233755778 2877436338\n4975681328 8700180183 2882263257 4734915691 514305523 6679823484 3306606453 585966808 3752282379 620585736",
"10 10 10 22\n7467038376 5724769290 292794712 2843504496 3381970101 14107954240 249131806 11770255275 6690322794 8545728314\n1873977926 4407421270 2094006548 1379118507 6003234687 4925540914 3902539811 4159176501 528020791 2877436338\n4975681328 8974383988 2882263257 4734915691 514305523 6679823484 3306606453 585966808 3752282379 620585736"
],
"output": [
"19\n17\n15\n14\n13\n12\n10\n8",
"23379871545\n22444657051\n22302177772\n22095691512\n21667941469\n21366963278\n21287912315\n21279176669\n21160477018\n21085311041\n21059876163\n21017997739\n20703329561\n20702387965\n20590247696\n20383761436\n20343962175\n20254073196\n20210218542\n20150096547",
"400\n310\n310\n301\n301",
"19\n",
"23379871545\n22444657051\n22302177772\n21667941469\n21366963278\n21287912315\n21279176669\n21085311041\n21059876163\n20831988327\n20703329561\n20702387965\n20590247696\n20343962175\n20254073196\n20210218542\n20150096547\n20007617268\n19982182390\n19953166481\n",
"23379871545\n22444657051\n22302177772\n21667941469\n21366963278\n21287912315\n21279176669\n21085311041\n21059876163\n20703329561\n20702387965\n20590247696\n20343962175\n20254073196\n20210218542\n20150096547\n20007617268\n19982182390\n19953166481\n19768115067\n",
"29085572915\n28007879142\n26984878039\n26791012411\n26409030931\n25959774566\n25713318638\n25658867851\n25086870255\n24956316154\n24846104618\n24690317535\n24461456735\n24227180423\n24114470427\n24009176482\n23863471306\n23768410845\n23665214062\n23566995986\n",
"29085572915\n28007879142\n26984878039\n26791012411\n26747873950\n26409030931\n25959774566\n25713318638\n25670180177\n25658867851\n25086870255\n24956316154\n24846104618\n24690317535\n24647179074\n24461456735\n24453313446\n24227180423\n24114470427\n24071331966\n",
"29085572915\n28007879142\n27489759498\n26984878039\n26791012411\n26747873950\n26409030931\n25959774566\n25713318638\n25670180177\n25195198994\n25152060533\n25086870255\n24956316154\n24846104618\n24690317535\n24647179074\n24461456735\n24453313446\n24227180423\n",
"29085572915\n28007879142\n27489759498\n26984878039\n26791012411\n26747873950\n26409030931\n25959774566\n25713318638\n25670180177\n25195198994\n25152060533\n25086870255\n24956316154\n24846104618\n24690317535\n24647179074\n24461456735\n24453313446\n24227180423\n24114470427\n24071331966\n",
"30311503626\n28016943122\n28007879142\n27973804661\n27489759498\n26984878039\n26409030931\n26312800966\n26072035329\n25959774566\n25713318638\n25679244157\n25670180177\n25195198994\n25152060533\n25089402017\n24956316154\n24690317535\n24647179074\n24643726091\n24461456735\n24227180423\n",
"30501510409\n30311503626\n28206949905\n28197885925\n28016943122\n28007879142\n27679766281\n27489759498\n27174884822\n26984878039\n26599037714\n26502807749\n26409030931\n26312800966\n26262042112\n26149781349\n26072035329\n25959774566\n25903325421\n25713318638\n25385205777\n25279408800\n",
"30501510409\n30311503626\n28206949905\n28197885925\n28064982315\n28016943122\n28007879142\n27679766281\n27489759498\n27174884822\n26984878039\n26599037714\n26502807749\n26409030931\n26312800966\n26262042112\n26149781349\n26072035329\n25959774566\n25903325421\n25770421811\n25761357831\n",
"30501510409\n30422418930\n30311503626\n28206949905\n28197885925\n28127858426\n28118794446\n28016943122\n28007879142\n27679766281\n27600674802\n27489759498\n27174884822\n27095793343\n26984878039\n26599037714\n26519946235\n26502807749\n26423716270\n26409030931\n26312800966\n26262042112\n",
"23379871545\n22444657051\n22302177772\n22095691512\n21667941469\n21366963278\n21287912315\n21279176669\n21160477018\n21085311041\n21059876163\n21017997739\n20703329561\n20702387965\n20590247696\n20383761436\n20343962175\n20254073196\n20210218542\n20150096547\n",
"29085572915\n28007879142\n26984878039\n26912844631\n26791012411\n26409030931\n25959774566\n25835150858\n25713318638\n25658867851\n25086870255\n24956316154\n24812149755\n24690317535\n24461456735\n24236302647\n24227180423\n24114470427\n24009176482\n23863471306\n",
"26791012411\n25713318638\n25385260602\n25195198994\n25086870255\n24846104618\n24690317535\n24453313446\n24307566829\n24114470427\n24009176482\n23863471306\n23789447185\n23768410845\n23665214062\n23491056838\n23417795380\n23375619673\n23284565726\n23250291201\n",
"30501510409\n30311503626\n28206949905\n28197885925\n28064982315\n28016943122\n28007879142\n27679766281\n27489759498\n27174884822\n26984878039\n26758371024\n26599037714\n26568364241\n26502807749\n26409030931\n26312800966\n26262042112\n26149781349\n26072035329\n25959774566\n25903325421\n",
"23379871545\n22444657051\n22302177772\n22095691512\n21667941469\n21366963278\n21287912315\n21279176669\n21160477018\n21059876163\n21017997739\n20703329561\n20702387965\n20590247696\n20383761436\n20343962175\n20254073196\n20210218542\n20082783245\n20003732282\n",
"23379871545\n22444657051\n22302177772\n21667941469\n21366963278\n21279176669\n21085311041\n21059876163\n20703329561\n20702387965\n20590247696\n20343962175\n20254073196\n20150096547\n20007617268\n19982182390\n19953166481\n19768115067\n19624694192\n19567246593\n",
"28007879142\n26984878039\n26409030931\n25959774566\n25835150858\n25713318638\n25658867851\n25127863965\n24956316154\n24812149755\n24690317535\n24461456735\n24236302647\n24227180423\n24114470427\n24009176482\n23787046282\n23665214062\n23566995986\n23486139567\n",
"29085572915\n28007879142\n27489759498\n27241514729\n26984878039\n26791012411\n26747873950\n25959774566\n25713318638\n25670180177\n25195198994\n25152060533\n25086870255\n24956316154\n24946954225\n24903815764\n24846104618\n24690317535\n24647179074\n24461456735\n24453313446\n24227180423\n",
"29085572915\n28007879142\n27489759498\n26984878039\n26791012411\n26747873950\n26409030931\n25959774566\n25713318638\n25670180177\n25195198994\n25152060533\n25086870255\n24846104618\n24690791002\n24690317535\n24647179074\n24461456735\n24453313446\n24227180423\n24114470427\n24071331966\n",
"30311503626\n29936613801\n28007879142\n27973804661\n27632989317\n27598914836\n27489759498\n27114869673\n26984878039\n26609988214\n26409030931\n26312800966\n26072035329\n26034141106\n25959774566\n25670180177\n25584884741\n25295290352\n25152060533\n25089402017\n24956316154\n24777170708\n",
"30501510409\n30311503626\n29375389856\n29185383073\n28206949905\n28197885925\n28064982315\n28016943122\n28007879142\n27679766281\n27489759498\n27174884822\n27071765372\n26984878039\n26938861762\n26881758589\n26599037714\n26553645728\n26502807749\n26409030931\n26363638945\n26312800966\n",
"23379871545\n22444657051\n22302177772\n22095691512\n21667941469\n21366963278\n21287912315\n21279176669\n21160477018\n21059876163\n21017997739\n20703329561\n20702387965\n20590247696\n20383761436\n20376417065\n20343962175\n20254073196\n20210218542\n20082783245\n",
"23379871545\n22444657051\n22302177772\n21667941469\n21366963278\n21287912315\n21279176669\n21085311041\n21059876163\n20831988327\n20703329561\n20702387965\n20590247696\n20343962175\n20210218542\n20150096547\n20007617268\n19982182390\n19953166481\n19896773833\n",
"28007879142\n26984878039\n26409030931\n25959774566\n25835150858\n25713318638\n25658867851\n25127863965\n24812149755\n24690317535\n24461456735\n24236302647\n24227180423\n24114470427\n24009176482\n23787046282\n23665214062\n23566995986\n23486139567\n23454182619\n",
"28811369110\n27733675337\n26791012411\n26710674234\n26473670145\n26134827126\n25713318638\n25685570761\n25395976372\n25384664046\n25086870255\n24846104618\n24690317535\n24682112349\n24453313446\n24372975269\n24187252930\n24114470427\n24009176482\n23952976618\n",
"29085572915\n28007879142\n27489759498\n26984878039\n26791012411\n26747873950\n26409030931\n25959774566\n25713318638\n25670180177\n25195198994\n25152060533\n25086870255\n24846104618\n24690791002\n24690317535\n24647179074\n24453313446\n24227180423\n24114470427\n24071331966\n24009176482\n",
"32096879946\n31721990121\n29759180981\n29384291156\n28098177286\n28007879142\n27857411649\n27632989317\n27489759498\n27114869673\n26984878039\n26874778337\n26609988214\n26429102411\n26409030931\n26034141106\n26004759215\n25959774566\n25760478321\n25670180177\n25584884741\n25519712684\n",
"30501510409\n30311503626\n29830396035\n29640389252\n28206949905\n28197885925\n28016943122\n28007879142\n27679766281\n27535835531\n27489759498\n27345828748\n26599037714\n26502807749\n26409030931\n26312800966\n26262042112\n26149781349\n26072035329\n25959774566\n25903325421\n25831693375\n",
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"30501510409\n30311503626\n28206949905\n28197885925\n28064982315\n28016943122\n28007879142\n27174884822\n26984878039\n26599037714\n26502807749\n26409030931\n26312800966\n26262042112\n26149781349\n26072035329\n25959774566\n25903325421\n25770421811\n25761357831\n25713318638\n25279408800\n",
"30501510409\n30422418930\n30311503626\n28206949905\n28197885925\n28127858426\n28118794446\n28016943122\n28007879142\n27679766281\n27600674802\n27489759498\n27174884822\n27095793343\n26984878039\n26502807749\n26423716270\n26312800966\n26262042112\n26182950633\n26149781349\n26072035329\n",
"22444657051\n21667941469\n21366963278\n21287912315\n21160477018\n21059876163\n20702387965\n20590247696\n20383761436\n20343962175\n20210218542\n20150096547\n20082783245\n20003732282\n19982182390\n19775696130\n19768115067\n19624694192\n19567246593\n19418207932\n",
"23379871545\n22444657051\n22302177772\n21667941469\n21366963278\n21287912315\n21279176669\n21085311041\n20703329561\n20702387965\n20590247696\n20343962175\n20254073196\n20210218542\n20150096547\n20090375501\n20007617268\n19953166481\n19768115067\n19624694192\n",
"29085572915\n28007879142\n27489759498\n26984878039\n26791012411\n26409030931\n25959774566\n25713318638\n25195198994\n25086870255\n24956316154\n24846104618\n24690317535\n24461456735\n24227180423\n24114470427\n24009176482\n23954142667\n23863471306\n23768410845\n23665214062\n23491056838\n",
"30311503626\n28016943122\n28007879142\n27973804661\n27489759498\n26984878039\n26409030931\n26312800966\n26072035329\n25959774566\n25713318638\n25679244157\n25670180177\n25195198994\n25152060533\n25089402017\n24956316154\n24690317535\n24647179074\n24643726091\n24227180423\n24219382895\n",
"23379871545\n22444657051\n22302177772\n22095691512\n21667941469\n21366963278\n21287912315\n21279176669\n21244426254\n21160477018\n21059876163\n21017997739\n20703329561\n20702387965\n20590247696\n20383761436\n20343962175\n20254073196\n20210218542\n20166732481\n",
"23379871545\n22444657051\n22302177772\n21761491384\n21667941469\n21366963278\n21279176669\n21085311041\n20703329561\n20702387965\n20683797611\n20590247696\n20343962175\n20254073196\n20150096547\n20007617268\n19953166481\n19768115067\n19660796508\n19624694192\n",
"23379871545\n22514420981\n22444657051\n22302177772\n21667941469\n21436727208\n21366963278\n21279176669\n21085311041\n21059876163\n20703329561\n20702387965\n20590247696\n20413726105\n20343962175\n20254073196\n20219860477\n20150096547\n20007617268\n19982182390\n",
"28007879142\n26984878039\n26409030931\n25959774566\n25835150858\n25713318638\n25658867851\n25127863965\n24956316154\n24812149755\n24690317535\n24461456735\n24236302647\n24227180423\n24114470427\n24009176482\n23787046282\n23665214062\n23645772208\n23486139567\n",
"32735970313\n31658276540\n31140156896\n30891912127\n30635275437\n30441409809\n29610171964\n29363716036\n28845596392\n28737267653\n28606713552\n28597351623\n28496502016\n28340714933\n28111854133\n27877577821\n27659573880\n27513868704\n27418808243\n27315611460\n27260756417\n27141454236\n",
"30501510409\n30311503626\n29375389856\n29185383073\n28206949905\n28197885925\n28064982315\n28016943122\n28007879142\n27679766281\n27635827233\n27489759498\n27174884822\n27071765372\n26984878039\n26938861762\n26881758589\n26599037714\n26553645728\n26509706680\n26502807749\n26409030931\n",
"40566151074\n38271590570\n38262526590\n37744406946\n37239525487\n36663678379\n36567448414\n36326682777\n36214422014\n35967966086\n35449846442\n35344049465\n35210963602\n34944964983\n34898373539\n34716104183\n34709447781\n34474030343\n34369117875\n34263823930\n34023058293\n33919861510\n",
"25587631945\n24509938172\n23486937069\n23379871545\n23293071441\n22911089961\n22461833596\n22444657051\n22302177772\n22215377668\n22160926881\n21667941469\n21588929285\n21458375184\n21366963278\n21348163648\n21287912315\n21279176669\n21192376565\n21085311041\n",
"28811369110\n27733675337\n26791012411\n26710674234\n26473670145\n26134827126\n25713318638\n25685570761\n25395976372\n25384664046\n25086870255\n24846104618\n24690317535\n24682112349\n24453313446\n24372975269\n24287688075\n24187252930\n24114470427\n24009176482\n",
"29085572915\n28007879142\n27489759498\n27241514729\n26984878039\n26791012411\n26747873950\n25959774566\n25713318638\n25670180177\n25195198994\n25176344776\n25152060533\n25086870255\n24956316154\n24946954225\n24903815764\n24846104618\n24690317535\n24647179074\n24461456735\n24453313446\n"
]
}
| 5ATCODER
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
The Patisserie AtCoder sells cakes with number-shaped candles. There are X, Y and Z kinds of cakes with 1-shaped, 2-shaped and 3-shaped candles, respectively. Each cake has an integer value called deliciousness, as follows:
* The deliciousness of the cakes with 1-shaped candles are A_1, A_2, ..., A_X.
* The deliciousness of the cakes with 2-shaped candles are B_1, B_2, ..., B_Y.
* The deliciousness of the cakes with 3-shaped candles are C_1, C_2, ..., C_Z.
Takahashi decides to buy three cakes, one for each of the three shapes of the candles, to celebrate ABC 123.
There are X \times Y \times Z such ways to choose three cakes.
We will arrange these X \times Y \times Z ways in descending order of the sum of the deliciousness of the cakes.
Print the sums of the deliciousness of the cakes for the first, second, ..., K-th ways in this list.
Constraints
* 1 \leq X \leq 1 \ 000
* 1 \leq Y \leq 1 \ 000
* 1 \leq Z \leq 1 \ 000
* 1 \leq K \leq \min(3 \ 000, X \times Y \times Z)
* 1 \leq A_i \leq 10 \ 000 \ 000 \ 000
* 1 \leq B_i \leq 10 \ 000 \ 000 \ 000
* 1 \leq C_i \leq 10 \ 000 \ 000 \ 000
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
X Y Z K
A_1 \ A_2 \ A_3 \ ... \ A_X
B_1 \ B_2 \ B_3 \ ... \ B_Y
C_1 \ C_2 \ C_3 \ ... \ C_Z
Output
Print K lines. The i-th line should contain the i-th value stated in the problem statement.
Examples
Input
2 2 2 8
4 6
1 5
3 8
Output
19
17
15
14
13
12
10
8
Input
3 3 3 5
1 10 100
2 20 200
1 10 100
Output
400
310
310
301
301
Input
10 10 10 20
7467038376 5724769290 292794712 2843504496 3381970101 8402252870 249131806 6310293640 6690322794 6082257488
1873977926 2576529623 1144842195 1379118507 6003234687 4925540914 3902539811 3326692703 484657758 2877436338
4975681328 8974383988 2882263257 7690203955 514305523 6679823484 4263279310 585966808 3752282379 620585736
Output
23379871545
22444657051
22302177772
22095691512
21667941469
21366963278
21287912315
21279176669
21160477018
21085311041
21059876163
21017997739
20703329561
20702387965
20590247696
20383761436
20343962175
20254073196
20210218542
20150096547
### Input:
2 2 2 8
4 6
1 5
3 8
### Output:
19
17
15
14
13
12
10
8
### Input:
10 10 10 20
7467038376 5724769290 292794712 2843504496 3381970101 8402252870 249131806 6310293640 6690322794 6082257488
1873977926 2576529623 1144842195 1379118507 6003234687 4925540914 3902539811 3326692703 484657758 2877436338
4975681328 8974383988 2882263257 7690203955 514305523 6679823484 4263279310 585966808 3752282379 620585736
### Output:
23379871545
22444657051
22302177772
22095691512
21667941469
21366963278
21287912315
21279176669
21160477018
21085311041
21059876163
21017997739
20703329561
20702387965
20590247696
20383761436
20343962175
20254073196
20210218542
20150096547
### Code:
from heapq import nlargest
x,y,z,k=map(int,input().split())
a=list(map(int,input().split()))
b=list(map(int,input().split()))
c=list(map(int,input().split()))
ab=nlargest(k,(x+y for x in a for y in b))
abc=nlargest(k,(xy+z for xy in ab for z in c))
for i in abc:
print(i)
|
p03221 AtCoder Beginner Contest 113 - ID_10695
|
In Republic of Atcoder, there are N prefectures, and a total of M cities that belong to those prefectures.
City i is established in year Y_i and belongs to Prefecture P_i.
You can assume that there are no multiple cities that are established in the same year.
It is decided to allocate a 12-digit ID number to each city.
If City i is the x-th established city among the cities that belong to Prefecture i, the first six digits of the ID number of City i is P_i, and the last six digits of the ID number is x.
Here, if P_i or x (or both) has less than six digits, zeros are added to the left until it has six digits.
Find the ID numbers for all the cities.
Note that there can be a prefecture with no cities.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq M \leq 10^5
* 1 \leq P_i \leq N
* 1 \leq Y_i \leq 10^9
* Y_i are all different.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
P_1 Y_1
:
P_M Y_M
Output
Print the ID numbers for all the cities, in ascending order of indices (City 1, City 2, ...).
Examples
Input
2 3
1 32
2 63
1 12
Output
000001000002
000002000001
000001000001
Input
2 3
2 55
2 77
2 99
Output
000002000001
000002000002
000002000003
|
from collections import defaultdict
(n, m), *q = [[*map(int, i.split())] for i in open(0)]
d = defaultdict(list)
for k, v in q:
d[k].append(v)
c = defaultdict(dict)
for k, v in d.items():
for i, j in enumerate(sorted(v)):
c[k][j] = i + 1
for p, y in q:
print("{:0>6}{:0>6}".format(p, c[p][y]))
|
{
"input": [
"2 3\n1 32\n2 63\n1 12",
"2 3\n2 55\n2 77\n2 99",
"2 3\n1 55\n2 77\n2 99",
"2 3\n2 32\n2 63\n1 12",
"2 1\n2 55\n2 77\n2 99",
"2 2\n2 55\n2 77\n2 99",
"2 3\n2 55\n2 77\n2 195",
"2 3\n1 32\n2 63\n1 6",
"2 3\n2 39\n2 16\n1 12",
"2 2\n2 55\n2 29\n2 195",
"2 3\n2 96\n2 77\n2 195",
"2 1\n1 16\n2 77\n2 195",
"2 3\n1 32\n2 63\n2 16",
"2 3\n1 15\n2 64\n1 72",
"2 2\n2 55\n1 29\n1 195",
"2 2\n1 16\n2 77\n2 195",
"3 3\n2 39\n1 84\n1 131",
"4 3\n2 32\n2 49\n2 12",
"4 3\n2 33\n3 77\n1 99",
"4 3\n2 5\n2 49\n2 12",
"4 3\n3 33\n3 77\n1 99",
"2 2\n1 4\n1 68\n4 639",
"4 3\n3 33\n1 70\n1 175",
"4 3\n4 33\n1 70\n1 175",
"3 3\n3 26\n2 77\n1 131",
"2 3\n1 15\n1 58\n1 72",
"4 3\n2 5\n4 49\n1 12",
"4 3\n1 33\n3 70\n1 175",
"4 3\n2 59\n2 49\n2 12",
"2 3\n2 4\n1 7\n2 528",
"4 3\n1 0\n1 70\n2 118",
"4 3\n2 27\n2 36\n4 675",
"3 1\n3 2\n4 32\n-2 195",
"3 2\n2 59\n3 21\n0 100",
"8 3\n1 95\n3 42\n1 64",
"5 2\n1 63\n4 63\n0 9",
"6 3\n1 3\n2 16\n4 138",
"3 2\n1 90\n1 0\n1 178",
"2 3\n2 32\n2 46\n1 12",
"2 3\n2 39\n2 46\n1 12",
"2 2\n2 55\n2 77\n2 195",
"2 3\n2 26\n2 77\n2 195",
"2 3\n2 26\n2 77\n1 195",
"2 3\n2 26\n2 32\n1 195",
"2 3\n2 26\n2 59\n1 195",
"2 3\n2 26\n2 59\n1 359",
"2 1\n2 87\n2 77\n2 99",
"2 2\n2 55\n2 77\n0 99",
"2 3\n2 16\n2 77\n2 195",
"2 3\n2 26\n2 77\n1 131",
"2 3\n2 26\n2 32\n1 239",
"2 3\n2 37\n2 59\n1 195",
"2 3\n2 26\n2 59\n1 72",
"2 3\n1 32\n2 63\n1 10",
"4 1\n2 87\n2 77\n2 99",
"2 2\n2 55\n2 29\n1 195",
"2 1\n2 96\n2 77\n2 195",
"2 3\n1 16\n2 77\n2 195",
"3 3\n2 26\n2 77\n1 131",
"2 3\n2 26\n2 58\n1 239",
"2 3\n2 37\n2 59\n2 195",
"2 3\n2 16\n2 59\n1 72",
"2 3\n1 32\n2 63\n1 16",
"4 1\n2 19\n2 77\n2 99",
"2 2\n2 18\n2 29\n1 195",
"2 1\n2 96\n2 77\n4 195",
"2 3\n2 15\n2 59\n1 72",
"2 2\n2 96\n2 77\n4 195",
"2 1\n1 16\n2 77\n2 267",
"2 3\n2 15\n2 48\n1 72",
"2 2\n2 26\n2 77\n4 195",
"2 1\n1 16\n2 77\n3 267",
"2 3\n2 15\n2 64\n1 72",
"2 2\n2 32\n2 77\n4 195",
"2 3\n1 15\n2 58\n1 72",
"2 3\n1 15\n2 58\n2 72",
"2 3\n2 55\n2 77\n1 99",
"2 3\n1 55\n2 42\n2 99",
"2 3\n2 32\n2 55\n1 12",
"2 1\n2 55\n2 34\n2 99",
"2 3\n2 32\n2 67\n1 12",
"2 3\n2 75\n2 46\n1 12",
"2 2\n2 55\n2 77\n0 195",
"2 3\n2 25\n2 32\n1 195",
"2 3\n2 26\n2 59\n1 642",
"2 3\n1 32\n2 63\n1 4",
"2 1\n2 87\n1 77\n2 99",
"2 3\n2 39\n2 0\n1 12",
"2 2\n2 55\n2 29\n0 195",
"2 3\n2 96\n2 117\n2 195",
"2 3\n2 22\n2 77\n2 195",
"2 3\n2 26\n2 59\n1 139",
"2 3\n1 32\n2 63\n1 9",
"4 1\n2 43\n2 77\n2 99",
"3 1\n2 96\n2 77\n2 195",
"3 3\n2 26\n2 84\n1 131",
"2 2\n2 26\n2 58\n1 239",
"2 3\n2 37\n2 104\n2 195",
"2 3\n2 28\n2 59\n1 72",
"2 3\n1 32\n2 83\n1 16",
"2 1\n2 96\n2 85\n4 195",
"2 2\n2 96\n2 77\n4 110"
],
"output": [
"000001000002\n000002000001\n000001000001",
"000002000001\n000002000002\n000002000003",
"000001000001\n000002000001\n000002000002\n",
"000002000001\n000002000002\n000001000001\n",
"000002000001\n",
"000002000001\n000002000002\n",
"000002000001\n000002000002\n000002000003\n",
"000001000002\n000002000001\n000001000001\n",
"000002000002\n000002000001\n000001000001\n",
"000002000002\n000002000001\n",
"000002000002\n000002000001\n000002000003\n",
"000001000001\n",
"000001000001\n000002000002\n000002000001\n",
"000001000001\n000002000001\n000001000002\n",
"000002000001\n000001000001\n",
"000001000001\n000002000001\n",
"000002000001\n000001000001\n000001000002\n",
"000002000002\n000002000003\n000002000001\n",
"000002000001\n000003000001\n000001000001\n",
"000002000001\n000002000003\n000002000002\n",
"000003000001\n000003000002\n000001000001\n",
"000001000001\n000001000002\n",
"000003000001\n000001000001\n000001000002\n",
"000004000001\n000001000001\n000001000002\n",
"000003000001\n000002000001\n000001000001\n",
"000001000001\n000001000002\n000001000003\n",
"000002000001\n000004000001\n000001000001\n",
"000001000001\n000003000001\n000001000002\n",
"000002000003\n000002000002\n000002000001\n",
"000002000001\n000001000001\n000002000002\n",
"000001000001\n000001000002\n000002000001\n",
"000002000001\n000002000002\n000004000001\n",
"000003000001\n",
"000002000001\n000003000001\n",
"000001000002\n000003000001\n000001000001\n",
"000001000001\n000004000001\n",
"000001000001\n000002000001\n000004000001\n",
"000001000002\n000001000001\n",
"000002000001\n000002000002\n000001000001\n",
"000002000001\n000002000002\n000001000001\n",
"000002000001\n000002000002\n",
"000002000001\n000002000002\n000002000003\n",
"000002000001\n000002000002\n000001000001\n",
"000002000001\n000002000002\n000001000001\n",
"000002000001\n000002000002\n000001000001\n",
"000002000001\n000002000002\n000001000001\n",
"000002000001\n",
"000002000001\n000002000002\n",
"000002000001\n000002000002\n000002000003\n",
"000002000001\n000002000002\n000001000001\n",
"000002000001\n000002000002\n000001000001\n",
"000002000001\n000002000002\n000001000001\n",
"000002000001\n000002000002\n000001000001\n",
"000001000002\n000002000001\n000001000001\n",
"000002000001\n",
"000002000002\n000002000001\n",
"000002000001\n",
"000001000001\n000002000001\n000002000002\n",
"000002000001\n000002000002\n000001000001\n",
"000002000001\n000002000002\n000001000001\n",
"000002000001\n000002000002\n000002000003\n",
"000002000001\n000002000002\n000001000001\n",
"000001000002\n000002000001\n000001000001\n",
"000002000001\n",
"000002000001\n000002000002\n",
"000002000001\n",
"000002000001\n000002000002\n000001000001\n",
"000002000002\n000002000001\n",
"000001000001\n",
"000002000001\n000002000002\n000001000001\n",
"000002000001\n000002000002\n",
"000001000001\n",
"000002000001\n000002000002\n000001000001\n",
"000002000001\n000002000002\n",
"000001000001\n000002000001\n000001000002\n",
"000001000001\n000002000001\n000002000002\n",
"000002000001\n000002000002\n000001000001\n",
"000001000001\n000002000001\n000002000002\n",
"000002000001\n000002000002\n000001000001\n",
"000002000001\n",
"000002000001\n000002000002\n000001000001\n",
"000002000002\n000002000001\n000001000001\n",
"000002000001\n000002000002\n",
"000002000001\n000002000002\n000001000001\n",
"000002000001\n000002000002\n000001000001\n",
"000001000002\n000002000001\n000001000001\n",
"000002000001\n",
"000002000002\n000002000001\n000001000001\n",
"000002000002\n000002000001\n",
"000002000001\n000002000002\n000002000003\n",
"000002000001\n000002000002\n000002000003\n",
"000002000001\n000002000002\n000001000001\n",
"000001000002\n000002000001\n000001000001\n",
"000002000001\n",
"000002000001\n",
"000002000001\n000002000002\n000001000001\n",
"000002000001\n000002000002\n",
"000002000001\n000002000002\n000002000003\n",
"000002000001\n000002000002\n000001000001\n",
"000001000002\n000002000001\n000001000001\n",
"000002000001\n",
"000002000002\n000002000001\n"
]
}
| 5ATCODER
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
In Republic of Atcoder, there are N prefectures, and a total of M cities that belong to those prefectures.
City i is established in year Y_i and belongs to Prefecture P_i.
You can assume that there are no multiple cities that are established in the same year.
It is decided to allocate a 12-digit ID number to each city.
If City i is the x-th established city among the cities that belong to Prefecture i, the first six digits of the ID number of City i is P_i, and the last six digits of the ID number is x.
Here, if P_i or x (or both) has less than six digits, zeros are added to the left until it has six digits.
Find the ID numbers for all the cities.
Note that there can be a prefecture with no cities.
Constraints
* 1 \leq N \leq 10^5
* 1 \leq M \leq 10^5
* 1 \leq P_i \leq N
* 1 \leq Y_i \leq 10^9
* Y_i are all different.
* All values in input are integers.
Input
Input is given from Standard Input in the following format:
N M
P_1 Y_1
:
P_M Y_M
Output
Print the ID numbers for all the cities, in ascending order of indices (City 1, City 2, ...).
Examples
Input
2 3
1 32
2 63
1 12
Output
000001000002
000002000001
000001000001
Input
2 3
2 55
2 77
2 99
Output
000002000001
000002000002
000002000003
### Input:
2 3
1 32
2 63
1 12
### Output:
000001000002
000002000001
000001000001
### Input:
2 3
2 55
2 77
2 99
### Output:
000002000001
000002000002
000002000003
### Code:
from collections import defaultdict
(n, m), *q = [[*map(int, i.split())] for i in open(0)]
d = defaultdict(list)
for k, v in q:
d[k].append(v)
c = defaultdict(dict)
for k, v in d.items():
for i, j in enumerate(sorted(v)):
c[k][j] = i + 1
for p, y in q:
print("{:0>6}{:0>6}".format(p, c[p][y]))
|
p03369 AtCoder Beginner Contest 095 - Something on It_10699
|
In "Takahashi-ya", a ramen restaurant, a bowl of ramen costs 700 yen (the currency of Japan), plus 100 yen for each kind of topping (boiled egg, sliced pork, green onions).
A customer ordered a bowl of ramen and told which toppings to put on his ramen to a clerk. The clerk took a memo of the order as a string S. S is three characters long, and if the first character in S is `o`, it means the ramen should be topped with boiled egg; if that character is `x`, it means the ramen should not be topped with boiled egg. Similarly, the second and third characters in S mean the presence or absence of sliced pork and green onions on top of the ramen.
Write a program that, when S is given, prints the price of the corresponding bowl of ramen.
Constraints
* S is a string of length 3.
* Each character in S is `o` or `x`.
Input
Input is given from Standard Input in the following format:
S
Output
Print the price of the bowl of ramen corresponding to S.
Examples
Input
oxo
Output
900
Input
ooo
Output
1000
Input
xxx
Output
700
|
s = input().count('o')
print(700 + s*100)
|
{
"input": [
"oxo",
"xxx",
"ooo",
"pxo",
"yxx",
"opo",
"oxp",
"xyx",
"opn",
"xpo",
"xzx",
"npo",
"opx",
"yzx",
"npn",
"xpn",
"xzy",
"mpn",
"npx",
"wzy",
"mpm",
"nxp",
"zwy",
"npm",
"mxp",
"ywz",
"nmp",
"nxo",
"yzw",
"nnp",
"xno",
"wzz",
"onp",
"xoo",
"zzw",
"pno",
"oox",
"vzy",
"mpo",
"onx",
"yzv",
"mqo",
"oxn",
"zzv",
"qmo",
"own",
"xzv",
"qno",
"nwo",
"xvz",
"onq",
"owo",
"xvy",
"ooq",
"pxn",
"yvx",
"qoo",
"pxm",
"zvx",
"oqo",
"myp",
"zwx",
"oro",
"mzp",
"xwz",
"ppo",
"mzo",
"xw{",
"opp",
"ozm",
"ww{",
"pop",
"omz",
"wv{",
"pnp",
"zmo",
"xv{",
"qop",
"{mo",
"xw|",
"qpo",
"{lo",
"wx|",
"opq",
"ol{",
"xx|",
"oor",
"ok{",
"xy|",
"nor",
"{ko",
"|yx",
"oos",
"{kp",
"|yy",
"soo",
"pk{",
"|yw",
"spo",
"|kp",
"x|w",
"sqo",
"pk|"
],
"output": [
"900",
"700",
"1000",
"800\n",
"700\n",
"900\n",
"800\n",
"700\n",
"800\n",
"800\n",
"700\n",
"800\n",
"800\n",
"700\n",
"700\n",
"700\n",
"700\n",
"700\n",
"700\n",
"700\n",
"700\n",
"700\n",
"700\n",
"700\n",
"700\n",
"700\n",
"700\n",
"800\n",
"700\n",
"700\n",
"800\n",
"700\n",
"800\n",
"900\n",
"700\n",
"800\n",
"900\n",
"700\n",
"800\n",
"800\n",
"700\n",
"800\n",
"800\n",
"700\n",
"800\n",
"800\n",
"700\n",
"800\n",
"800\n",
"700\n",
"800\n",
"900\n",
"700\n",
"900\n",
"700\n",
"700\n",
"900\n",
"700\n",
"700\n",
"900\n",
"700\n",
"700\n",
"900\n",
"700\n",
"700\n",
"800\n",
"800\n",
"700\n",
"800\n",
"800\n",
"700\n",
"800\n",
"800\n",
"700\n",
"700\n",
"800\n",
"700\n",
"800\n",
"800\n",
"700\n",
"800\n",
"800\n",
"700\n",
"800\n",
"800\n",
"700\n",
"900\n",
"800\n",
"700\n",
"800\n",
"800\n",
"700\n",
"900\n",
"700\n",
"700\n",
"900\n",
"700\n",
"700\n",
"800\n",
"700\n",
"700\n",
"800\n",
"700\n"
]
}
| 5ATCODER
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
In "Takahashi-ya", a ramen restaurant, a bowl of ramen costs 700 yen (the currency of Japan), plus 100 yen for each kind of topping (boiled egg, sliced pork, green onions).
A customer ordered a bowl of ramen and told which toppings to put on his ramen to a clerk. The clerk took a memo of the order as a string S. S is three characters long, and if the first character in S is `o`, it means the ramen should be topped with boiled egg; if that character is `x`, it means the ramen should not be topped with boiled egg. Similarly, the second and third characters in S mean the presence or absence of sliced pork and green onions on top of the ramen.
Write a program that, when S is given, prints the price of the corresponding bowl of ramen.
Constraints
* S is a string of length 3.
* Each character in S is `o` or `x`.
Input
Input is given from Standard Input in the following format:
S
Output
Print the price of the bowl of ramen corresponding to S.
Examples
Input
oxo
Output
900
Input
ooo
Output
1000
Input
xxx
Output
700
### Input:
oxo
### Output:
900
### Input:
xxx
### Output:
700
### Code:
s = input().count('o')
print(700 + s*100)
|
p03845 AtCoder Beginner Contest 050 - Contest with Drinks Easy_10706
|
Joisino is about to compete in the final round of a certain programming competition. In this contest, there are N problems, numbered 1 through N. Joisino knows that it takes her T_i seconds to solve problem i(1≦i≦N).
Also, there are M kinds of drinks offered to the contestants, numbered 1 through M. If Joisino takes drink i(1≦i≦M), her brain will be stimulated and the time it takes for her to solve problem P_i will become X_i seconds. It does not affect the time to solve the other problems.
A contestant is allowed to take exactly one of the drinks before the start of the contest. For each drink, Joisino wants to know how many seconds it takes her to solve all the problems if she takes that drink. Here, assume that the time it takes her to solve all the problems is equal to the sum of the time it takes for her to solve individual problems. Your task is to write a program to calculate it instead of her.
Constraints
* All input values are integers.
* 1≦N≦100
* 1≦T_i≦10^5
* 1≦M≦100
* 1≦P_i≦N
* 1≦X_i≦10^5
Input
The input is given from Standard Input in the following format:
N
T_1 T_2 ... T_N
M
P_1 X_1
P_2 X_2
:
P_M X_M
Output
For each drink, calculate how many seconds it takes Joisino to solve all the problems if she takes that drink, and print the results, one per line.
Examples
Input
3
2 1 4
2
1 1
2 3
Output
6
9
Input
5
7 2 3 8 5
3
4 2
1 7
4 13
Output
19
25
30
|
N = int(input())
T = list(map(int,input().split()))
M = int(input())
sumT = sum(T)
for _ in range(M):
p,x = map(int,input().split())
print(sumT+x-T[p-1])
|
{
"input": [
"3\n2 1 4\n2\n1 1\n2 3",
"5\n7 2 3 8 5\n3\n4 2\n1 7\n4 13",
"3\n2 1 4\n2\n1 1\n0 3",
"5\n7 2 3 10 5\n3\n4 2\n1 7\n4 13",
"3\n2 1 4\n2\n1 1\n0 6",
"5\n7 4 3 10 5\n3\n4 2\n1 7\n4 13",
"3\n2 1 4\n2\n1 0\n2 3",
"3\n2 1 4\n2\n1 0\n0 3",
"5\n7 2 3 10 5\n3\n4 2\n1 7\n4 20",
"3\n1 1 4\n2\n1 1\n0 6",
"5\n7 4 3 10 5\n3\n4 2\n1 7\n3 13",
"3\n2 0 4\n2\n1 0\n0 3",
"5\n7 2 3 10 0\n3\n4 2\n1 7\n4 20",
"3\n1 1 0\n2\n1 1\n0 6",
"5\n7 4 1 10 5\n3\n4 2\n1 7\n3 13",
"5\n7 4 3 10 0\n3\n4 2\n1 7\n4 20",
"3\n1 1 0\n2\n1 1\n0 8",
"5\n7 4 1 10 5\n3\n4 2\n1 7\n3 7",
"5\n7 4 3 10 0\n3\n4 2\n1 1\n4 20",
"3\n0 1 0\n2\n1 1\n0 8",
"5\n7 5 1 10 5\n3\n4 2\n1 7\n3 7",
"3\n0 1 0\n1\n1 1\n0 8",
"5\n7 5 1 10 5\n3\n4 3\n1 7\n3 7",
"3\n0 1 -1\n1\n1 1\n0 8",
"5\n7 5 1 10 5\n3\n4 3\n1 11\n3 7",
"5\n7 5 1 10 6\n3\n4 3\n1 11\n3 7",
"3\n1 1 -1\n2\n1 1\n0 2",
"5\n7 8 1 10 6\n3\n4 3\n1 11\n3 7",
"3\n1 1 -1\n2\n1 0\n0 2",
"5\n7 8 0 10 6\n3\n4 3\n1 11\n3 7",
"3\n1 1 -1\n2\n1 -1\n0 2",
"5\n7 0 0 10 6\n3\n4 3\n1 11\n3 7",
"3\n1 1 -1\n2\n1 -1\n0 3",
"5\n7 0 0 10 6\n3\n4 3\n1 19\n3 7",
"5\n7 0 0 7 6\n3\n4 3\n1 19\n3 7",
"5\n7 0 0 7 6\n3\n4 3\n1 19\n3 8",
"5\n7 0 0 6 6\n3\n4 3\n1 19\n3 8",
"3\n2 1 4\n2\n1 1\n2 5",
"5\n7 2 4 8 5\n3\n4 2\n1 7\n4 13",
"3\n0 1 4\n2\n1 1\n0 3",
"5\n7 2 0 10 5\n3\n4 2\n1 7\n4 13",
"5\n7 4 3 10 5\n3\n4 4\n1 7\n4 13",
"3\n0 2 4\n2\n1 0\n2 3",
"5\n7 2 3 10 5\n3\n4 2\n2 7\n4 20",
"3\n1 1 4\n2\n1 2\n0 6",
"5\n7 4 3 10 5\n3\n1 2\n1 7\n3 13",
"3\n2 0 4\n2\n0 0\n0 3",
"5\n7 2 1 10 0\n3\n4 2\n1 7\n4 20",
"3\n1 1 0\n2\n1 2\n0 6",
"5\n7 4 1 10 5\n3\n4 2\n1 7\n3 14",
"5\n7 4 3 10 1\n3\n4 2\n1 7\n4 20",
"3\n1 1 1\n2\n1 1\n0 8",
"5\n11 4 1 10 5\n3\n4 2\n1 7\n3 7",
"5\n7 4 3 10 0\n3\n4 2\n1 2\n4 20",
"3\n0 1 0\n2\n2 1\n0 8",
"5\n7 5 1 10 5\n3\n3 2\n1 7\n3 7",
"5\n7 3 1 10 5\n3\n4 2\n1 7\n3 7",
"5\n7 5 1 10 5\n3\n4 3\n1 11\n3 12",
"5\n7 5 1 10 6\n3\n4 3\n2 11\n3 7",
"3\n1 0 -1\n2\n1 1\n0 2",
"5\n1 4 1 10 6\n3\n4 3\n1 11\n3 7",
"3\n1 1 -1\n2\n1 1\n0 3",
"5\n7 8 1 10 6\n3\n4 3\n0 11\n3 7",
"5\n7 8 0 10 7\n3\n4 3\n1 11\n3 7",
"3\n1 1 -1\n2\n1 -1\n1 2",
"5\n7 0 0 10 6\n3\n3 3\n1 11\n3 7",
"3\n1 1 -1\n2\n1 -1\n0 5",
"5\n7 0 0 6 6\n3\n4 3\n1 19\n3 7",
"5\n2 0 0 7 6\n3\n4 3\n1 19\n3 7",
"5\n7 0 0 7 6\n3\n4 3\n1 19\n3 3",
"5\n7 0 0 6 6\n3\n4 0\n1 19\n3 8",
"3\n3 1 4\n2\n1 1\n2 5",
"5\n7 2 4 8 5\n3\n4 0\n1 7\n4 13",
"3\n0 1 4\n2\n1 1\n0 2",
"5\n7 2 0 10 5\n3\n4 2\n1 7\n4 7",
"5\n7 4 3 10 5\n3\n1 4\n1 7\n4 13",
"3\n0 2 4\n2\n0 0\n2 3",
"5\n7 0 3 10 5\n3\n4 2\n2 7\n4 20",
"5\n7 4 3 16 5\n3\n1 2\n1 7\n3 13",
"5\n7 2 1 10 0\n3\n3 2\n1 7\n4 20",
"3\n1 2 0\n2\n1 2\n0 6",
"5\n7 4 1 10 4\n3\n4 2\n1 7\n3 14",
"5\n7 4 3 10 1\n3\n4 2\n1 7\n2 20",
"3\n1 1 2\n2\n1 1\n0 8",
"5\n11 4 0 10 5\n3\n4 2\n1 7\n3 7",
"5\n7 4 3 10 0\n3\n4 2\n1 2\n4 10",
"5\n7 5 1 19 5\n3\n3 2\n1 7\n3 7",
"5\n7 3 1 10 5\n3\n4 2\n1 0\n3 7",
"5\n7 5 1 10 5\n3\n4 3\n2 11\n3 12",
"3\n2 1 -1\n1\n1 0\n0 8",
"5\n7 5 1 10 6\n3\n3 3\n2 11\n3 7",
"3\n1 0 -1\n2\n2 1\n0 2",
"5\n1 4 1 10 6\n3\n4 0\n1 11\n3 7",
"5\n7 8 1 10 11\n3\n4 3\n0 11\n3 7",
"5\n7 1 0 10 7\n3\n4 3\n1 11\n3 7",
"3\n1 1 -1\n1\n1 -1\n0 2",
"5\n14 0 0 6 6\n3\n4 3\n1 19\n3 7",
"5\n7 0 0 7 6\n3\n4 3\n1 19\n4 3",
"5\n7 0 0 6 6\n3\n4 0\n1 12\n3 8",
"3\n3 0 4\n2\n1 1\n2 5",
"5\n7 2 4 6 5\n3\n4 0\n1 7\n4 13",
"5\n7 2 0 0 5\n3\n4 2\n1 7\n4 7"
],
"output": [
"6\n9",
"19\n25\n30",
"6\n6\n",
"19\n27\n30\n",
"6\n9\n",
"21\n29\n32\n",
"5\n9\n",
"5\n6\n",
"19\n27\n37\n",
"6\n8\n",
"21\n29\n39\n",
"4\n5\n",
"14\n22\n32\n",
"2\n8\n",
"19\n27\n39\n",
"16\n24\n34\n",
"2\n10\n",
"19\n27\n33\n",
"16\n18\n34\n",
"2\n9\n",
"20\n28\n34\n",
"2\n",
"21\n28\n34\n",
"1\n",
"21\n32\n34\n",
"22\n33\n35\n",
"1\n4\n",
"25\n36\n38\n",
"0\n4\n",
"24\n35\n38\n",
"-1\n4\n",
"16\n27\n30\n",
"-1\n5\n",
"16\n35\n30\n",
"16\n32\n27\n",
"16\n32\n28\n",
"16\n31\n27\n",
"6\n11\n",
"20\n26\n31\n",
"6\n4\n",
"16\n24\n27\n",
"23\n29\n32\n",
"6\n7\n",
"19\n32\n37\n",
"7\n8\n",
"24\n29\n39\n",
"2\n5\n",
"12\n20\n30\n",
"3\n8\n",
"19\n27\n40\n",
"17\n25\n35\n",
"3\n10\n",
"23\n27\n37\n",
"16\n19\n34\n",
"1\n9\n",
"29\n28\n34\n",
"18\n26\n32\n",
"21\n32\n39\n",
"22\n35\n35\n",
"0\n3\n",
"15\n32\n28\n",
"1\n5\n",
"25\n37\n38\n",
"25\n36\n39\n",
"-1\n2\n",
"26\n27\n30\n",
"-1\n7\n",
"16\n31\n26\n",
"11\n32\n22\n",
"16\n32\n23\n",
"13\n31\n27\n",
"6\n12\n",
"18\n26\n31\n",
"6\n3\n",
"16\n24\n21\n",
"26\n29\n32\n",
"2\n7\n",
"17\n32\n35\n",
"30\n35\n45\n",
"21\n20\n30\n",
"4\n9\n",
"18\n26\n39\n",
"17\n25\n41\n",
"4\n10\n",
"22\n26\n37\n",
"16\n19\n24\n",
"38\n37\n43\n",
"18\n19\n32\n",
"21\n34\n39\n",
"0\n",
"31\n35\n35\n",
"1\n3\n",
"12\n32\n28\n",
"30\n37\n43\n",
"18\n29\n32\n",
"-1\n",
"23\n31\n33\n",
"16\n32\n16\n",
"13\n24\n27\n",
"5\n12\n",
"18\n24\n31\n",
"16\n14\n21\n"
]
}
| 5ATCODER
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Joisino is about to compete in the final round of a certain programming competition. In this contest, there are N problems, numbered 1 through N. Joisino knows that it takes her T_i seconds to solve problem i(1≦i≦N).
Also, there are M kinds of drinks offered to the contestants, numbered 1 through M. If Joisino takes drink i(1≦i≦M), her brain will be stimulated and the time it takes for her to solve problem P_i will become X_i seconds. It does not affect the time to solve the other problems.
A contestant is allowed to take exactly one of the drinks before the start of the contest. For each drink, Joisino wants to know how many seconds it takes her to solve all the problems if she takes that drink. Here, assume that the time it takes her to solve all the problems is equal to the sum of the time it takes for her to solve individual problems. Your task is to write a program to calculate it instead of her.
Constraints
* All input values are integers.
* 1≦N≦100
* 1≦T_i≦10^5
* 1≦M≦100
* 1≦P_i≦N
* 1≦X_i≦10^5
Input
The input is given from Standard Input in the following format:
N
T_1 T_2 ... T_N
M
P_1 X_1
P_2 X_2
:
P_M X_M
Output
For each drink, calculate how many seconds it takes Joisino to solve all the problems if she takes that drink, and print the results, one per line.
Examples
Input
3
2 1 4
2
1 1
2 3
Output
6
9
Input
5
7 2 3 8 5
3
4 2
1 7
4 13
Output
19
25
30
### Input:
3
2 1 4
2
1 1
2 3
### Output:
6
9
### Input:
5
7 2 3 8 5
3
4 2
1 7
4 13
### Output:
19
25
30
### Code:
N = int(input())
T = list(map(int,input().split()))
M = int(input())
sumT = sum(T)
for _ in range(M):
p,x = map(int,input().split())
print(sumT+x-T[p-1])
|
p04012 AtCoder Beginner Contest 044 - Beautiful Strings_10710
|
Let w be a string consisting of lowercase letters. We will call w beautiful if the following condition is satisfied:
* Each lowercase letter of the English alphabet occurs even number of times in w.
You are given the string w. Determine if w is beautiful.
Constraints
* 1 \leq |w| \leq 100
* w consists of lowercase letters (`a`-`z`).
Input
The input is given from Standard Input in the following format:
w
Output
Print `Yes` if w is beautiful. Print `No` otherwise.
Examples
Input
abaccaba
Output
Yes
Input
hthth
Output
No
|
s=input()
for k in s:
if s.count(k)%2!=0:
print('No')
break
else:
print('Yes')
|
{
"input": [
"abaccaba",
"hthth",
"ab`ccaba",
"ab`cc`ba",
"hthtg",
"hghtt",
"`b`cc`ba",
"hgtth",
"ab`cc`b`",
"hgtuh",
"`b`cc`ca",
"hgsth",
"`b_cc`ca",
"hfsth",
"`b_dc`ca",
"hfsti",
"`b_dc`da",
"hgsti",
"ad`cd_b`",
"hgssi",
"ad`cd_a`",
"issgh",
"`a_dc`da",
"igssh",
"ad`cc_a`",
"ihssh",
"a``cc_ad",
"ihsrh",
"a`_cc_ad",
"ihsri",
"a__cc`ad",
"irshi",
"a__cd`ad",
"rishi",
"da`dc__a",
"rjshi",
"da`dc_`a",
"rjshj",
"da_dc_`a",
"rjsij",
"a`_cd_ad",
"jisjr",
"da^dc_`a",
"ijsjr",
"a`_cd^ad",
"ijskr",
"`a_cd^ad",
"ijsrk",
"`ac_d^ad",
"ijsrj",
"da^d_ca`",
"ijrrj",
"`^c_daad",
"jrrji",
"`^c`daad",
"jrsji",
"daad`c^`",
"jrsjj",
"daac`c^`",
"jjsrj",
"d^ac`ca`",
"krsjj",
"d^bc`ca`",
"krtjj",
"d^bc_ca`",
"krtij",
"`ac_cb^d",
"kjtjr",
"c^bd_ca`",
"tjkjr",
"`ac_db^c",
"tikjr",
"`ac_db_c",
"rjkit",
"c_bd_ca`",
"rjkti",
"`accdb__",
"rkkti",
"__bdcca`",
"rkkui",
"__bdc`ac",
"iukkr",
"`_bdc`ac",
"krkui",
"ca`cdb_`",
"iukrk",
"c``cdb_a",
"itkrk",
"ca`cdb_a",
"htkrk",
"a_bdc`ac",
"hrktk",
"a_b`cdac",
"ktkrh",
"a_a`cdac",
"kthrk",
"cadc`a_a",
"kthqk",
"dadc`a_a",
"kqhtk",
"dadc`b_a",
"kphtk"
],
"output": [
"Yes",
"No",
"No\n",
"Yes\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n",
"No\n"
]
}
| 5ATCODER
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Let w be a string consisting of lowercase letters. We will call w beautiful if the following condition is satisfied:
* Each lowercase letter of the English alphabet occurs even number of times in w.
You are given the string w. Determine if w is beautiful.
Constraints
* 1 \leq |w| \leq 100
* w consists of lowercase letters (`a`-`z`).
Input
The input is given from Standard Input in the following format:
w
Output
Print `Yes` if w is beautiful. Print `No` otherwise.
Examples
Input
abaccaba
Output
Yes
Input
hthth
Output
No
### Input:
abaccaba
### Output:
Yes
### Input:
hthth
### Output:
No
### Code:
s=input()
for k in s:
if s.count(k)%2!=0:
print('No')
break
else:
print('Yes')
|
p00098 Maximum Sum Sequence II_10714
|
Matrix of given integers
a1,1 a1,2 ... a1, n
a2,1 a2,2 ... a2, n
::
an, 1 an, 2 ... an, n
Then, create a program that outputs the maximum value of the sum of one or more consecutive terms (submatrix) in the vertical and horizontal directions and ends.
Input
The input data is given in the following format.
n
a1,1 a1,2 ... a1, n
a2,1 a2,2 ... a2, n
::
an, 1 an, 2 ... an, n
n is 1 or more and 100 or less, and ai, j is -10000 or more and 10000 or less.
Output
Print the maximum value on one line.
Examples
Input
3
1 -2 3
-4 5 6
7 8 -9
Output
16
Input
4
1 3 -9 2
2 7 -1 5
-8 3 2 -1
5 0 -3 1
Output
15
|
n = int(input())
s = [[0 for i in range(n + 1)] for j in range(n + 1)]
for r in range(n):
inp = list(map(int, input().split()))
for c in range(n):
s[r + 1][c + 1] = inp[c] + s[r][c + 1]
ans = -10001
for r_end in range(1, n + 1):
for r_start in range(r_end):
dp = [-10001]
for c in range(1, n + 1):
s_tmp = s[r_end][c] - s[r_start][c]
dp.append(max(dp[c - 1] + s_tmp, s_tmp))
ans = max(ans, max(dp))
print(ans)
|
{
"input": [
"3\n1 -2 3\n-4 5 6\n7 8 -9",
"4\n1 3 -9 2\n2 7 -1 5\n-8 3 2 -1\n5 0 -3 1",
"3\n1 -2 3\n-1 5 6\n7 8 -9",
"4\n1 3 -9 2\n2 7 -1 5\n-8 3 2 -1\n5 -1 -3 1",
"3\n1 -2 3\n-1 5 6\n6 8 -15",
"4\n1 3 -9 0\n2 7 -1 5\n-8 3 2 -2\n3 -1 -3 1",
"3\n1 -2 5\n-1 3 1\n6 8 -25",
"4\n1 3 -9 0\n2 7 -1 5\n-8 3 0 -2\n3 0 -5 1",
"3\n2 -4 5\n-1 3 1\n4 11 -43",
"3\n3 -4 5\n-1 3 1\n8 11 -69",
"3\n3 -4 5\n-2 3 1\n8 11 -42",
"3\n3 -4 5\n-2 3 1\n16 11 -42",
"3\n5 -4 5\n-2 3 1\n16 11 -68",
"3\n7 -4 5\n-2 3 1\n16 11 -49",
"3\n7 -4 5\n0 3 1\n16 11 -49",
"3\n5 -6 9\n0 1 0\n32 1 -57",
"3\n4 -6 9\n0 1 0\n32 0 -57",
"3\n4 -6 9\n0 1 0\n58 0 -57",
"3\n1 -6 9\n0 0 0\n58 0 -57",
"3\n1 -7 9\n0 0 0\n83 0 -57",
"3\n0 -7 13\n0 0 0\n83 0 -57",
"3\n-2 -7 13\n0 0 -1\n24 0 -84",
"3\n-5 -18 3\n1 0 -2\n29 0 -36",
"3\n-5 -18 0\n1 -1 -2\n0 1 -36",
"3\n-4 -18 0\n1 -1 -2\n0 2 -36",
"3\n-1 -22 1\n-2 -1 -1\n-1 3 -43",
"3\n-1 1 1\n-1 0 -1\n-1 3 -43",
"3\n1 -2 3\n-1 5 6\n7 8 -2",
"3\n3 -4 5\n0 3 1\n8 11 -59",
"3\n3 -4 5\n-2 3 1\n14 11 -42",
"3\n10 -4 5\n-2 3 1\n16 11 -68",
"3\n8 -4 9\n0 1 0\n16 11 -57",
"3\n5 -6 9\n1 1 0\n32 0 -57",
"3\n4 -6 9\n-1 0 0\n58 0 -57",
"3\n2 -6 9\n0 0 0\n58 0 -57",
"3\n-2 -7 3\n0 0 -1\n45 0 -48",
"3\n-2 -18 3\n0 0 0\n9 0 -24",
"3\n-4 -18 3\n0 0 0\n51 0 -36",
"3\n-5 -18 3\n1 0 -2\n46 0 -36",
"3\n1 -2 5\n-1 2 1\n6 2 -3",
"3\n9 -4 5\n-2 3 1\n16 19 -49",
"3\n-1 -7 13\n0 0 0\n90 0 -57",
"4\n1 3 -9 2\n2 4 -1 5\n-8 3 2 -1\n5 -1 -6 1",
"3\n-1 -2 12\n0 0 0\n83 0 -3",
"3\n-2 -5 3\n0 -1 -1\n35 -1 -48",
"3\n-2 -18 3\n2 0 0\n24 1 -26",
"3\n-5 -7 3\n0 1 -2\n41 0 -36",
"3\n-1 1 1\n-2 1 -1\n0 3 -43",
"4\n1 3 -9 2\n2 4 -1 5\n-8 3 0 -1\n5 -1 -6 1",
"3\n2 -4 5\n-1 2 0\n1 4 -25",
"3\n5 -4 6\n-2 3 2\n32 16 -49",
"3\n12 -1 5\n0 1 1\n16 11 -10",
"3\n7 -1 0\n0 1 1\n16 21 -6",
"3\n-1 -7 21\n1 0 0\n90 0 -57",
"3\n-1 -2 12\n0 0 0\n164 0 -3",
"3\n-2 -7 3\n0 0 1\n45 0 0",
"3\n2 -4 5\n0 2 0\n1 4 -25",
"3\n1 -1 5\n0 2 1\n10 11 -59",
"3\n5 -7 6\n-2 3 2\n32 16 -49",
"3\n-1 -2 12\n1 0 0\n164 0 -3",
"3\n-1 -22 0\n0 -1 -1\n0 0 -112",
"3\n15 -1 5\n0 1 1\n16 11 -5",
"3\n0 -10 12\n-1 1 0\n39 1 -7",
"3\n2 -11 0\n0 0 0\n104 -2 -57",
"3\n-1 -2 12\n1 0 0\n116 0 -3",
"3\n-2 -11 3\n0 0 0\n8 0 -55",
"3\n-1 -2 12\n0 0 0\n116 0 -3",
"3\n0 -10 32\n-1 1 0\n39 1 -7",
"3\n1 -7 0\n0 1 1\n145 -1 -23",
"3\n1 -2 3\n-1 5 6\n7 8 -15",
"4\n1 3 -9 2\n2 7 -1 5\n-8 3 2 -1\n3 -1 -3 1",
"4\n1 3 -9 0\n2 7 -1 5\n-8 3 2 -1\n3 -1 -3 1",
"3\n1 -2 5\n-1 5 6\n6 8 -15",
"3\n1 -2 5\n-1 5 6\n6 8 -25",
"4\n1 3 -9 0\n2 7 -1 5\n-8 3 2 -2\n3 0 -3 1",
"3\n1 -2 5\n-1 5 1\n6 8 -25",
"4\n1 3 -9 0\n2 7 -1 5\n-8 3 2 -2\n3 0 -5 1",
"3\n1 -2 5\n-1 2 1\n6 8 -25",
"3\n1 -2 5\n-1 2 1\n6 11 -25",
"3\n1 -2 5\n-1 2 1\n4 11 -25",
"3\n1 -4 5\n-1 2 1\n4 11 -25",
"3\n2 -4 5\n-1 2 1\n4 11 -25",
"3\n2 -4 5\n-1 2 1\n4 11 -34",
"3\n2 -4 5\n-1 2 1\n4 11 -43",
"3\n2 -4 5\n-1 3 1\n4 11 -69",
"3\n3 -4 5\n-1 3 1\n4 11 -69",
"3\n3 -4 5\n-1 3 1\n8 11 -59",
"3\n3 -4 5\n-1 3 1\n8 11 -26",
"3\n3 -4 5\n-1 3 1\n8 11 -42",
"3\n3 -4 5\n-2 3 1\n16 11 -68",
"3\n5 -4 5\n-2 3 1\n16 11 -49",
"3\n7 -4 5\n0 1 1\n16 11 -49",
"3\n7 -4 5\n0 1 1\n16 11 -73",
"3\n7 -4 5\n0 1 1\n16 11 -57",
"3\n3 -4 5\n0 1 1\n16 11 -57",
"3\n5 -4 5\n0 1 1\n16 11 -57",
"3\n5 -4 5\n0 1 0\n16 11 -57",
"3\n5 -4 9\n0 1 0\n16 11 -57",
"3\n5 -4 9\n0 1 -1\n16 11 -57",
"3\n5 -4 9\n0 1 -2\n16 11 -57",
"3\n5 -6 9\n0 1 -2\n16 11 -57",
"3\n5 -6 9\n0 1 0\n16 11 -57"
],
"output": [
"16",
"15",
"19\n",
"15\n",
"18\n",
"14\n",
"16\n",
"13\n",
"17\n",
"21\n",
"20\n",
"28\n",
"29\n",
"31\n",
"33\n",
"37\n",
"36\n",
"62\n",
"59\n",
"84\n",
"83\n",
"24\n",
"30\n",
"1\n",
"2\n",
"3\n",
"4\n",
"25\n",
"22\n",
"26\n",
"34\n",
"32\n",
"38\n",
"61\n",
"60\n",
"45\n",
"9\n",
"51\n",
"47\n",
"11\n",
"41\n",
"90\n",
"12\n",
"89\n",
"35\n",
"27\n",
"42\n",
"5\n",
"10\n",
"6\n",
"50\n",
"39\n",
"44\n",
"91\n",
"170\n",
"46\n",
"7\n",
"23\n",
"49\n",
"171\n",
"0\n",
"43\n",
"40\n",
"106\n",
"123\n",
"8\n",
"122\n",
"55\n",
"146\n",
"19\n",
"15\n",
"15\n",
"18\n",
"18\n",
"14\n",
"18\n",
"14\n",
"15\n",
"18\n",
"16\n",
"16\n",
"16\n",
"16\n",
"16\n",
"17\n",
"17\n",
"21\n",
"21\n",
"21\n",
"28\n",
"29\n",
"31\n",
"31\n",
"31\n",
"28\n",
"29\n",
"29\n",
"29\n",
"29\n",
"29\n",
"28\n",
"28\n"
]
}
| 6AIZU
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Matrix of given integers
a1,1 a1,2 ... a1, n
a2,1 a2,2 ... a2, n
::
an, 1 an, 2 ... an, n
Then, create a program that outputs the maximum value of the sum of one or more consecutive terms (submatrix) in the vertical and horizontal directions and ends.
Input
The input data is given in the following format.
n
a1,1 a1,2 ... a1, n
a2,1 a2,2 ... a2, n
::
an, 1 an, 2 ... an, n
n is 1 or more and 100 or less, and ai, j is -10000 or more and 10000 or less.
Output
Print the maximum value on one line.
Examples
Input
3
1 -2 3
-4 5 6
7 8 -9
Output
16
Input
4
1 3 -9 2
2 7 -1 5
-8 3 2 -1
5 0 -3 1
Output
15
### Input:
3
1 -2 3
-4 5 6
7 8 -9
### Output:
16
### Input:
4
1 3 -9 2
2 7 -1 5
-8 3 2 -1
5 0 -3 1
### Output:
15
### Code:
n = int(input())
s = [[0 for i in range(n + 1)] for j in range(n + 1)]
for r in range(n):
inp = list(map(int, input().split()))
for c in range(n):
s[r + 1][c + 1] = inp[c] + s[r][c + 1]
ans = -10001
for r_end in range(1, n + 1):
for r_start in range(r_end):
dp = [-10001]
for c in range(1, n + 1):
s_tmp = s[r_end][c] - s[r_start][c]
dp.append(max(dp[c - 1] + s_tmp, s_tmp))
ans = max(ans, max(dp))
print(ans)
|
p00230 Ninja Climbing_10718
|
Ninja Atsushi guards the town from the roof of the Ninja Building from early morning to late night every day. This Ninja Building is two adjacent buildings of the same floor, and Atsushi's daily routine is to jump between buildings and head to the rooftop for security.
Because these two buildings are cleaned frequently, there are ladders and slippery areas that can help you climb the building. Moreover, the position of ladders and slippery parts changes every day. Therefore, Atsushi has to think about how to get to the roof every day.
Atsushi jumps over the walls of two buildings of the same floor, aiming for the rooftop of the building. Jumps can be started on the first floor of either building. When jumping to the opposite building, you can jump to the same floor, one floor up, or two floors up.
There are three types of walls, and the movement after jumping to each wall is decided.
* 0. Ordinary wall: Do not move up and down. The next jump will be made from there.
* 1. Ladder: The ladder spans two or more floors and moves to the top of the current ladder. The next jump will be made from there.
* 2. Sliding wall: A normal wall or slides down to the top of the ladder. The next jump will be made from there.
Also, the walls run from the first floor to the top floor just below the roof, and the roof can only be reached from the top floor of the building. Also, the wall on the bottom floor of the building will not be a slippery wall.
Create a program that takes in the number of floors n of the two buildings and the type of wall of the two buildings, and outputs the minimum number of jumps to reach the top floor and reach the rooftop. You may reach the roof of either building. However, if Atsushi cannot reach the roof of either building, please output "NA".
<image>
Input
A sequence of multiple datasets is given as input. The end of the input is indicated by a single line of zeros. Each dataset is given in the following format:
n
a1 a2 ... an
b1 b2 ... bn
The first line gives the building floor n (3 ≤ n ≤ 100). The second line gives the wall information ai from the first floor to the nth floor of the first building, and the third line gives the wall information bi from the first floor to the nth floor of the second building. ai and bi represent the information of the wall on the i-th floor, 0 is the ordinary wall, 1 is the ladder (straddling the i-th floor and the i + 1-floor), and 2 is the sliding wall.
The number of datasets does not exceed 60.
Output
Outputs the number of jumps on one line for each input dataset.
Example
Input
8
0 0 0 2 2 2 0 0
1 1 1 1 0 0 0 0
4
1 1 2 2
0 0 2 2
0
Output
4
NA
|
def bfs(b):
mem=[[False for i in range(n)]for j in range(2)]
st=[0,0]
for i in range(2):
if b[i][0]!=1:continue
while st[i]<n-1 and b[i][st[i]+1]==1:
st[i]+=1
if st[i]==n-1:return 0
mem[0][st[0]]=True
mem[1][st[1]]=True
que=[[0,st[0],0],[1,st[1],0]]
while len(que)!=0:
d=que.pop(0)
des=(d[0]+1)%2
cst=d[2]+1
for i in range(3):
fl=d[1]+i
if fl>=n:break
state=b[des][fl]
if state!=2 and fl==n-1:
return cst
if state==0:
if mem[des][fl]==False:
que.append([des,fl,cst])
mem[des][fl]=True
elif state==1:
k=1
while True:
if fl+k>=n:return cst
if b[des][fl+k]!=1:
if mem[des][fl+k-1]==False:
que.append([des,fl+k-1,cst])
mem[des][fl+k-1]=True
break
else: k+=1
elif state==2:
k=1
while True:
if b[des][fl-k]!=2:
if mem[des][fl-k]==False:
que.append([des,fl-k,cst])
mem[des][fl-k]=True
break
else:k+=1
return -1
while True:
n=int(input())
if n==0:break
b=[[int(p)for p in input().split(" ")],[int(p)for p in input().split(" ")]]
count=bfs(b)
print(str(count)if count>=0 else "NA")
|
{
"input": [
"8\n0 0 0 2 2 2 0 0\n1 1 1 1 0 0 0 0\n4\n1 1 2 2\n0 0 2 2\n0",
"8\n0 0 0 2 2 2 0 0\n1 1 1 1 1 0 0 0\n4\n1 1 2 2\n0 0 2 2\n0",
"8\n0 0 0 2 2 2 0 0\n1 1 1 1 1 0 0 0\n2\n1 1 2 2\n0 0 2 2\n0",
"8\n0 0 0 2 2 2 0 0\n0 1 1 1 1 0 0 0\n2\n1 1 2 2\n0 0 2 2\n0",
"8\n0 0 0 2 2 2 0 1\n1 1 1 1 0 0 0 0\n4\n1 1 2 2\n0 0 2 2\n0",
"8\n0 0 0 2 2 2 0 0\n1 1 2 1 1 0 0 0\n2\n1 1 2 2\n0 0 2 2\n0",
"8\n0 0 0 2 2 1 0 0\n1 1 1 1 1 0 0 -1\n4\n1 1 2 3\n0 0 2 2\n0",
"8\n0 0 0 2 2 1 1 0\n1 0 1 1 1 0 0 -1\n4\n1 1 4 5\n-1 0 2 2\n0",
"8\n0 0 0 2 2 1 1 0\n1 0 1 1 1 0 0 -1\n4\n1 1 4 5\n-1 0 2 1\n0",
"8\n0 0 0 2 2 2 0 -1\n1 1 1 1 2 0 0 1\n2\n1 1 2 2\n0 0 2 2\n0",
"8\n0 0 0 2 2 2 0 1\n1 1 1 1 0 0 0 0\n4\n1 0 2 1\n0 0 2 2\n0",
"8\n0 0 0 2 2 1 1 0\n1 0 1 0 1 0 0 -1\n4\n1 1 4 5\n-1 0 2 1\n0",
"8\n0 0 0 2 2 1 0 0\n1 1 1 1 1 0 1 -1\n0\n0 1 4 3\n0 0 2 2\n0",
"8\n0 0 0 2 2 1 0 0\n1 2 1 1 1 0 1 -1\n0\n0 2 4 3\n0 0 2 2\n0",
"8\n0 0 0 2 2 2 0 0\n1 1 1 1 2 0 0 -1\n4\n1 1 2 2\n0 0 2 2\n0",
"8\n0 0 0 2 2 1 0 0\n1 1 1 1 1 0 0 -1\n4\n1 1 2 3\n0 0 2 4\n0",
"8\n0 0 0 2 2 2 0 0\n2 1 1 1 1 0 -1 0\n4\n1 1 2 2\n-1 0 2 2\n0",
"8\n0 0 -1 2 2 2 0 -1\n1 1 1 1 1 1 -1 0\n2\n1 1 2 2\n0 -1 4 2\n0",
"8\n0 0 0 2 4 1 0 0\n1 1 1 1 1 1 1 -1\n0\n0 2 4 3\n0 0 2 2\n0",
"8\n0 0 0 2 1 2 0 0\n1 2 1 1 2 -1 0 -1\n0\n0 3 4 3\n0 0 2 2\n0",
"8\n0 0 0 2 2 2 0 0\n1 2 1 1 2 -1 2 -1\n0\n0 3 0 3\n0 0 2 2\n0",
"8\n0 0 0 2 2 2 2 0\n1 2 1 1 0 -1 0 0\n4\n1 1 2 4\n0 0 2 2\n0",
"8\n0 0 0 2 2 2 0 -1\n1 1 1 1 1 0 0 0\n2\n1 1 2 2\n0 0 2 2\n0",
"8\n0 0 0 2 2 2 0 0\n1 1 1 1 1 0 0 -1\n4\n1 1 2 2\n0 0 2 2\n0",
"8\n0 0 0 2 2 2 0 0\n0 1 1 1 1 1 0 0\n2\n1 1 2 2\n0 0 2 2\n0",
"8\n0 0 0 2 2 2 0 -1\n1 2 1 1 1 0 0 0\n2\n1 1 2 2\n0 0 2 2\n0",
"8\n0 0 0 2 2 1 0 0\n1 1 1 1 1 0 0 -1\n4\n1 1 2 2\n0 0 2 2\n0",
"8\n0 0 0 2 2 2 0 0\n1 1 2 1 0 0 0 0\n2\n1 1 2 2\n0 0 2 2\n0",
"8\n0 0 0 2 2 2 0 0\n0 1 1 0 1 1 0 0\n2\n1 1 2 2\n0 0 2 2\n0",
"8\n0 0 0 2 2 2 0 -1\n1 2 1 1 1 0 0 0\n2\n1 1 2 2\n0 -1 2 2\n0",
"8\n0 0 0 2 2 2 0 0\n1 2 2 1 0 0 0 0\n2\n1 1 2 2\n0 0 2 2\n0",
"8\n0 0 0 2 2 2 0 0\n0 1 1 0 1 1 0 0\n2\n1 1 2 2\n0 0 2 0\n0",
"8\n0 0 0 2 2 2 0 -1\n1 2 1 1 1 0 -1 0\n2\n1 1 2 2\n0 -1 2 2\n0",
"8\n0 0 0 2 2 1 0 0\n1 1 1 1 1 0 0 -1\n4\n1 1 4 3\n0 0 2 2\n0",
"8\n1 0 0 2 2 2 0 0\n1 2 2 1 0 0 0 0\n2\n1 1 2 2\n0 0 2 2\n0",
"8\n0 0 0 2 2 2 0 0\n0 1 1 0 0 1 0 0\n2\n1 1 2 2\n0 0 2 0\n0",
"8\n0 0 0 2 2 2 0 -1\n1 2 1 2 1 0 -1 0\n2\n1 1 2 2\n0 -1 2 2\n0",
"8\n0 0 0 2 2 1 1 0\n1 1 1 1 1 0 0 -1\n4\n1 1 4 3\n0 0 2 2\n0",
"8\n1 0 0 2 2 2 0 0\n1 2 2 1 0 0 0 0\n2\n1 1 2 2\n0 1 2 2\n0",
"8\n0 0 0 2 2 2 0 0\n0 1 1 -1 0 1 0 0\n2\n1 1 2 2\n0 0 2 0\n0",
"8\n0 0 0 2 2 2 0 -1\n1 2 0 2 1 0 -1 0\n2\n1 1 2 2\n0 -1 2 2\n0",
"8\n0 0 0 2 2 1 1 0\n1 1 1 1 1 0 0 -1\n4\n1 1 4 3\n-1 0 2 2\n0",
"8\n0 0 0 2 2 2 0 0\n0 1 1 -1 0 1 0 0\n2\n1 1 2 2\n0 1 2 0\n0",
"8\n0 0 0 2 2 1 0 -1\n1 2 0 2 1 0 -1 0\n2\n1 1 2 2\n0 -1 2 2\n0",
"8\n0 0 0 2 2 1 1 0\n1 1 1 1 1 0 0 -1\n4\n1 1 4 5\n-1 0 2 2\n0",
"8\n0 0 0 2 2 2 0 0\n0 1 1 -1 0 2 0 0\n2\n1 1 2 2\n0 1 2 0\n0",
"8\n0 0 0 2 3 1 0 -1\n1 2 0 2 1 0 -1 0\n2\n1 1 2 2\n0 -1 2 2\n0",
"8\n0 0 0 2 4 2 0 0\n0 1 1 -1 0 2 0 0\n2\n1 1 2 2\n0 1 2 0\n0",
"8\n0 0 0 2 3 1 0 -1\n1 2 0 2 1 0 -1 0\n2\n1 1 2 2\n0 -1 2 2\n-1",
"8\n0 0 0 2 2 1 1 0\n1 0 1 1 1 0 0 -1\n4\n1 1 4 5\n-1 1 2 2\n0",
"8\n0 0 0 2 3 1 0 -1\n1 2 0 4 1 0 -1 0\n2\n1 1 2 2\n0 -1 2 2\n-1",
"8\n0 0 0 2 2 2 0 0\n1 1 1 2 0 0 0 0\n4\n1 1 2 2\n0 0 2 2\n0",
"8\n0 0 0 2 2 2 0 0\n1 1 1 1 1 0 0 0\n4\n1 1 2 2\n0 1 2 2\n0",
"8\n0 0 0 2 2 2 0 0\n1 1 1 1 1 0 0 0\n2\n1 1 2 2\n0 0 2 3\n0",
"8\n0 0 0 2 2 2 0 0\n0 1 1 1 0 0 0 0\n2\n1 1 2 2\n0 0 2 2\n0",
"8\n0 0 0 2 2 2 0 -1\n1 1 1 1 1 0 0 1\n2\n1 1 2 2\n0 0 2 2\n0",
"8\n0 0 0 2 2 2 0 1\n1 1 1 1 0 0 0 0\n4\n1 0 2 2\n0 0 2 2\n0",
"8\n0 0 0 2 2 2 0 0\n1 1 1 1 1 0 0 -1\n4\n1 1 2 2\n0 1 2 2\n0",
"8\n0 0 0 2 2 3 0 0\n1 1 2 1 1 0 0 0\n2\n1 1 2 2\n0 0 2 2\n0",
"8\n0 0 0 2 2 1 0 0\n1 1 1 1 1 0 0 -1\n4\n1 1 2 2\n0 1 2 2\n0",
"8\n0 0 0 2 2 0 0 0\n1 1 2 1 0 0 0 0\n2\n1 1 2 2\n0 0 2 2\n0",
"8\n0 0 0 2 2 2 0 0\n0 1 1 0 1 1 0 1\n2\n1 1 2 2\n0 0 2 2\n0",
"8\n0 0 0 2 2 2 0 -1\n1 2 2 1 1 0 0 0\n2\n1 1 2 2\n0 -1 2 2\n0",
"8\n0 1 0 2 2 1 0 0\n1 1 1 1 1 0 0 -1\n4\n1 1 2 3\n0 0 2 2\n0",
"8\n0 0 0 2 2 2 0 0\n1 2 2 1 0 0 0 0\n2\n1 1 2 2\n0 0 2 2\n-1",
"8\n0 0 0 2 2 2 0 -1\n0 1 1 0 1 1 0 0\n2\n1 1 2 2\n0 0 2 0\n0",
"8\n0 0 0 2 2 2 0 -1\n1 1 1 1 1 0 -1 0\n2\n1 1 2 2\n0 -1 2 2\n0",
"8\n0 0 0 2 2 1 0 1\n1 1 1 1 1 0 0 -1\n4\n1 1 4 3\n0 0 2 2\n0",
"8\n1 0 1 2 2 2 0 0\n1 2 2 1 0 0 0 0\n2\n1 1 2 2\n0 0 2 2\n0",
"8\n1 0 0 2 2 2 0 1\n1 2 2 1 0 0 0 0\n2\n1 1 2 2\n0 1 2 2\n0",
"8\n0 0 0 2 1 2 0 0\n0 1 1 -1 0 1 0 0\n2\n1 1 2 2\n0 0 2 0\n0",
"8\n0 -1 0 2 2 2 0 -1\n1 2 0 2 1 0 -1 0\n2\n1 1 2 2\n0 -1 2 2\n0",
"8\n0 0 0 2 2 1 1 0\n1 1 1 1 1 0 0 -1\n4\n1 1 4 3\n-2 0 2 2\n0",
"8\n0 0 0 2 2 2 0 0\n0 1 1 -1 0 1 0 0\n2\n1 1 2 2\n0 1 4 0\n0",
"8\n0 0 0 2 2 1 0 -1\n1 2 0 2 1 0 0 0\n2\n1 1 2 2\n0 -1 2 2\n0",
"8\n0 0 -1 2 2 1 1 0\n1 1 1 1 1 0 0 -1\n4\n1 1 4 5\n-1 0 2 2\n0",
"8\n0 0 0 2 4 2 0 0\n0 2 1 -1 0 2 0 0\n2\n1 1 2 2\n0 1 2 0\n0",
"8\n0 0 0 2 3 1 0 -1\n1 2 -1 2 1 0 -1 0\n2\n1 1 2 2\n0 -1 2 2\n-1",
"8\n0 0 0 2 0 1 1 0\n1 0 1 1 1 0 0 -1\n4\n1 1 4 5\n-1 1 2 2\n0",
"8\n0 0 0 2 3 1 0 -1\n1 2 0 7 1 0 -1 0\n2\n1 1 2 2\n0 -1 2 2\n-1",
"8\n0 0 0 2 2 2 0 0\n1 1 1 1 1 0 -1 0\n4\n1 1 2 2\n0 0 2 2\n0",
"8\n0 0 0 2 2 2 0 0\n1 1 1 1 0 0 0 0\n2\n1 1 2 2\n0 0 2 3\n0",
"8\n0 0 0 2 2 2 0 0\n0 1 1 1 0 0 0 0\n2\n1 1 2 2\n0 0 4 2\n0",
"8\n0 0 0 2 2 2 0 0\n1 1 1 1 1 0 0 -1\n4\n1 1 2 2\n-1 1 2 2\n0",
"8\n0 0 0 2 2 1 0 0\n1 1 1 1 1 0 0 -1\n4\n1 1 2 2\n1 1 2 2\n0",
"8\n0 0 0 2 2 0 0 0\n1 1 2 1 -1 0 0 0\n2\n1 1 2 2\n0 0 2 2\n0",
"8\n0 0 0 2 3 2 0 0\n0 1 1 0 1 1 0 1\n2\n1 1 2 2\n0 0 2 2\n0",
"8\n0 0 0 2 2 2 1 -1\n1 2 2 1 1 0 0 0\n2\n1 1 2 2\n0 -1 2 2\n0",
"8\n0 1 0 2 2 1 0 0\n1 1 1 1 1 0 0 -1\n4\n1 1 2 3\n0 0 0 2\n0",
"8\n0 0 -1 2 2 2 0 -1\n1 1 1 1 1 0 -1 0\n2\n1 1 2 2\n0 -1 2 2\n0",
"8\n0 0 0 2 2 1 0 1\n1 1 1 1 1 0 1 -1\n4\n1 1 4 3\n0 0 2 2\n0",
"8\n1 0 1 2 2 2 0 0\n1 2 2 1 0 0 0 -1\n2\n1 1 2 2\n0 0 2 2\n0",
"8\n1 0 0 2 2 2 0 1\n1 2 2 1 0 0 0 1\n2\n1 1 2 2\n0 1 2 2\n0",
"8\n0 0 0 2 4 1 1 0\n1 1 1 1 1 0 0 -1\n4\n1 1 4 3\n-2 0 2 2\n0",
"8\n0 0 0 2 2 2 0 0\n0 1 1 -1 0 1 0 0\n2\n1 1 2 2\n0 1 4 0\n-1",
"8\n0 0 0 2 4 2 0 0\n0 2 1 -1 0 2 0 0\n2\n1 1 2 2\n0 1 2 1\n0",
"8\n0 0 1 2 0 1 1 0\n1 0 1 1 1 0 0 -1\n4\n1 1 4 5\n-1 1 2 2\n0",
"8\n0 0 0 2 3 1 0 -1\n1 2 0 7 1 0 -1 0\n2\n1 1 2 2\n0 -1 2 2\n-2",
"8\n0 0 0 2 2 2 0 0\n1 1 1 1 1 0 -1 0\n4\n1 1 2 2\n-1 0 2 2\n0",
"8\n0 0 0 2 2 2 0 0\n1 1 1 1 0 0 1 0\n2\n1 1 2 2\n0 0 2 3\n0",
"8\n0 0 0 2 1 2 0 0\n0 1 1 1 0 0 0 0\n2\n1 1 2 2\n0 0 4 2\n0"
],
"output": [
"4\nNA",
"2\nNA\n",
"2\n0\n",
"3\n0\n",
"4\nNA\n",
"4\n0\n",
"2\n2\n",
"3\n2\n",
"3\n1\n",
"NA\n0\n",
"4\n2\n",
"4\n1\n",
"2\n",
"3\n",
"NA\nNA\n",
"2\n1\n",
"3\nNA\n",
"1\n0\n",
"1\n",
"4\n",
"NA\n",
"NA\n2\n",
"2\n0\n",
"2\nNA\n",
"2\n0\n",
"3\n0\n",
"2\nNA\n",
"4\n0\n",
"3\n0\n",
"3\n0\n",
"4\n0\n",
"3\n0\n",
"3\n0\n",
"2\n2\n",
"4\n0\n",
"4\n0\n",
"4\n0\n",
"2\n2\n",
"4\n0\n",
"4\n0\n",
"4\n0\n",
"2\n2\n",
"4\n0\n",
"4\n0\n",
"2\n2\n",
"4\n0\n",
"4\n0\n",
"4\n0\n",
"4\n0\n",
"3\n2\n",
"4\n0\n",
"4\nNA\n",
"2\nNA\n",
"2\n0\n",
"4\n0\n",
"2\n0\n",
"4\nNA\n",
"2\nNA\n",
"4\n0\n",
"2\nNA\n",
"4\n0\n",
"3\n0\n",
"4\n0\n",
"2\n2\n",
"4\n0\n",
"3\n0\n",
"2\n0\n",
"2\n2\n",
"4\n0\n",
"4\n0\n",
"4\n0\n",
"4\n0\n",
"2\n2\n",
"4\n0\n",
"4\n0\n",
"2\n2\n",
"4\n0\n",
"4\n0\n",
"3\n2\n",
"4\n0\n",
"2\nNA\n",
"4\n0\n",
"4\n0\n",
"2\nNA\n",
"2\nNA\n",
"4\n0\n",
"3\n0\n",
"4\n0\n",
"2\n2\n",
"2\n0\n",
"2\n2\n",
"4\n0\n",
"4\n0\n",
"2\n2\n",
"4\n0\n",
"4\n0\n",
"3\n2\n",
"4\n0\n",
"2\nNA\n",
"4\n0\n",
"4\n0\n"
]
}
| 6AIZU
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Ninja Atsushi guards the town from the roof of the Ninja Building from early morning to late night every day. This Ninja Building is two adjacent buildings of the same floor, and Atsushi's daily routine is to jump between buildings and head to the rooftop for security.
Because these two buildings are cleaned frequently, there are ladders and slippery areas that can help you climb the building. Moreover, the position of ladders and slippery parts changes every day. Therefore, Atsushi has to think about how to get to the roof every day.
Atsushi jumps over the walls of two buildings of the same floor, aiming for the rooftop of the building. Jumps can be started on the first floor of either building. When jumping to the opposite building, you can jump to the same floor, one floor up, or two floors up.
There are three types of walls, and the movement after jumping to each wall is decided.
* 0. Ordinary wall: Do not move up and down. The next jump will be made from there.
* 1. Ladder: The ladder spans two or more floors and moves to the top of the current ladder. The next jump will be made from there.
* 2. Sliding wall: A normal wall or slides down to the top of the ladder. The next jump will be made from there.
Also, the walls run from the first floor to the top floor just below the roof, and the roof can only be reached from the top floor of the building. Also, the wall on the bottom floor of the building will not be a slippery wall.
Create a program that takes in the number of floors n of the two buildings and the type of wall of the two buildings, and outputs the minimum number of jumps to reach the top floor and reach the rooftop. You may reach the roof of either building. However, if Atsushi cannot reach the roof of either building, please output "NA".
<image>
Input
A sequence of multiple datasets is given as input. The end of the input is indicated by a single line of zeros. Each dataset is given in the following format:
n
a1 a2 ... an
b1 b2 ... bn
The first line gives the building floor n (3 ≤ n ≤ 100). The second line gives the wall information ai from the first floor to the nth floor of the first building, and the third line gives the wall information bi from the first floor to the nth floor of the second building. ai and bi represent the information of the wall on the i-th floor, 0 is the ordinary wall, 1 is the ladder (straddling the i-th floor and the i + 1-floor), and 2 is the sliding wall.
The number of datasets does not exceed 60.
Output
Outputs the number of jumps on one line for each input dataset.
Example
Input
8
0 0 0 2 2 2 0 0
1 1 1 1 0 0 0 0
4
1 1 2 2
0 0 2 2
0
Output
4
NA
### Input:
8
0 0 0 2 2 2 0 0
1 1 1 1 0 0 0 0
4
1 1 2 2
0 0 2 2
0
### Output:
4
NA
### Input:
8
0 0 0 2 2 2 0 0
1 1 1 1 1 0 0 0
4
1 1 2 2
0 0 2 2
0
### Output:
2
NA
### Code:
def bfs(b):
mem=[[False for i in range(n)]for j in range(2)]
st=[0,0]
for i in range(2):
if b[i][0]!=1:continue
while st[i]<n-1 and b[i][st[i]+1]==1:
st[i]+=1
if st[i]==n-1:return 0
mem[0][st[0]]=True
mem[1][st[1]]=True
que=[[0,st[0],0],[1,st[1],0]]
while len(que)!=0:
d=que.pop(0)
des=(d[0]+1)%2
cst=d[2]+1
for i in range(3):
fl=d[1]+i
if fl>=n:break
state=b[des][fl]
if state!=2 and fl==n-1:
return cst
if state==0:
if mem[des][fl]==False:
que.append([des,fl,cst])
mem[des][fl]=True
elif state==1:
k=1
while True:
if fl+k>=n:return cst
if b[des][fl+k]!=1:
if mem[des][fl+k-1]==False:
que.append([des,fl+k-1,cst])
mem[des][fl+k-1]=True
break
else: k+=1
elif state==2:
k=1
while True:
if b[des][fl-k]!=2:
if mem[des][fl-k]==False:
que.append([des,fl-k,cst])
mem[des][fl-k]=True
break
else:k+=1
return -1
while True:
n=int(input())
if n==0:break
b=[[int(p)for p in input().split(" ")],[int(p)for p in input().split(" ")]]
count=bfs(b)
print(str(count)if count>=0 else "NA")
|
p00392 Common-Prime Sort_10721
|
You are now examining a unique method to sort a sequence of numbers in increasing order. The method only allows swapping of two numbers that have a common prime factor. For example, a sequence [6, 4, 2, 3, 7] can be sorted using the following steps.
Step 0: 6 4 2 3 7 (given sequence)
Step 1: 2 4 6 3 7 (elements 6 and 2 swapped)
Step 2: 2 6 4 3 7 (elements 4 and 6 swapped)
Step 3: 2 3 4 6 7 (elements 6 and 3 swapped)
Depending on the nature of the sequence, however, this approach may fail to complete the sorting. You have given a name "Coprime sort" to this approach and are now examining if a given sequence is coprime-sortable.
Make a program to determine if a given sequence can be sorted in increasing order by iterating an arbitrary number of swapping operations of two elements that have a common prime number.
Input
The input is given in the following format.
$N$
$a_1$ $a_2$ $...$ $a_N$
The first line provides the number of elements included in the sequence $N$ ($2 \leq N \leq 10^5$). The second line provides an array of integers $a_i$ ($2 \leq a_i \leq 10^5$) that constitute the sequence.
Output
Output "1" if the sequence is coprime-sortable in increasing order, or "0" otherwise.
Examples
Input
5
6 4 2 3 7
Output
1
Input
7
2 9 6 5 6 7 3
Output
0
|
from collections import defaultdict
def main():
def primes(n):
is_prime = [True] * (n + 1)
is_prime[0] = is_prime[1] = False
for i in range(2, int(n ** (1 / 2)) + 1):
if is_prime[i]:
for j in range(i * i, n + 1, i):
is_prime[j] = False
return [i for i in range(n + 1) if is_prime[i]]
prime_list = primes(100000)
solvers = [[] for _ in range(100001)]
for p in prime_list:
for i in range(p, 100001, p):
solvers[i].append(p)
n = int(input())
a_list = list(map(int, input().split()))
parent = [i for i in range(100001)]
def find(x):
if x == parent[x]:
return x
parent[x] = find(parent[x])
return parent[x]
for i, v in enumerate(a_list):
p_rep = find(min(solvers[v]))
for s in solvers[v]:
parent[find(s)] = p_rep
parent[find(v)] = p_rep
dic = defaultdict(set)
for i, v in enumerate(a_list):
dic[find(v)].add(i)
a_list.sort()
for i, v in enumerate(a_list):
if i not in dic[find(v)]:
print(0)
break
else:
print(1)
main()
|
{
"input": [
"5\n6 4 2 3 7",
"7\n2 9 6 5 6 7 3",
"5\n6 2 2 3 7",
"5\n6 1 2 2 14",
"5\n6 2 2 2 7",
"5\n6 2 2 2 14",
"5\n6 1 2 2 18",
"5\n5 1 2 2 18",
"5\n6 4 2 3 11",
"7\n2 9 6 5 6 7 5",
"5\n10 4 2 3 7",
"5\n10 2 2 2 7",
"5\n6 2 2 2 1",
"5\n3 1 2 2 14",
"5\n6 1 4 2 18",
"5\n5 1 2 3 18",
"7\n4 9 6 5 6 7 5",
"5\n10 6 2 3 7",
"5\n10 2 2 4 7",
"5\n11 2 2 2 1",
"5\n6 1 2 2 20",
"5\n6 1 4 3 18",
"5\n5 1 2 3 16",
"7\n4 7 6 5 6 7 5",
"5\n10 6 2 1 7",
"5\n10 4 2 4 7",
"5\n11 1 2 2 1",
"5\n6 1 2 2 23",
"5\n6 1 4 3 3",
"7\n4 7 6 4 6 7 5",
"5\n12 6 2 1 7",
"5\n10 4 3 4 7",
"5\n6 1 2 2 1",
"5\n11 1 2 2 23",
"5\n6 1 5 3 3",
"5\n12 6 2 1 13",
"5\n10 8 3 4 7",
"5\n6 2 1 2 1",
"5\n4 1 5 3 3",
"5\n10 8 3 4 14",
"5\n11 2 1 2 1",
"5\n4 1 5 3 5",
"5\n7 8 3 4 14",
"5\n4 1 5 5 5",
"5\n7 8 3 1 14",
"5\n4 1 5 5 9",
"5\n4 1 5 5 11",
"5\n4 2 5 5 11",
"5\n4 2 5 5 16",
"5\n5 2 5 5 16",
"5\n10 2 5 5 16",
"5\n10 2 9 5 16",
"5\n10 2 9 7 16",
"5\n10 2 14 7 16",
"5\n6 4 2 2 7",
"7\n2 9 6 5 6 7 6",
"5\n6 2 4 3 7",
"5\n10 2 2 2 4",
"5\n6 2 4 2 14",
"5\n6 1 2 2 11",
"5\n2 1 2 2 18",
"5\n6 4 2 3 5",
"7\n2 9 6 5 5 7 5",
"5\n10 2 2 2 3",
"5\n6 4 2 2 1",
"5\n3 1 2 2 24",
"7\n4 9 6 5 6 1 5",
"5\n12 6 2 3 7",
"5\n14 2 2 4 7",
"5\n17 2 2 2 1",
"5\n6 1 2 1 20",
"5\n6 1 1 3 18",
"5\n1 1 2 3 16",
"7\n4 7 6 5 6 12 5",
"5\n4 6 2 1 7",
"5\n10 4 2 4 5",
"5\n1 2 2 2 1",
"5\n8 1 2 2 23",
"5\n6 2 4 3 3",
"7\n4 7 6 4 6 13 5",
"5\n12 6 2 1 6",
"5\n10 4 5 4 7",
"5\n6 1 3 2 1",
"5\n11 1 2 4 23",
"5\n6 1 5 5 3",
"5\n4 6 2 1 13",
"5\n19 8 3 4 7",
"5\n4 1 7 3 3",
"5\n10 8 3 5 14",
"5\n17 2 1 2 1",
"5\n7 8 3 4 27",
"5\n4 1 5 6 5",
"5\n7 8 3 2 14",
"5\n4 1 5 1 9",
"5\n4 1 6 5 11",
"5\n4 2 5 2 11",
"5\n12 2 5 5 16",
"5\n10 2 5 8 16",
"5\n10 2 9 7 20",
"5\n10 2 14 7 25",
"5\n3 2 4 3 7",
"5\n10 4 2 2 4"
],
"output": [
"1",
"0",
"1\n",
"0\n",
"1\n",
"1\n",
"0\n",
"0\n",
"1\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
"0\n",
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}
| 6AIZU
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You are now examining a unique method to sort a sequence of numbers in increasing order. The method only allows swapping of two numbers that have a common prime factor. For example, a sequence [6, 4, 2, 3, 7] can be sorted using the following steps.
Step 0: 6 4 2 3 7 (given sequence)
Step 1: 2 4 6 3 7 (elements 6 and 2 swapped)
Step 2: 2 6 4 3 7 (elements 4 and 6 swapped)
Step 3: 2 3 4 6 7 (elements 6 and 3 swapped)
Depending on the nature of the sequence, however, this approach may fail to complete the sorting. You have given a name "Coprime sort" to this approach and are now examining if a given sequence is coprime-sortable.
Make a program to determine if a given sequence can be sorted in increasing order by iterating an arbitrary number of swapping operations of two elements that have a common prime number.
Input
The input is given in the following format.
$N$
$a_1$ $a_2$ $...$ $a_N$
The first line provides the number of elements included in the sequence $N$ ($2 \leq N \leq 10^5$). The second line provides an array of integers $a_i$ ($2 \leq a_i \leq 10^5$) that constitute the sequence.
Output
Output "1" if the sequence is coprime-sortable in increasing order, or "0" otherwise.
Examples
Input
5
6 4 2 3 7
Output
1
Input
7
2 9 6 5 6 7 3
Output
0
### Input:
5
6 4 2 3 7
### Output:
1
### Input:
7
2 9 6 5 6 7 3
### Output:
0
### Code:
from collections import defaultdict
def main():
def primes(n):
is_prime = [True] * (n + 1)
is_prime[0] = is_prime[1] = False
for i in range(2, int(n ** (1 / 2)) + 1):
if is_prime[i]:
for j in range(i * i, n + 1, i):
is_prime[j] = False
return [i for i in range(n + 1) if is_prime[i]]
prime_list = primes(100000)
solvers = [[] for _ in range(100001)]
for p in prime_list:
for i in range(p, 100001, p):
solvers[i].append(p)
n = int(input())
a_list = list(map(int, input().split()))
parent = [i for i in range(100001)]
def find(x):
if x == parent[x]:
return x
parent[x] = find(parent[x])
return parent[x]
for i, v in enumerate(a_list):
p_rep = find(min(solvers[v]))
for s in solvers[v]:
parent[find(s)] = p_rep
parent[find(v)] = p_rep
dic = defaultdict(set)
for i, v in enumerate(a_list):
dic[find(v)].add(i)
a_list.sort()
for i, v in enumerate(a_list):
if i not in dic[find(v)]:
print(0)
break
else:
print(1)
main()
|
p00884 Membership Management_10728
|
Peter is a senior manager of Agile Change Management (ACM) Inc., where each employee is a member of one or more task groups. Since ACM is agile, task groups are often reorganized and their members frequently change, so membership management is his constant headache.
Peter updates the membership information whenever any changes occur: for instance, the following line written by him means that Carol and Alice are the members of the Design Group.
design:carol,alice.
The name preceding the colon is the group name and the names following it specify its members.
A smaller task group may be included in a larger one. So, a group name can appear as a member of another group, for instance, as follows.
development:alice,bob,design,eve.
Simply unfolding the design above gives the following membership specification, which is equivalent to the original.
development:alice,bob,carol,alice,eve.
In this case, however, alice occurs twice. After removing one of the duplicates, we have the following more concise specification.
development:alice,bob,carol,eve.
Your mission in this problem is to write a program that, given group specifications, identifies group members.
Note that Peter's specifications can include deeply nested groups. In the following, for instance, the group one contains a single member dave.
one:another.
another:yetanother.
yetanother:dave.
Input
The input is a sequence of datasets, each being in the following format.
n
group1:member1,1,...,member1,m1.
.
.
.
groupi:memberi,1,...,memberi,mi.
.
.
.
groupn:membern,1,...,membern,mn.
The first line contains n, which represents the number of groups and is a positive integer no more than 100. Each of the following n lines contains the membership information of a group: groupi (1 ≤ i ≤ n) is the name of the i-th task group and is followed by a colon (:) and then the list of its mi member s that are delimited by a comma (,) and terminated by a period (.).
Those group names are mutually different. Each mi (1 ≤ i ≤ n) is between 1 and 10, inclusive. A member is another group name if it is one of group1, group2,..., or groupn. Otherwise it is an employee name.
There are no circular (or recursive) definitions of group(s). You may assume that mi member names of a group are mutually different.
Each group or employee name is a non-empty character string of length between 1 and 15, inclusive, and consists of lowercase letters.
The end of the input is indicated by a line containing a zero.
Output
For each dataset, output the number of employees included in the first group of the dataset, that is group1, in a line. No extra characters should occur in the output.
Example
Input
2
development:alice,bob,design,eve.
design:carol,alice.
3
one:another.
another:yetanother.
yetanother:dave.
3
friends:alice,bob,bestfriends,carol,fran,badcompany.
bestfriends:eve,alice.
badcompany:dave,carol.
5
a:b,c,d,e.
b:c,d,e,f.
c:d,e,f,g.
d:e,f,g,h.
e:f,g,h,i.
4
aa:bb.
cc:dd,ee.
ff:gg.
bb:cc.
0
Output
4
1
6
4
2
|
import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools
sys.setrecursionlimit(10**7)
inf = 10**20
eps = 1.0 / 10**10
mod = 998244353
dd = [(0,-1),(1,0),(0,1),(-1,0)]
ddn = [(0,-1),(1,-1),(1,0),(1,1),(0,1),(-1,-1),(-1,0),(-1,1)]
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()
def pf(s): return print(s, flush=True)
def main():
rr = []
while True:
n = I()
if n == 0:
break
a = [S().split(':') for _ in range(n)]
ts = set([c[0] for c in a])
ms = {}
for t,m in a:
ms[t] = m[:-1].split(',')
fm = {}
def f(c):
if c in fm:
return fm[c]
if c in ts:
s = set()
for k in ms[c]:
s |= f(k)
fm[c] = s
return s
fm[c] = set([c])
return fm[c]
r = f(a[0][0])
rr.append(len(r))
return '\n'.join(map(str,rr))
print(main())
|
{
"input": [
"2\ndevelopment:alice,bob,design,eve.\ndesign:carol,alice.\n3\none:another.\nanother:yetanother.\nyetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,g,h,i.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,design,eve.\ndesign:carol,alice.\n3\none:another.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,g,h,i.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,design,eve.\ndesign:carol,amice.\n3\none:another.\nanother:yetanother.\nyetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,g,h,i.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,design,eve.\noesign:cardl,alice.\n3\nohe:anotner.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,g,h,i.\n4\naa:bb.\ndc:dd,ee.\nff:gg.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carol,alice.\n3\none:anotheq.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,bbdcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n0\na:b,c,d,e.\nb:c,e,d,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,h,i,h.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,design,eve.\ndesign:carol,alice.\n3\nohe:anotner.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alire,bob,bestfriends,carol,fcan,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,g,h,i.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carol,alice.\n3\none:anotheq.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,bbdcompany.\nbestfriends:eve,aljce.\nbadcompany:dave,carol.\n0\na:b,c,d,e.\nb:c,e,d,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,h,i,h.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n1",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carol,alice.\n3\noneoan:theq.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,e,d,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,h,h,i.\n0\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:bc.\n0",
"2\ndevelopment:alice,bob,design,eve.\noesign:cardl,alice.\n3\nohe:anotner.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carnl.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,g,h,i.\n4\naa:bb.\ndc:dd,ee.\nff:gh.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,design,eve.\ndesign:carol,amice.\n3\none:another.\nanother:yetanother.\nyetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbestfrjends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,e,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,g,h,i.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:dc.\n0",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carol,alice.\n0\none:another.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:akice,bob,bestfriends,carol,fran,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,g,h,i.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,design,eve.\noesign:cardl,alice.\n3\nohe:anotnes.\nanother:yetanother.\nxetanother:dave.\n0\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,g,h,i.\n4\naa:bb.\ndc:dd,ee.\nff:gh.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,design,eve.\ndesign:carol,amice.\n3\none:another.\nanother:yetanother.\nyetanother:dave.\n0\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,g,h,i.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,design,eve.\ndesign:carol,alice.\n3\nohe:anotner.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,g,h,i.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,design,eve.\ndesign:carol,alice.\n3\nohe:anotner.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fram,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,g,h,i.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carol,alice.\n3\none:another.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,g,h,i.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,design,eve.\noesign:cardl,alice.\n3\nohe:anotner.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,g,h,i.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carol,alice.\n3\none:another.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,h,h,i.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,design,eve.\ndesign:carol,alice.\n3\nohe:anotner.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbestfridnds:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,g,h,i.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carol,alice.\n3\none:another.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,e,d,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,h,h,i.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,design,eve.\ndesign:carol,amice.\n3\none:another.\nanother:yetanother.\nyetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,e,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,g,h,i.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carol,alice.\n3\none:tnoaher.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,h,h,i.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,design,eve.\noesign:cardl,alice.\n3\nohe:anotner.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,g,h,i.\n4\naa:bb.\ndc:dd,ee.\nff:gh.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,design,eve.\ndesign:carol,alice.\n3\nohe:anotner.\nanother:yetanother.\nxetanother:dave.\n3\neriends:alice,bob,bestfriends,carol,fran,badcompany.\nbestfridnds:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,g,h,i.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carol,alice.\n3\none:tnoaher.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbertfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,h,h,i.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,design,eve.\noesign:cardl,alice.\n3\nohe:anotnes.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,g,h,i.\n4\naa:bb.\ndc:dd,ee.\nff:gh.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,design,eve.\ndesign:carol,alice.\n3\nohe:anotner.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,g,h,j.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carol,alice.\n3\none:anotheq.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,e,d,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,h,h,i.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,design,eve.\ndesign:carol,amice.\n3\none:another.\nanother:yetanother.\nyetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbestfrjends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,e,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,g,h,i.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,design,eve.\noesign:cardl,alice.\n3\nohe:anotnes.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,g,h,i.\n4\naa:bb.\ndc:ed,ee.\nff:gh.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carol,alice.\n3\none:anotheq.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,bbdcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,e,d,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,h,h,i.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,design,eve.\noesign:cardl,alice.\n3\nohe:anotnes.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,g,h,i.\n4\naa:bb.\ndc:ed,ee.\nfe:gh.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carol,alice.\n3\none:anotheq.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,bbdcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,e,d,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,h,i,h.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carol,alice.\n3\none:anotheq.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,bbdcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n0\na:b,c,d,e.\nb:c,e,d,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,h,i,h.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n1",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carol,alice.\n3\none:anotheq.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,bbdcompany.\nbfstfriends:eve,alice.\nbadcompany:dave,carol.\n0\na:b,c,d,e.\nb:c,e,d,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,h,i,h.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n1",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carol,alice.\n3\none:anotheq.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,bbdcompany.\nbfstfriends:eve,alice.\nbadcompany:dave,carol.\n0\na:b,c,d,e.\nb:c,e,d,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,h,i,h.\n4\naa9bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n1",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carnl,alice.\n3\none:anotheq.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,bbdcompany.\nbfstfriends:eve,alice.\nbadcompany:dave,carol.\n0\na:b,c,d,e.\nb:c,e,d,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,h,i,h.\n4\naa9bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n1",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carnl,alice.\n3\none:anotheq.\nantoher:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,bbdcompany.\nbfstfriends:eve,alice.\nbadcompany:dave,carol.\n0\na:b,c,d,e.\nb:c,e,d,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,h,i,h.\n4\naa9bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n1",
"2\ndevelopment:alice,bob,design,eve.\ndesign:carol,alice.\n3\none:another.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,g,h,i.\n4\naa:bb.\ncc:dd,ee.\nff:gf.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,design,eve.\ndesign:carol,alice.\n3\nohe:anotner.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fram,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,g,h,i.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cb.\n0",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carol,alide.\n3\none:another.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,g,h,i.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,design,eve.\noesign:cardl,alice.\n3\nohe:anotner.\naoother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,g,h,i.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,design,eve.\ndesign:carol,alice.\n3\nohe:anotner.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\nj:f,g,h,e.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carol,alice.\n3\noneoan:theq.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,e,d,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,h,h,i.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carol,alice.\n3\none:anotheq.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,bbdcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n0\na:b,c,d,e.\nb:c,e,d,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,h,i,h.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n2",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carol,alice.\n3\none:anotheq.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,bbdcompany.\nbfstfriends:eve,alice.\nbadcompany:dave,carol.\n0\na:b,c,d,e.\nb:c,e,d,f.\nc:d,e,f,g.\nd:e,g,g,h.\ne:f,h,i,h.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n1",
"2\ndevelopment:alice,dob,besign,eve.\ndesign:carol,alice.\n3\nohe:anotner.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alire,bob,bestfriends,carol,fcan,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,g,h,i.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,design,eve.\noesign:cardl,alice.\n3\nohe:anotner.\naoother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,h,h,i.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carol,alice.\n3\noneoan:theq.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,e,d,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,h,h,i.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:bc.\n0",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carol,alice.\n3\none:anotheq.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,bbdcompamy.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n0\na:b,c,d,e.\nb:c,e,d,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,h,i,h.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n2",
"2\ndevelopment:alice,bob,design,eve.\noesign:cardl,alice.\n3\nohe:anotner.\naoother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,h,h,i.\n4\naa:bb.\ncc:de,ed.\nff:gg.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,design,eve.\ndesign:carol,alice.\n3\none:another.\nanother:yetanother.\nyetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,g.\ne:f,g,h,i.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,design,eve.\ndesign:carol,alice.\n3\none:another.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,g,h,i.\n4\naa:ba.\ncc:dd,ee.\nff:gg.\nbb:cc.\n0",
"2\ndbvelopment:alice,boe,design,eve.\ndesign:carol,alice.\n3\nohe:anotner.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,g,h,i.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carol,alice.\n3\none:another.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:akice,bob,bestfriends,carol,fran,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,g,h,i.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,design,eve.\noesign:cardl,alice.\n3\nohe:anotner.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,g,h,i.\n4\naa:bb.\ncd:cd,ee.\nff:gg.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carol,alice.\n3\none:tnoaher.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,h,h,i.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbc:cb.\n0",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carol,alice.\n3\none:tnoaher.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbertfriendt:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,h,h,i.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carol,alice.\n3\none:anotheq.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,bbdcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n0\na:b,c,d,e.\nb:c,e,d,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,h+i,h.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carol,alice.\n3\none:anotheq.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,bbdcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n0\na:b,c,d,e.\nb:c,e,d,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,h,i,h.\n4\naa:bb.\n.ee,dd:cc\nff:gg.\nbb:cc.\n1",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carol,alice.\n3\none:anotheq.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,bbdcompany.\nbfstfriends:eve,alice.\nbadcompany:dave,carol.\n0\na:b,c,d,e.\nb:c,e,d,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,h,i,h.\n4\naa:bb.\ncc:dd,ee.\nff:hg.\nbb:cc.\n1",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carol,alice.\n3\none:anotheq.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,bbdcompany.\nbfstfriends:eve,alice.\nbadcompany:dave,carol.\n0\n.e,d,c,b:a\nb:c,e,d,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,h,i,h.\n4\naa9bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n1",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carnl,alice.\n3\none:anotheq.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,bbdcompany.\nbfstfriends:eve,alice.\nbadcompany:dave,carol.\n0\na:b,c,d,e.\na:c,e,d,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,h,i,h.\n4\naa9bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n1",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carnl,alice.\n3\none:anotheq.\nantoher:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,bbdcompany.\nbfstfriends:eve,alice.\nbadcompany:dave,carol.\n0\na:b,c,d,e.\nb:c,e,d,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,h,i,h.\n4\naa9bb.\ncc:dd,ee.\nff:gf.\nbb:cc.\n1",
"2\ndevelopment:alice,bob,dvsign,eee.\ndesign:carol,alice.\n3\nohe:anotner.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fram,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,g,h,i.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cb.\n0",
"2\ndevelopment:alice,bob,design,eve.\ndesign:barol,alice.\n3\nohe:anotner.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\nj:f,g,h,e.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carol,alice.\n3\none:anotheq.\nanother:yetanouher.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,bbdcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n0\na:b,c,d,e.\nb:c,e,d,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,h,i,h.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n2",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carol,alice.\n3\none:anotheq.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,bbdcompany.\nbestfriends:eve,aljce.\nbadcompany:dave,carol.\n0\na:b,c,d,e.\nb:b,e,d,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,h,i,h.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n1",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carol,alice.\n3\none:anotheq.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,bbdcompany.\nbfstfriends:eve,alice.\nbadcompany:dave,carol.\n0\na:,,cbd,e.\nb:c,e,d,f.\nc:d,e,f,g.\nd:e,g,g,h.\ne:f,h,i,h.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n1",
"2\ndevelopment:alice,dob,besign,eve.\ndesign:carol,alice.\n3\nohe:anotner.\nanoeher:yttanother.\nxetanother:dave.\n3\nfriends:alire,bob,bestfriends,carol,fcan,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,g,h,i.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carol,alice.\n3\none:anotheq.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,bbdcompamy.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n0\na:b,c,d,e.\nb:c,e,d,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,h,i,h.\n4\n.bb:aa\ncc:dd,ee.\nff:gg.\nbb:cc.\n2",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carol,alice.\n3\noneoan:theq.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,e,d,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,h,h,i.\n0\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:bc.\n-1",
"2\ndevelopment:alice,bob,design,eve.\ndesign:carol,alice.\n3\none:another.\nanother:yetanother.\nyetanother:dave.\n3\nfriends:alice,bnb,bestfriends,carol,fran,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,g.\ne:f,g,h,i.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,design,eve.\ndesign:carol,alice.\n3\neno:another.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,g,h,i.\n4\naa:ba.\ncc:dd,ee.\nff:gg.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carol,alice.\n3\nond:tnoaher.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbertfriendt:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,h,h,i.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,design,eve.\ndesign:carol,amice.\n3\none:another.\nanother:yetanother.\nyetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbestfrjends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,e,e.\nb:d,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,g,h,i.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:dc.\n0",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carol,alice.\n3\none:anotheq.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,bbdcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n0\n.e,d,c,b:a\nb:c,e,d,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,h,i,h.\n4\naa:bb.\n.ee,dd:cc\nff:gg.\nbb:cc.\n1",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carol,alice.\n3\none:anotheq.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,bbdcompany.\nbfstfriends:eve,alice.\nbadcrmpany:dave,caool.\n0\na:b,c,d,e.\nb:c,e,d,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,h,i,h.\n4\naa:bb.\ncc:dd,ee.\nff:hg.\nbb:cc.\n1",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carol,alice.\n3\none:anotheq.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,bbdcompany.\nbfstfriends:eve,alice.\nbadcompany:dave,carol.\n0\n.e,d,c,b:a\nb:c,e,d,f.\nc:d,e,f,g.\nd:e,f,g,h.\n,:feh,i,h.\n4\naa9bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n1",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carnl,alice.\n3\none:anotheq.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,bbdcompany.\nbfstfrienes:eve,alice.\nbadcompany:dave,carol.\n0\na:b,c,d,e.\na:c,e,d,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,h,i,h.\n4\naa9bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n1",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carnl,alice.\n3\none:anotheq.\nanthher:yetanotoer.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,bbdcompany.\nbfstfriends:eve,alice.\nbadcompany:dave,carol.\n0\na:b,c,d,e.\nb:c,e,d,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,h,i,h.\n4\naa9bb.\ncc:dd,ee.\nff:gf.\nbb:cc.\n1",
"2\ndevelopment:alice,bob,dvsign,eee.\ndesign:carol,alice.\n3\nohe:anotner.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fram,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,g,h,i.\n4\naa:bb.\ncd:dd,ee.\nff:gg.\nbb:cb.\n0",
"2\ndevelopment:alice,bob,design,eve.\ndesign:barol,alice.\n3\nohe:anotner.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\nj:f,g,h,e.\n4\naa:bb.\ncc:dd,ed.\nff:gg.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carol,alice.\n3\none:anotheq.\nanother:yetanouher.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,bbdcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n0\na:b,c,d,e.\nb:c,e,d,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,h,i,h.\n8\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n2",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carol,alice.\n3\none:anotheq.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,bbdcompany.\nbestfriends:eve,aljce.\nbadcompany:dave,carol.\n0\na:b,c,d,e.\nb:b,e,d,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,h,i,h.\n0\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n1",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carol,alice.\n3\none:anotheq.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,bbdcompany.\nbfstfriends:eve,alice.\nbadcompany:dave,carol.\n0\na:,,cbd,e.\nb:c,e,d,f.\nc:d,e,f,g.\nd:e,g,g,h.\ne:f,h,i,h.\n4\naa:bb/\ncc:dd,ee.\nff:gg.\nbb:cc.\n1",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carol,alice.\n3\none:anotheq.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,bbdcompamy.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n0\na:b,c,d,e.\nb:c,e,d,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,h,i,h.\n4\n.bb:aa\ncc:dd,ee.\nff;gg.\nbb:cc.\n2",
"2\ndevelopment:alice,bob,design,eve.\ndesign:carol,alice.\n3\none:another.\nanother:yetanother.\nyetanother:dave.\n3\nfriends:alice,bnb,bestfriends,carol,fran,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,e,g.\nd:e,f,g,g.\ne:f,g,h,i.\n4\naa:bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,design,eve.\ndesign:carol,alice.\n3\neno:another.\nanother:yetanother.\nxetbnother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,g,h,i.\n4\naa:ba.\ncc:dd,ee.\nff:gg.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carol,alice.\n0\none:another.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:akice,bob,bestfriends,carol,fran,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,g,h,i.\n4\naa:bb.\ncc:dd,ee.\nff:gg/\nbb:cc.\n0",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carol,alice.\n3\none:anotheq.\nanother:yetanother.\nxetaoother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,bbdcompany.\nbfstfriends:eve,alice.\nbadcrmpany:dave,caool.\n0\na:b,c,d,e.\nb:c,e,d,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,h,i,h.\n4\naa:bb.\ncc:dd,ee.\nff:hg.\nbb:cc.\n1",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carol,alice.\n3\none:anotheq.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,bbdcompany.\nbfstfriends:eve,alice.\nbadcompany:dave,carol.\n0\n.e,d,c,b:a\nb:c,e,d,f.\nc:d,e,f,g.\nd:e,f,g,h.\n-:feh,i,h.\n4\naa9bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n1",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carnl,alice.\n3\none:anotheq.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,bbdcompany.\nbfstfrienes:eve,alice.\nbadcompany:dave,carol.\n0\na:b,c,d,e.\na:c,e,d,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,h,i,h.\n4\n.bb9aa\ncc:dd,ee.\nff:gg.\nbb:cc.\n1",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carnl,alice.\n3\none:anotheq.\nanthher:yetanotoer.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,bbdcompany.\nbfstfriends:eve,alice.\nbadcompany:dave,carol.\n0\na:b,c,d,e.\nb:c,e,d,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,h,i,h.\n4\naa9bb.\ncc:dd,ee.\nfe:gf.\nbb:cc.\n1",
"2\ndevelopment:alice,bob,dvsign,eee.\ndesign:carol,alice.\n3\nohe:anotner.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fram,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,g,h,i.\n4\naa:bb.\ncd:dd,ee/\nff:gg.\nbb:cb.\n0",
"2\ndevelopment:alice,bob,design,eve.\ndesign:barol,alice.\n3\nohe:anotner.\nanother:yetanother.\nxethnotaer:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,badcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\nj:f,g,h,e.\n4\naa:bb.\ncc:dd,ed.\nff:gg.\nbb:cc.\n0",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carol,alice.\n3\none:anotheq.\nanother:yetanouher.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,bbdcompany.\nbestfriends:eve,alice.\nbadcompany:dave,carol.\n0\na:b,c,d,e.\nb:c,e,d,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,h,i,h.\n8\naa:bb.\ncc:dd,ee.\nff:gg.\nbc:cc.\n2",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carol,alice.\n0\none:another.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:akice,bob,bestfriends,carol,fran,badcompany.\nbestfriends:eve,alice.\n.lorac,evad:ynapmocdab\n5\na:b,c,d,e.\nb:c,d,e,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,g,h,i.\n4\naa:bb.\ncc:dd,ee.\nff:gg/\nbb:cc.\n0",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carol,alice.\n3\none:anotheq.\nanother:yetanother.\nxetaoother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,bbdcompany.\nbfstfriends:eve,alice.\nbadcrmpany:dave,c`ool.\n0\na:b,c,d,e.\nb:c,e,d,f.\nc:d,e,f,g.\nd:e,f,g,h.\ne:f,h,i,h.\n4\naa:bb.\ncc:dd,ee.\nff:hg.\nbb:cc.\n1",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carol,alice.\n3\none:anotheq.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,bbdcompbny.\nbfstfriends:eve,alice.\nbadcompany:dave,carol.\n0\n.e,d,c,b:a\nb:c,e,d,f.\nc:d,e,f,g.\nd:e,f,g,h.\n-:feh,i,h.\n4\naa9bb.\ncc:dd,ee.\nff:gg.\nbb:cc.\n1",
"2\ndevelopment:alice,bob,desifn,eve.\ndesign:carnl,alice.\n3\none:anotheq.\nanother:yetanother.\nxetanother:dave.\n3\nfriends:alice,bob,bestfriends,carol,fran,bbdcompany.\nbfstfrienes:eve,alice.\nbadcompany:dave,carol.\n0\na:b,c,d,e.\na:c,e,d,f.\nc:,,e,fdg.\nd:e,f,g,h.\ne:f,h,i,h.\n4\n.bb9aa\ncc:dd,ee.\nff:gg.\nbb:cc.\n1"
],
"output": [
"4\n1\n6\n4\n2",
"4\n1\n6\n4\n2\n",
"5\n1\n6\n4\n2\n",
"4\n1\n6\n4\n1\n",
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"4\n1\n7\n4\n2\n",
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"5\n1\n6\n4\n1\n",
"4\n",
"4\n1\n",
"5\n1\n",
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"4\n1\n6\n4\n2\n",
"4\n1\n6\n4\n2\n",
"4\n1\n6\n4\n2\n",
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"5\n1\n6\n4\n2\n",
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"4\n1\n6\n4\n2\n",
"4\n1\n6\n4\n1\n",
"4\n1\n6\n4\n2\n",
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"5\n1\n6\n4\n2\n",
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"4\n1\n6\n4\n1\n",
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"4\n1\n6\n4\n2\n",
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"4\n1\n7\n4\n2\n",
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"4\n1\n6\n4\n2\n",
"4\n1\n7\n4\n2\n",
"4\n1\n6\n4\n1\n",
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"4\n",
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]
}
| 6AIZU
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Peter is a senior manager of Agile Change Management (ACM) Inc., where each employee is a member of one or more task groups. Since ACM is agile, task groups are often reorganized and their members frequently change, so membership management is his constant headache.
Peter updates the membership information whenever any changes occur: for instance, the following line written by him means that Carol and Alice are the members of the Design Group.
design:carol,alice.
The name preceding the colon is the group name and the names following it specify its members.
A smaller task group may be included in a larger one. So, a group name can appear as a member of another group, for instance, as follows.
development:alice,bob,design,eve.
Simply unfolding the design above gives the following membership specification, which is equivalent to the original.
development:alice,bob,carol,alice,eve.
In this case, however, alice occurs twice. After removing one of the duplicates, we have the following more concise specification.
development:alice,bob,carol,eve.
Your mission in this problem is to write a program that, given group specifications, identifies group members.
Note that Peter's specifications can include deeply nested groups. In the following, for instance, the group one contains a single member dave.
one:another.
another:yetanother.
yetanother:dave.
Input
The input is a sequence of datasets, each being in the following format.
n
group1:member1,1,...,member1,m1.
.
.
.
groupi:memberi,1,...,memberi,mi.
.
.
.
groupn:membern,1,...,membern,mn.
The first line contains n, which represents the number of groups and is a positive integer no more than 100. Each of the following n lines contains the membership information of a group: groupi (1 ≤ i ≤ n) is the name of the i-th task group and is followed by a colon (:) and then the list of its mi member s that are delimited by a comma (,) and terminated by a period (.).
Those group names are mutually different. Each mi (1 ≤ i ≤ n) is between 1 and 10, inclusive. A member is another group name if it is one of group1, group2,..., or groupn. Otherwise it is an employee name.
There are no circular (or recursive) definitions of group(s). You may assume that mi member names of a group are mutually different.
Each group or employee name is a non-empty character string of length between 1 and 15, inclusive, and consists of lowercase letters.
The end of the input is indicated by a line containing a zero.
Output
For each dataset, output the number of employees included in the first group of the dataset, that is group1, in a line. No extra characters should occur in the output.
Example
Input
2
development:alice,bob,design,eve.
design:carol,alice.
3
one:another.
another:yetanother.
yetanother:dave.
3
friends:alice,bob,bestfriends,carol,fran,badcompany.
bestfriends:eve,alice.
badcompany:dave,carol.
5
a:b,c,d,e.
b:c,d,e,f.
c:d,e,f,g.
d:e,f,g,h.
e:f,g,h,i.
4
aa:bb.
cc:dd,ee.
ff:gg.
bb:cc.
0
Output
4
1
6
4
2
### Input:
2
development:alice,bob,design,eve.
design:carol,alice.
3
one:another.
another:yetanother.
yetanother:dave.
3
friends:alice,bob,bestfriends,carol,fran,badcompany.
bestfriends:eve,alice.
badcompany:dave,carol.
5
a:b,c,d,e.
b:c,d,e,f.
c:d,e,f,g.
d:e,f,g,h.
e:f,g,h,i.
4
aa:bb.
cc:dd,ee.
ff:gg.
bb:cc.
0
### Output:
4
1
6
4
2
### Input:
2
development:alice,bob,design,eve.
design:carol,alice.
3
one:another.
another:yetanother.
xetanother:dave.
3
friends:alice,bob,bestfriends,carol,fran,badcompany.
bestfriends:eve,alice.
badcompany:dave,carol.
5
a:b,c,d,e.
b:c,d,e,f.
c:d,e,f,g.
d:e,f,g,h.
e:f,g,h,i.
4
aa:bb.
cc:dd,ee.
ff:gg.
bb:cc.
0
### Output:
4
1
6
4
2
### Code:
import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools
sys.setrecursionlimit(10**7)
inf = 10**20
eps = 1.0 / 10**10
mod = 998244353
dd = [(0,-1),(1,0),(0,1),(-1,0)]
ddn = [(0,-1),(1,-1),(1,0),(1,1),(0,1),(-1,-1),(-1,0),(-1,1)]
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()
def pf(s): return print(s, flush=True)
def main():
rr = []
while True:
n = I()
if n == 0:
break
a = [S().split(':') for _ in range(n)]
ts = set([c[0] for c in a])
ms = {}
for t,m in a:
ms[t] = m[:-1].split(',')
fm = {}
def f(c):
if c in fm:
return fm[c]
if c in ts:
s = set()
for k in ms[c]:
s |= f(k)
fm[c] = s
return s
fm[c] = set([c])
return fm[c]
r = f(a[0][0])
rr.append(len(r))
return '\n'.join(map(str,rr))
print(main())
|
p01287 Colored Octahedra_10733
|
A young boy John is playing with eight triangular panels. These panels are all regular triangles of the same size, each painted in a single color; John is forming various octahedra with them.
While he enjoys his playing, his father is wondering how many octahedra can be made of these panels since he is a pseudo-mathematician. Your task is to help his father: write a program that reports the number of possible octahedra for given panels. Here, a pair of octahedra should be considered identical when they have the same combination of the colors allowing rotation.
Input
The input consists of multiple datasets. Each dataset has the following format:
Color1 Color2 ... Color8
Each Colori (1 ≤ i ≤ 8) is a string of up to 20 lowercase alphabets and represents the color of the i-th triangular panel.
The input ends with EOF.
Output
For each dataset, output the number of different octahedra that can be made of given panels.
Example
Input
blue blue blue blue blue blue blue blue
red blue blue blue blue blue blue blue
red red blue blue blue blue blue blue
Output
1
1
3
|
import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools
sys.setrecursionlimit(10**7)
inf = 10**20
eps = 1.0 / 10**13
mod = 10**9+7
dd = [(-1,0),(0,1),(1,0),(0,-1)]
ddn = [(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()
def pf(s): return print(s, flush=True)
# aa
# 1 2 4 5
# 2 3 1 6
# 3 4 2 7
# 4 1 3 8
# 5 8 6 1
# 6 5 7 2
# 7 6 8 3
# 8 7 5 4
#
def main():
rr = []
k = [
[2, 4, 5],
[3, 1, 6],
[4, 2, 7],
[1, 3, 8],
[8, 6, 1],
[5, 7, 2],
[6, 8, 3],
[7, 5, 4]
]
for i in range(8):
for j in range(3):
k[i][j] -= 1
ptn = []
for i in range(8):
for j in range(3):
t = [-1] * 8
t[0] = i
t[1] = k[i][j]
t[3] = k[i][(j+1)%3]
for l in range(8):
if l == i:
continue
if t[1] in k[l] and t[3] in k[l]:
t[2] = l
break
for l in range(4):
kl = k[t[l]]
for m in range(3):
if kl[m] not in t:
t[l+4] = kl[m]
break
ptn.append(t)
def f(a):
s = set()
r = 0
tc = 0
for t in itertools.permutations(a):
tc += 1
if t in s:
continue
r += 1
for p in ptn:
s.add(tuple(t[p[i]] for i in range(8)))
return r
while True:
a = LS()
if len(a) == 0:
break
rr.append(f(a))
return '\n'.join(map(str,rr))
print(main())
|
{
"input": [
"blue blue blue blue blue blue blue blue\nred blue blue blue blue blue blue blue\nred red blue blue blue blue blue blue",
"blue blue blue blue bluf blue blue blue\nred blue blue blue blue blue blue blue\nred red blue blue blue blue blue blue",
"blue blue blue blue bluf clue blue blue\nred blue blue blue blue blue blue blue\nred red blue blue blue blue blue blue",
"blue blue blue blue bluf cleu blue blue\nred blue blue blue blue blue blue eulb\nred red blue blue blue blue blue blue",
"blue blue eulb blue bluf cleu blue blue\nred blue blue blue blue blue blue eulb\nred red blue blue blue blue blue blue",
"blue blue eulb blue bluf cleu blue blue\nred blue blue blue blue blte blue eulb\nred red blue blue blue blue blue blue",
"blue blue eulb blue bluf cleu blue blue\nred blue blue blue beul blse blue eulb\nred red blue blue blue blue blue blue",
"blue blue eulb blue bluf cleu blue blue\nred blue blue blue beul blse blue eulb\nred red blue blue blue blue blue blte",
"blue blue eulb blud bluf cleu blue blue\nred blue blue blue beul blse blue eulb\nred red blue blue blue blue blue blte",
"blue blue eulb lbud bluf cleu blue blue\nred blue blue blue beul blse blue eulb\nred red blue bleu blue blue blue blte",
"blue blue eulb lbud bluf cleu blue blue\nred blue blue blue beul blse blue eulb\nred red blue bleu blue bkue blue blte",
"blue blue eulb lbud bluf cleu blue blue\nred blue blue blue beul blse blue eulb\nred red blue bleu blue bkue bmue blte",
"blue blue eulb lbud bluf cleu blue blue\nred bluf blue blue beul blse blue eulb\nred red blue bleu blue bkue bmud blte",
"blue blue eulb lbud bluf cleu blue bleu\nred bluf blue blue beul blse blue eulb\nred red blue bleu blue bkue bmud blte",
"bleu blue eulb lbud bluf cleu blue bleu\nred bluf blue blue beul blse blue eulb\nred red blue bleu blue bkue bmue blte",
"bleu blue eulb lbud bluf cleu blue bleu\nred bluf blue blue beul blse blue eulb\nrdd red blue bleu blue bkue bmue blte",
"bleu blue eulb lbud bluf cleu blue bleu\nred bluf bule blue beul blse blue eulb\nrdd red blue bleu blue bkue bmue blte",
"bleu blue eulb lbud bluf cleu blue bleu\nred flub bule blue beul blse blue eulb\nrdd red blue bleu eulb bkue cmue bltd",
"bleu blue eulb lbud bluf cleu bule bleu\nred flub bule blue beul blse blue eulb\nrdd red blue bleu eulb bkue cmue bltd",
"bleu blue eulb lbud bluf cleu bule bleu\nred flub bule blue beul blse blve eulb\nrdd red blue bleu eulb bkue cmue bltd",
"lbeu blue eulb lbud bluf cleu bule bleu\nder fmub blue bleu beul blse blve eulb\nqdd red eulb bleu eula bkue cmue bltd",
"lbet blue deul dlub cluf cneu ealu ufcm\ncer mfbu blse blev ctel sael bkvc lcue\neqd rdd amue dtla amue kbte mcud clud",
"blue blue blue blue bluf cleu blue blue\nred blue blue blue blue blue blue blue\nred red blue blue blue blue blue blue",
"blue blue eulb blue bluf cleu blue blue\nred blue blue blue blue blse blue eulb\nred red blue blue blue blue blue blue",
"blue blue eulb lbud bluf cleu blue blue\nred blue blue blue beul blse blue eulb\nred red blue blue blue blue blue blte",
"blue blue eulb lbud bluf cleu blue blue\nred blue blue blue beul blse blue eulb\nred red blue bleu blue bkue bmud blte",
"blue blue eulb lbud bluf cleu blue bleu\nred bluf blue blue beul blse blue eulb\nred red blue bleu blue bkue bmue blte",
"bleu blue eulb lbud bluf cleu blue bleu\nred bluf bule blue beul blse blue eulb\nrdd red blue bleu blue bkue bmue bltd",
"bleu blue eulb lbud bluf cleu blue bleu\nred flub bule blue beul blse blue eulb\nrdd red blue bleu blue bkue bmue bltd",
"bleu blue eulb lbud bluf cleu blue bleu\nred flub bule blue beul blse blue eulb\nrdd red blue bleu blue bkue cmue bltd",
"bleu blue eulb lbud bluf cleu bule bleu\nred flub bule bleu beul blse blve eulb\nrdd red blue bleu eulb bkue cmue bltd",
"bleu blue eulb lbud bluf cleu bule bleu\nred flub blue bleu beul blse blve eulb\nrdd red blue bleu eulb bkue cmue bltd",
"bleu blue eulb lbud bluf cleu bule bleu\nred flub blue bleu beul blse blve eulb\nrdd red blue bleu eula bkue cmue bltd",
"bleu blue eulb lbud bluf cleu bule bleu\nder flub blue bleu beul blse blve eulb\nrdd red blue bleu eula bkue cmue bltd",
"bleu blue eulb lbud bluf cleu bule bleu\nder flub blue bleu beul blse blve eulb\nqdd red blue bleu eula bkue cmue bltd",
"bleu blue eulb lbud bluf cleu bule bleu\nder fmub blue bleu beul blse blve eulb\nqdd red blue bleu eula bkue cmue bltd",
"bleu blue eulb lbud bluf cleu bule bleu\nder fmub blue bleu beul blse blve eulb\nqdd red eulb bleu eula bkue cmue bltd",
"lbeu blue eulb lbud bluf cleu bule bleu\nder fmub blue uelb beul blse blve eulb\nqdd red eulb bleu eula bkue cmue bltd",
"lbeu blue eulc lbud bluf cleu bule bleu\nder fmub blue uelb beul blse blve eulb\nqdd red eulb bleu eula bkue cmue bltd",
"lbeu blue eulc lbud bluf cleu bule bleu\nder fmub blue uelb beul blse blve eulb\nqdd red eulb bleu eula bkte cmue bltd",
"lbeu blue eulc lbud bluf cleu bule bleu\nder fmub blue uelb beul blse blve eulb\nqdd red eulb bleu eula bkte eumc bltd",
"lbeu blue eulc lbud bluf cleu bule bleu\nder fmub blue uelb beul bles blve eulb\nqdd red eulb bleu eula bkte eumc bltd",
"lbeu blue eulc lbud bluf cleu bule bleu\nder fmub blue uelb beul bles blve eulb\nqdd rdd eulb bleu eula bkte eumc bltd",
"lbeu blue eulc lbud bluf cleu bule bleu\nder fmub blue uelb ceul bles blve eulb\nqdd rdd eulb bleu eula bkte eumc bltd",
"lbeu blue eulc lbud bluf cleu bule bleu\nder fmub blue uelb ceul bles blve eulb\nqdd rdd eulb bleu eula bkte eumc cltd",
"lbeu blue euld lbud bluf cleu bule bleu\nder fmub blue uelb ceul bles blve eulb\nqdd rdd eulb bleu eula bkte eumc cltd",
"lbeu blue euld lbud bluf cleu bule bleu\nred fmub blue uelb ceul bles blve eulb\nqdd rdd eulb bleu eula bkte eumc cltd",
"lbeu blue euld lbud bluf cleu bule bleu\nred fmub blue uelb ceul bles blve eulb\nqdd rdd dulb bleu eula bkte eumc cltd",
"lbeu blue euld lbud bluf cleu bule bleu\nred fmub blue uelb ceul bles blve eulb\nqdd rdd dulb bleu eula bkte eucm cltd",
"lbeu blue euld lbud bluf cleu bule bleu\nred fmub blue uelb ceul bles blve eulb\nqdd rdd dulb bleu eula etkb eucm cltd",
"lbeu blue euld lbud bluf cleu bule bleu\nred fmub blue uelb ceul bles blve eulb\nqdd rdd dulb bldu eula etkb eucm cltd",
"lbeu blue euld lbud bluf cleu bule uelb\nred fmub blue uelb ceul bles blve eulb\nqdd rdd dulb bldu eula etkb eucm cltd",
"lbeu blue euld lbud fulb cleu bule uelb\nred fmub blue uelb ceul bles blve eulb\nqdd rdd dulb bldu eula etkb eucm cltd",
"lbeu blue euld lbud fulb cleu bule uelb\nred fmub blue uelb ceul bles blve eulb\nqdd rdd dulb bldu eula etbk eucm cltd",
"lbeu blue euld lbud fulb cleu bule uelb\nred fmub blue uelb ceul bles blve eulb\nqdd rdd dulb bldu alue etbk eucm cltd",
"lbeu blue euld lbud bluf cleu bule uelb\nred fmub blue uelb ceul bles blve eulb\nqdd rdd dulb bldu alue etbk eucm cltd",
"lbeu blue euld lbud bluf cleu bule uelb\nred fmub blue uelb ceul bles blve eulb\nqdd rdd blud bldu alue etbk eucm cltd",
"lbeu blue euld lbud bluf cleu bule uelb\nred fmub blue uelb cdul bles blve eulb\nqdd rdd blud bldu alue etbk eucm cltd",
"lbeu blue euld lbud bluf cleu bule uelb\nred fmub blue uelb cdul bles blve eulb\nqde rdd blud bldu alue etbk eucm cltd",
"lbeu blue euld lbud bluf cleu bule uelb\nred fmub blue bleu cdul bles blve eulb\nqde rdd blud bldu alue etbk eucm cltd",
"lbeu blue euld lbud bluf cleu bule uelb\nred fbum blue bleu cdul bles blve eulb\nqde rdd blud bldu alue etbk eucm cltd",
"lbeu blue euld lbud bluf cleu elub uelb\nred fbum blue bleu cdul bles blve eulb\nqde rdd blud bldu alue etbk eucm cltd",
"lbeu blue etld lbud bluf cleu elub uelb\nred fbum blue bleu cdul bles blve eulb\nqde rdd blud bldu alue etbk eucm cltd",
"lbeu blue etld lbud bluf cleu elub uelb\nred fbum blue bleu ludc bles blve eulb\nqde rdd blud bldu alue etbk eucm cltd",
"lbeu blue etld lbud bluf cleu elub uelb\nred fbum blue bleu luec bles blve eulb\nqde rdd blud bldu alue etbk eucm cltd",
"lbeu blue etld lbud bluf cleu elub uelb\nred fbum blue bleu luec bles blve eulb\nqde rdd blud bldu alue etbk eucm dtlc",
"lbeu blue etld lbud bluf cleu elub uelb\nred fbum blue bleu luec bles blve eulb\nqde rdd blud aldu alue etbk eucm dtlc",
"lbeu blue etld lbud bluf cleu elub uelb\nred ubfm blue bleu luec bles blve eulb\nqde rdd blud aldu alue etbk eucm dtlc",
"lbeu blue etld lbud bluf cleu elub uelb\nred ubfm blue bleu luec bles blve eulc\nqde rdd blud aldu alue etbk eucm dtlc",
"lbeu blue etld lbud bluf cleu elub uelb\nred ubfm blue bleu luec bles blve eulc\nqde rdd bmud aldu alue etbk eucm dtlc",
"lbeu blue etld lbud bluf cleu elub uemb\nred ubfm blue bleu luec bles blve eulc\nqde rdd bmud aldu alue etbk eucm dtlc",
"lbeu blue etld lbud bluf cleu elub uemb\nred ubfm blue bleu luec bles blve eulc\nqde rdd bmud aldu alue etbk eumc dtlc",
"lbeu blue etld blud bluf cleu elub uemb\nred ubfm blue bleu luec bles blve eulc\nqde rdd bmud aldu alue etbk eumc dtlc",
"lbeu blue etld blud bluf cmeu elub uemb\nred ubfm blue bleu luec bles blve eulc\nqde rdd bmud aldu alue etbk eumc dtlc",
"lbeu blue etld blud bluf cmeu elub uemb\nred ubfm blue bleu luec bles blve eulc\nqde rdd amud aldu alue etbk eumc dtlc",
"lbeu blue etld blud bluf cmeu elub uemb\nred ubfm blte bleu luec bles blve eulc\nqde rdd amud aldu alue etbk eumc dtlc",
"lbeu blue etld blud bluf cmeu elub uemb\nred ubfm blse bleu luec bles blve eulc\nqde rdd amud aldu alue etbk eumc dtlc",
"lbeu blue etld blud bluf cmeu elub uemb\nred ubfm blse bleu luec bles blve eulc\nqde rdd duma aldu alue etbk eumc dtlc",
"lbeu blue eltd blud bluf cmeu elub uemb\nred ubfm blse bleu luec bles blve eulc\nqde rdd duma aldu alue etbk eumc dtlc",
"lbeu blue eltd blud bluf cmeu elub uebm\nred ubfm blse bleu luec bles blve eulc\nqde rdd duma aldu alue etbk eumc dtlc",
"lbeu blue eltd blud bluf cmeu elub uebm\nred ubfm blse bleu luec bles blve eucl\nqde rdd duma aldu alue etbk eumc dtlc",
"lbeu blue eltd blud bluf cneu elub uebm\nred ubfm blse bleu luec bles blve eucl\nqde rdd duma aldu alue etbk eumc dtlc",
"lbeu blue eltd blud bluf cneu elub ufbm\nred ubfm blse bleu luec bles blve eucl\nqde rdd duma aldu alue etbk eumc dtlc",
"lbeu blue eltd dulb bluf cneu elub ufbm\nred ubfm blse bleu luec bles blve eucl\nqde rdd duma aldu alue etbk eumc dtlc",
"lbeu blue eltd dulb bluf cneu elub ufbm\nred ubfm blse bleu luec bles blve eucl\nqde ddr duma aldu alue etbk eumc dtlc",
"lbeu blue eltd dulb bluf cneu elub ufbm\nred ubfm blse bleu luec bles blve eucl\nqde ddr amud aldu alue etbk eumc dtlc",
"lbeu blue eltd dulb bluf cneu elub ufbm\nred ubfm blse bleu luec bles blue eucl\nqde ddr amud aldu alue etbk eumc dtlc",
"lbeu blue eltd buld bluf cneu elub ufbm\nred ubfm blse bleu luec bles blue eucl\nqde ddr amud aldu alue etbk eumc dtlc",
"lbeu blue eltd buld bluf cneu elub ufbm\nred ubfm blse bleu luec bles blue eucl\nqde ddr amue aldu alue etbk eumc dtlc",
"lbeu blue eltd buld bluf cneu elub ufbm\nred ubfm blse bleu luec bles blue eucl\nqde ddr euma aldu alue etbk eumc dtlc",
"lbeu blue eltd buld fulb cneu elub ufbm\nred ubfm blse bleu luec bles blue eucl\nqde ddr euma aldu alue etbk eumc dtlc",
"lbet blue eltd buld fulb cneu elub ufbm\nred ubfm blse bleu luec bles blue eucl\nqde ddr euma aldu alue etbk eumc dtlc",
"lbet blue eltd buld fulb cneu elua ufbm\nred ubfm blse bleu luec bles blue eucl\nqde ddr euma aldu alue etbk eumc dtlc",
"lbet blue eltd buld fulb cneu elua ufbm\nred ubfm blse bleu luec bles blue eucl\nqde ddr euma aldu amue etbk eumc dtlc",
"lbet blue eltd buld fulb cneu elua ufbm\nred ubfm blse bleu luec bles blue eucl\nqde ddr euma aldt amue etbk eumc dtlc",
"lbet blue tled buld fulb cneu elua ufbm\nred ubfm blse bleu luec bles blue eucl\nqde ddr euma aldt amue etbk eumc dtlc",
"lbet blue tled buld fulb cneu elua ufbm\nred ubfm blse bleu luec bles blue eucl\nqde ddr euma aldt amue etbk eumc dulc",
"lbet blue tled buld fulb cneu elua ufbm\nred ubfm blse bleu luec bles blue eucl\nqde ddr euma aldt amue etbk cmue dulc",
"lbet blte tled buld fulb cneu elua ufbm\nred ubfm blse bleu luec bles blue eucl\nqde ddr euma aldt amue etbk cmue dulc",
"lbet blte tled buld fulb cneu elua ufbm\nred ubfm blse bleu luec bles blue eucl\nqde rdd euma aldt amue etbk cmue dulc",
"lbet blte tled dlub fulb cneu elua ufbm\nred ubfm blse bleu luec bles blue eucl\nqde rdd euma aldt amue etbk cmue dulc"
],
"output": [
"1\n1\n3",
"1\n1\n3\n",
"3\n1\n3\n",
"3\n3\n3\n",
"14\n3\n3\n",
"14\n14\n3\n",
"14\n70\n3\n",
"14\n70\n7\n",
"70\n70\n7\n",
"70\n70\n35\n",
"70\n70\n140\n",
"70\n70\n420\n",
"70\n280\n420\n",
"280\n280\n420\n",
"420\n280\n420\n",
"420\n280\n840\n",
"420\n840\n840\n",
"420\n840\n1680\n",
"840\n840\n1680\n",
"840\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n840\n",
"3\n1\n3\n",
"14\n14\n3\n",
"70\n70\n7\n",
"70\n70\n420\n",
"280\n280\n420\n",
"420\n840\n840\n",
"420\n840\n840\n",
"420\n840\n840\n",
"840\n1680\n1680\n",
"840\n1680\n1680\n",
"840\n1680\n1680\n",
"840\n1680\n1680\n",
"840\n1680\n1680\n",
"840\n1680\n1680\n",
"840\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n",
"1680\n1680\n1680\n"
]
}
| 6AIZU
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
A young boy John is playing with eight triangular panels. These panels are all regular triangles of the same size, each painted in a single color; John is forming various octahedra with them.
While he enjoys his playing, his father is wondering how many octahedra can be made of these panels since he is a pseudo-mathematician. Your task is to help his father: write a program that reports the number of possible octahedra for given panels. Here, a pair of octahedra should be considered identical when they have the same combination of the colors allowing rotation.
Input
The input consists of multiple datasets. Each dataset has the following format:
Color1 Color2 ... Color8
Each Colori (1 ≤ i ≤ 8) is a string of up to 20 lowercase alphabets and represents the color of the i-th triangular panel.
The input ends with EOF.
Output
For each dataset, output the number of different octahedra that can be made of given panels.
Example
Input
blue blue blue blue blue blue blue blue
red blue blue blue blue blue blue blue
red red blue blue blue blue blue blue
Output
1
1
3
### Input:
blue blue blue blue blue blue blue blue
red blue blue blue blue blue blue blue
red red blue blue blue blue blue blue
### Output:
1
1
3
### Input:
blue blue blue blue bluf blue blue blue
red blue blue blue blue blue blue blue
red red blue blue blue blue blue blue
### Output:
1
1
3
### Code:
import math,string,itertools,fractions,heapq,collections,re,array,bisect,sys,random,time,copy,functools
sys.setrecursionlimit(10**7)
inf = 10**20
eps = 1.0 / 10**13
mod = 10**9+7
dd = [(-1,0),(0,1),(1,0),(0,-1)]
ddn = [(-1,0),(-1,1),(0,1),(1,1),(1,0),(1,-1),(0,-1),(-1,-1)]
def LI(): return [int(x) for x in sys.stdin.readline().split()]
def LI_(): return [int(x)-1 for x in sys.stdin.readline().split()]
def LF(): return [float(x) for x in sys.stdin.readline().split()]
def LS(): return sys.stdin.readline().split()
def I(): return int(sys.stdin.readline())
def F(): return float(sys.stdin.readline())
def S(): return input()
def pf(s): return print(s, flush=True)
# aa
# 1 2 4 5
# 2 3 1 6
# 3 4 2 7
# 4 1 3 8
# 5 8 6 1
# 6 5 7 2
# 7 6 8 3
# 8 7 5 4
#
def main():
rr = []
k = [
[2, 4, 5],
[3, 1, 6],
[4, 2, 7],
[1, 3, 8],
[8, 6, 1],
[5, 7, 2],
[6, 8, 3],
[7, 5, 4]
]
for i in range(8):
for j in range(3):
k[i][j] -= 1
ptn = []
for i in range(8):
for j in range(3):
t = [-1] * 8
t[0] = i
t[1] = k[i][j]
t[3] = k[i][(j+1)%3]
for l in range(8):
if l == i:
continue
if t[1] in k[l] and t[3] in k[l]:
t[2] = l
break
for l in range(4):
kl = k[t[l]]
for m in range(3):
if kl[m] not in t:
t[l+4] = kl[m]
break
ptn.append(t)
def f(a):
s = set()
r = 0
tc = 0
for t in itertools.permutations(a):
tc += 1
if t in s:
continue
r += 1
for p in ptn:
s.add(tuple(t[p[i]] for i in range(8)))
return r
while True:
a = LS()
if len(a) == 0:
break
rr.append(f(a))
return '\n'.join(map(str,rr))
print(main())
|
p01768 Shopping_10739
|
Problem statement
2D, who is good at cooking, is trying to make lunch. Cooking requires all N ingredients a_ {0}, a_ {1},…, a_ {N−1}.
Now, 2D's refrigerator doesn't contain any ingredients, so I have to go to the supermarket to buy it. At the supermarket, you can buy the material a_ {i} for the price x_ {i} yen.
2D is also a wizard and can use M types of magic. The i-th magic can be changed to the material t_ {i} by applying it to the material s_ {i}, and conversely to s_ {i} by applying it to the material t_ {i}. In addition, you can repeatedly use multiple spells on a single material. For example, you can get r from p using the magic of changing from p to q and the magic of changing from q to r.
2D decided to use the power of magic to prepare the materials as cheaply as possible. Find the minimum sum of the prices of the ingredients that 2D needs to buy to complete the dish.
input
The input is given in the following format.
N
a_ {0} x_ {0}
...
a_ {N−1} x_ {N−1}
M
s_ {0} t_ {0}
...
s_ {M−1} t_ {M−1}
Constraint
* All numbers are integers
* All material names consist of at least 1 and no more than 10 lowercase letters.
* If i ≠ j, then a_ {i} ≠ a_ {j}
* 1 \ ≤ x_ {i} \ ≤ 1,000
* 1 \ ≤ N \ ≤ 5,000
* 0 \ ≤ M \ ≤ {\ rm min} (N (N−1) / 2, 1000)
* s_ {i} ≠ t_ {i}
* There is no duplication in the pair of s_ {i}, t_ {i}
* s_ {i}, t_ {i} are included in a_ {0},…, a_ {N−1}
output
Print the answer in one line.
sample
Sample input 1
2
tako 2
yaki 1
1
tako yaki
You can magically turn a cheap yaki into a tako, so buy two yaki.
Sample output 1
2
Sample input 2
Five
a 1
b 2
c 2
d 4
e 3
Five
b a
a c
c d
e b
c b
Sample output 2
Five
As shown below, all materials can be changed from a.
* a: a as it is
* b: a-> c-> b
* c: a-> c
* d: a-> c-> d
* e: a-> b-> e
<image>
Example
Input
2
tako 2
yaki 1
1
tako yaki
Output
2
|
n = int(input())
dic = {}
price = []
for i in range(n):
a, x = input().split()
dic[a] = i
price.append(int(x))
parent = [i for i in range(n)]
def find(x):
if parent[x] == x:return x
parent[x] = find(parent[x])
return parent[x]
m = int(input())
for _ in range(m):
s, t = input().split()
si, ti = dic[s], dic[t]
ps = find(si)
pt = find(ti)
parent[ps] = parent[pt]
groups = {}
for i in range(n):
if find(i) in groups:
min_price, cnt = groups[find(i)]
groups[find(i)] = (min(min_price, price[i]), cnt + 1)
else:
groups[find(i)] = (price[i], 1)
print(sum([v[0] * v[1] for _, v in groups.items()]))
|
{
"input": [
"2\ntako 2\nyaki 1\n1\ntako yaki",
"2\ntako 2\nyaki 1\n0\ntako yaki",
"2\ntako 3\nyaji 1\n-1\noakt yaki",
"2\ntako 1\nyaij 1\n-2\noajt yaki",
"2\ntako 1\njiay 0\n-2\nouja yakg",
"2\npaks 1\naxii -1\n-3\nokua hx`j",
"2\npaks 0\naxii -1\n-1\nnkua hx`j",
"2\ntako 4\nyaji 1\n0\ntbko yaki",
"2\ntbko 6\nyaji 1\n-1\noajs yaki",
"2\noakt 1\njiax 5\n-2\noaju ikay",
"2\ntcko 6\nijay 2\n-1\noais yaki",
"2\noakt 1\njixa 8\n-2\noaju ikay",
"2\ntako -1\njiay -1\n0\npuja yakh",
"2\npaks -2\nayhi -1\n0\nmauk j`xh",
"2\ntako 2\nyaji 1\n0\ntako yaki",
"2\ntako 2\nyaji 1\n0\noakt yaki",
"2\ntako 2\nyaji 1\n-1\noakt yaki",
"2\ntako 3\nijay 1\n-1\noakt yaki",
"2\ntako 3\nijay 1\n-1\noajt yaki",
"2\ntako 2\nijay 1\n-1\noajt yaki",
"2\ntako 2\nyaji 1\n-1\noajt yaki",
"2\ntako 2\nyaji 1\n-2\noajt yaki",
"2\ntako 2\nyaij 1\n-2\noajt yaki",
"2\ntako 3\nyaij 1\n-2\noajt yaki",
"2\ntako 1\nyaij 1\n-2\noaju yaki",
"2\ntako 1\nyaij 1\n-2\nouja yaki",
"2\ntako 1\njiay 1\n-2\nouja yaki",
"2\ntako 1\njiay 1\n-2\nouja yakh",
"2\ntako 1\njiay 1\n-2\nouja yakg",
"2\nsako 1\njiay 0\n-2\nouja yakg",
"2\nsako 1\njiay 0\n-2\nouka yakg",
"2\nsako 1\njiay 0\n-2\nouka gkay",
"2\nsako 1\njiay 0\n-2\nakuo gkay",
"2\nsako 1\njiya 0\n-2\nakuo gkay",
"2\nsakp 1\njiya 0\n-2\nakuo gkay",
"2\nsakp 1\njiya 1\n-2\nakuo gkay",
"2\nsakp 1\njixa 1\n-2\nakuo gkay",
"2\nsakp 1\nijxa 1\n-2\nakuo gkay",
"2\nsakp 1\nijxa 1\n-2\nokua gkay",
"2\nsakp 1\nijxa 0\n-2\nokua gkay",
"2\nsakp 1\naxji 0\n-2\nokua gkay",
"2\nsakp 1\naxji 0\n-2\nokua gkax",
"2\nsakp 2\naxji 0\n-2\nokua gkax",
"2\nsakp 2\naxij 0\n-2\nokua gkax",
"2\nsakp 2\naxij 0\n-3\nokua gkax",
"2\nsakp 2\naxij 0\n-3\nokua gk`x",
"2\nsakp 2\naxii 0\n-3\nokua gk`x",
"2\nsakp 1\naxii 0\n-3\nokua gk`x",
"2\nsakp 1\naxii 0\n-3\nokua hk`x",
"2\nsakp 1\naxii 0\n-3\nokua hx`k",
"2\npaks 1\naxii 0\n-3\nokua hx`k",
"2\npaks 1\naxii 0\n-3\nokua k`xh",
"2\npaks 1\naxii 0\n-3\nokua hx`j",
"2\npaks 1\naxii -1\n-1\nokua hx`j",
"2\npaks 2\naxii -1\n-1\nokua hx`j",
"2\npaks 2\naxii -1\n-1\nnkua hx`j",
"2\npaks 2\niixa -1\n-1\nnkua hx`j",
"2\npaks 2\nayii -1\n-1\nnkua hx`j",
"2\npaks 2\nayii 0\n-1\nnkua hx`j",
"2\npaks 2\nayii 0\n-1\nnkua hxaj",
"2\npaks 2\nayii 0\n0\nnkua hxaj",
"2\npaks 2\nayii 0\n0\nokua hxaj",
"2\npaks 2\nayii 0\n0\nauko hxaj",
"2\ntako 2\nybki 1\n0\ntako yaki",
"2\ntako 2\nyaji 1\n0\ntbko yaki",
"2\ntako 2\nyaji 1\n0\ntkao yaki",
"2\ntoka 2\nyaji 1\n-1\noakt yaki",
"2\ntako 3\nyaji 1\n-1\ntako yaki",
"2\ntako 3\nijay 1\n-1\ntkao yaki",
"2\ntako 3\nyaji 1\n-1\noajt yaki",
"2\ntako 0\nijay 1\n-1\noajt yaki",
"2\ntako 2\nyaji 1\n-1\noajs yaki",
"2\ntako 2\nyaji 1\n-2\ntjao yaki",
"2\ntako 2\nyaij 1\n-2\nojat yaki",
"2\ntako 3\nyaij 0\n-2\noajt yaki",
"2\ntako 1\nyaij 1\n-2\noajt ykai",
"2\ntako 1\nyaij 1\n-2\noaju ikay",
"2\ntako 1\nyaij 1\n-2\najuo yaki",
"2\ntako 1\njiay 2\n-2\nouja yaki",
"2\ntako 1\njiay 1\n-1\nouja yakh",
"2\ntako 1\njiay 1\n0\nouja yakg",
"2\ntako 1\njiay 0\n-2\najuo yakg",
"2\nsako 1\njiya 0\n-2\nouja yakg",
"2\nasko 1\njiay 0\n-2\nouka yakg",
"2\nsako 1\njiay 0\n-2\nakuo yakg",
"2\nsako 1\njiay 0\n-2\najuo gkay",
"2\nsako 1\njiya 0\n-2\naouk gkay",
"2\npkas 1\njiya 0\n-2\nakuo gkay",
"2\nsakp 1\njiya 1\n-2\nakuo gkby",
"2\nsakp 1\njixa 1\n-2\nkauo gkay",
"2\nsakp 1\nijxa 1\n-4\nakuo gkay",
"2\nsakp 0\nijxa 1\n-2\nokua gkay",
"2\nsakp 1\niixa 0\n-2\nokua gkay",
"2\nsakp 0\naxji 0\n-2\nokua gkay",
"2\npaks 1\naxji 0\n-2\nokua gkax",
"2\nsakp 2\naxii 0\n-2\nokua gkax",
"2\nsakp 4\naxij 0\n-2\nokua gkax",
"2\nsakp 3\naxij 0\n-3\nokua gkax",
"2\nsakp 1\naxij 0\n-3\nokua gk`x",
"2\ntakp 2\naxii 0\n-3\nokua gk`x",
"2\nsakp 1\naxii 0\n-3\nauko gk`x"
],
"output": [
"2",
"3\n",
"4\n",
"2\n",
"1\n",
"0\n",
"-1\n",
"5\n",
"7\n",
"6\n",
"8\n",
"9\n",
"-2\n",
"-3\n",
"3\n",
"3\n",
"3\n",
"4\n",
"4\n",
"3\n",
"3\n",
"3\n",
"3\n",
"4\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"2\n",
"2\n",
"2\n",
"2\n",
"1\n",
"1\n",
"1\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"0\n",
"1\n",
"1\n",
"1\n",
"1\n",
"2\n",
"2\n",
"2\n",
"2\n",
"2\n",
"3\n",
"3\n",
"3\n",
"3\n",
"4\n",
"4\n",
"4\n",
"1\n",
"3\n",
"3\n",
"3\n",
"3\n",
"2\n",
"2\n",
"2\n",
"3\n",
"2\n",
"2\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"2\n",
"2\n",
"2\n",
"1\n",
"1\n",
"0\n",
"1\n",
"2\n",
"4\n",
"3\n",
"1\n",
"2\n",
"1\n"
]
}
| 6AIZU
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Problem statement
2D, who is good at cooking, is trying to make lunch. Cooking requires all N ingredients a_ {0}, a_ {1},…, a_ {N−1}.
Now, 2D's refrigerator doesn't contain any ingredients, so I have to go to the supermarket to buy it. At the supermarket, you can buy the material a_ {i} for the price x_ {i} yen.
2D is also a wizard and can use M types of magic. The i-th magic can be changed to the material t_ {i} by applying it to the material s_ {i}, and conversely to s_ {i} by applying it to the material t_ {i}. In addition, you can repeatedly use multiple spells on a single material. For example, you can get r from p using the magic of changing from p to q and the magic of changing from q to r.
2D decided to use the power of magic to prepare the materials as cheaply as possible. Find the minimum sum of the prices of the ingredients that 2D needs to buy to complete the dish.
input
The input is given in the following format.
N
a_ {0} x_ {0}
...
a_ {N−1} x_ {N−1}
M
s_ {0} t_ {0}
...
s_ {M−1} t_ {M−1}
Constraint
* All numbers are integers
* All material names consist of at least 1 and no more than 10 lowercase letters.
* If i ≠ j, then a_ {i} ≠ a_ {j}
* 1 \ ≤ x_ {i} \ ≤ 1,000
* 1 \ ≤ N \ ≤ 5,000
* 0 \ ≤ M \ ≤ {\ rm min} (N (N−1) / 2, 1000)
* s_ {i} ≠ t_ {i}
* There is no duplication in the pair of s_ {i}, t_ {i}
* s_ {i}, t_ {i} are included in a_ {0},…, a_ {N−1}
output
Print the answer in one line.
sample
Sample input 1
2
tako 2
yaki 1
1
tako yaki
You can magically turn a cheap yaki into a tako, so buy two yaki.
Sample output 1
2
Sample input 2
Five
a 1
b 2
c 2
d 4
e 3
Five
b a
a c
c d
e b
c b
Sample output 2
Five
As shown below, all materials can be changed from a.
* a: a as it is
* b: a-> c-> b
* c: a-> c
* d: a-> c-> d
* e: a-> b-> e
<image>
Example
Input
2
tako 2
yaki 1
1
tako yaki
Output
2
### Input:
2
tako 2
yaki 1
1
tako yaki
### Output:
2
### Input:
2
tako 2
yaki 1
0
tako yaki
### Output:
3
### Code:
n = int(input())
dic = {}
price = []
for i in range(n):
a, x = input().split()
dic[a] = i
price.append(int(x))
parent = [i for i in range(n)]
def find(x):
if parent[x] == x:return x
parent[x] = find(parent[x])
return parent[x]
m = int(input())
for _ in range(m):
s, t = input().split()
si, ti = dic[s], dic[t]
ps = find(si)
pt = find(ti)
parent[ps] = parent[pt]
groups = {}
for i in range(n):
if find(i) in groups:
min_price, cnt = groups[find(i)]
groups[find(i)] = (min(min_price, price[i]), cnt + 1)
else:
groups[find(i)] = (price[i], 1)
print(sum([v[0] * v[1] for _, v in groups.items()]))
|
p02039 Othello_10743
|
problem
Prepare the Othello board. The upper left is $ (1,1) $ and the lower right is $ (8,8) $. The board to be prepared here is $ (5,4) as follows. ) There is no $ black stone.
........
........
........
... ox ...
.... o ...
........
........
........
Kuroishi: x Shiraishi: o
8x8 board
From this state, Black starts Othello first.
AOR Ika-chan plays $ q $ times according to the following rules.
A rectangular area is given, with the upper left as the cell in the $ a $ and $ b $ columns, and the lower right as the cell in the $ c $ and $ d $ columns.
AOR Ika-chan puts black stones and white stones alternately according to the rules of Othello (reference: Wikipedia Othello) so as to maximize the number of stones contained in this rectangular area.
When no more stones can be placed (when both Shiraishi and Kuroishi have to pass or when all the boards are filled), the game ends.
In each game, output the number of stones when the number of stones contained in the area is maximized.
Since the number of inputs and outputs may increase, it is recommended to use high-speed functions for input and output.
output
In each game, output the number of stones in the area when the number of stones is maximized. Also, output a line break at the end.
Example
Input
3
1 1 8 8
2 4 3 8
8 8 8 8
Output
48
7
1
|
q = int(input())
li = [input().split() for i in range(q)]
for i in li:
a, b, c, d = map(int, i)
ans = 0
for j in range(a, c+1):
for k in range(b, d+1):
ans += 0 if j%2 == 1 and k%2 == 0 else 1
print(ans)
|
{
"input": [
"3\n1 1 8 8\n2 4 3 8\n8 8 8 8",
"3\n1 1 8 8\n2 4 3 8\n8 3 8 8",
"3\n1 1 8 8\n2 3 3 8\n8 3 8 8",
"3\n1 1 8 7\n2 3 3 8\n8 3 8 8",
"3\n1 1 8 7\n2 3 3 4\n8 3 8 8",
"3\n1 1 8 7\n2 3 3 4\n8 3 8 2",
"3\n1 1 1 8\n2 3 3 8\n8 3 8 8",
"3\n1 1 8 7\n2 3 3 8\n8 3 8 3",
"3\n1 1 8 7\n2 3 3 6\n8 3 8 8",
"3\n1 1 8 7\n2 1 3 4\n8 3 8 2",
"3\n1 1 8 7\n2 3 3 8\n8 3 8 5",
"3\n1 1 8 7\n1 3 3 6\n8 3 8 8",
"3\n0 1 8 7\n1 3 3 6\n8 3 8 8",
"3\n1 1 8 8\n2 4 6 8\n8 3 8 8",
"3\n1 1 8 8\n2 3 3 8\n8 1 8 8",
"3\n1 1 8 7\n2 3 6 8\n8 3 8 8",
"3\n1 1 8 7\n2 3 3 4\n8 4 8 8",
"3\n1 1 8 7\n1 3 3 4\n8 3 8 2",
"3\n1 1 1 8\n2 4 3 8\n8 3 8 8",
"3\n1 1 8 7\n2 3 3 8\n9 3 8 3",
"3\n1 1 4 7\n2 1 3 4\n8 3 8 2",
"3\n0 1 8 7\n1 6 3 6\n8 3 8 8",
"3\n1 1 8 1\n2 4 6 8\n8 3 8 8",
"3\n1 1 8 8\n2 3 3 4\n8 1 8 8",
"3\n1 1 8 6\n2 3 3 4\n8 4 8 8",
"3\n1 1 1 8\n2 4 3 8\n8 1 8 8",
"3\n1 1 4 7\n2 1 3 4\n8 1 8 2",
"3\n0 1 8 7\n1 6 3 6\n8 5 8 8",
"3\n1 1 10 1\n2 4 6 8\n8 3 8 8",
"3\n2 1 8 8\n2 3 3 4\n8 1 8 8",
"3\n1 1 8 7\n2 3 3 7\n9 5 8 3",
"3\n2 1 4 7\n2 1 3 4\n8 1 8 2",
"3\n0 1 4 7\n1 6 3 6\n8 5 8 8",
"3\n1 1 10 1\n2 4 6 8\n8 3 8 4",
"3\n2 1 8 8\n2 3 3 4\n7 1 8 8",
"3\n1 1 1 8\n2 4 4 8\n8 1 8 6",
"3\n1 1 8 7\n4 3 3 7\n9 5 8 3",
"3\n2 1 4 7\n2 1 3 0\n8 1 8 2",
"3\n1 1 10 0\n2 4 6 8\n8 3 8 4",
"3\n1 1 2 8\n2 4 4 8\n8 1 8 6",
"3\n1 1 10 0\n2 5 6 8\n8 3 8 4",
"3\n1 1 2 8\n2 3 4 8\n8 1 8 6",
"3\n1 1 2 8\n2 3 4 8\n8 1 8 8",
"3\n1 1 2 8\n2 3 4 8\n8 1 8 0",
"3\n1 1 2 6\n2 3 4 8\n8 1 8 0",
"3\n1 1 8 4\n2 4 3 8\n8 8 8 8",
"3\n0 1 8 8\n2 4 3 8\n8 3 8 8",
"3\n1 1 8 9\n2 3 3 8\n8 3 8 8",
"3\n2 1 8 7\n2 3 3 4\n8 3 8 8",
"3\n1 1 1 8\n4 3 3 8\n8 3 8 8",
"3\n1 1 8 6\n2 3 3 8\n8 3 8 3",
"3\n1 1 8 0\n2 1 3 4\n8 3 8 2",
"3\n1 1 8 7\n3 3 3 8\n8 3 8 5",
"3\n1 1 8 7\n1 4 3 6\n8 3 8 8",
"3\n0 1 8 7\n2 3 3 6\n8 3 8 8",
"3\n1 1 8 7\n0 3 6 8\n8 3 8 8",
"3\n1 1 3 7\n1 3 3 4\n8 3 8 2",
"3\n1 2 1 8\n2 4 3 8\n8 3 8 8",
"3\n1 2 8 7\n2 3 3 8\n9 3 8 3",
"3\n1 1 8 8\n2 3 3 4\n8 0 8 8",
"3\n1 1 8 6\n2 3 5 4\n8 4 8 8",
"3\n1 1 1 8\n2 8 3 8\n8 1 8 8",
"3\n1 1 4 7\n2 1 3 6\n8 1 8 2",
"3\n0 1 8 7\n1 6 3 6\n8 2 8 8",
"3\n1 1 10 1\n2 4 6 8\n6 3 8 8",
"3\n0 1 8 8\n2 3 3 4\n8 1 8 8",
"3\n0 1 4 7\n1 6 3 6\n8 5 8 4",
"3\n1 1 10 1\n2 4 6 5\n8 3 8 4",
"3\n1 1 8 7\n1 3 3 7\n9 5 8 3",
"3\n1 1 10 0\n3 4 6 8\n8 3 8 4",
"3\n1 1 2 8\n2 7 4 8\n8 1 8 6",
"3\n1 1 2 8\n2 5 4 8\n8 1 8 6",
"3\n0 1 10 0\n2 5 6 8\n8 3 8 5",
"3\n0 1 2 8\n2 3 4 8\n8 1 8 8",
"3\n1 1 1 6\n2 3 4 8\n8 1 8 0",
"3\n1 1 8 4\n2 4 6 8\n8 8 8 8",
"3\n2 1 8 7\n2 3 3 4\n3 3 8 8",
"3\n1 1 8 7\n2 4 3 4\n8 3 6 2",
"3\n1 2 8 6\n2 3 3 8\n8 3 8 3",
"3\n1 1 8 0\n2 1 6 4\n8 3 8 2",
"3\n0 1 8 7\n2 3 3 6\n8 3 8 6",
"3\n1 1 8 7\n0 3 6 8\n8 0 8 8",
"3\n1 1 3 7\n1 3 2 4\n8 3 8 2",
"3\n1 2 1 8\n2 4 3 9\n8 3 8 8",
"3\n1 1 8 2\n2 3 5 4\n8 4 8 8",
"3\n1 1 1 5\n2 8 3 8\n8 1 8 8",
"3\n1 1 4 7\n2 1 3 6\n8 0 8 2",
"3\n2 1 10 1\n2 4 6 8\n6 3 8 8",
"3\n0 1 8 8\n2 3 3 3\n8 1 8 8",
"3\n0 1 4 2\n1 6 3 6\n8 5 8 4",
"3\n1 1 10 0\n3 7 6 8\n8 3 8 4",
"3\n0 1 2 8\n2 3 4 6\n8 1 8 8",
"3\n1 1 1 6\n2 3 3 8\n8 1 8 0",
"3\n1 2 8 4\n2 4 6 8\n8 8 8 8",
"3\n1 2 8 6\n2 2 3 8\n8 3 8 3",
"3\n0 1 8 7\n2 3 3 6\n8 4 8 6",
"3\n1 1 8 7\n0 3 6 9\n8 0 8 8",
"3\n1 2 1 8\n2 4 3 9\n3 3 8 8",
"3\n1 1 8 2\n2 3 5 4\n9 4 8 8",
"3\n1 1 1 5\n0 8 3 8\n8 1 8 8",
"3\n0 1 8 8\n2 3 3 3\n5 1 8 8"
],
"output": [
"48\n7\n1",
"48\n7\n6\n",
"48\n9\n6\n",
"44\n9\n6\n",
"44\n3\n6\n",
"44\n3\n0\n",
"4\n9\n6\n",
"44\n9\n1\n",
"44\n6\n6\n",
"44\n6\n0\n",
"44\n9\n3\n",
"44\n8\n6\n",
"51\n8\n6\n",
"48\n19\n6\n",
"48\n9\n8\n",
"44\n24\n6\n",
"44\n3\n5\n",
"44\n4\n0\n",
"4\n7\n6\n",
"44\n9\n0\n",
"22\n6\n0\n",
"51\n1\n6\n",
"8\n19\n6\n",
"48\n3\n8\n",
"36\n3\n5\n",
"4\n7\n8\n",
"22\n6\n2\n",
"51\n1\n4\n",
"10\n19\n6\n",
"44\n3\n8\n",
"44\n8\n0\n",
"18\n6\n2\n",
"29\n1\n4\n",
"10\n19\n2\n",
"44\n3\n12\n",
"4\n12\n6\n",
"44\n0\n0\n",
"18\n0\n2\n",
"0\n19\n2\n",
"12\n12\n6\n",
"0\n16\n2\n",
"12\n15\n6\n",
"12\n15\n8\n",
"12\n15\n0\n",
"9\n15\n0\n",
"24\n7\n1\n",
"56\n7\n6\n",
"56\n9\n6\n",
"40\n3\n6\n",
"4\n0\n6\n",
"36\n9\n1\n",
"0\n6\n0\n",
"44\n3\n3\n",
"44\n5\n6\n",
"51\n6\n6\n",
"44\n33\n6\n",
"15\n4\n0\n",
"3\n7\n6\n",
"36\n9\n0\n",
"48\n3\n9\n",
"36\n6\n5\n",
"4\n1\n8\n",
"22\n9\n2\n",
"51\n1\n7\n",
"10\n19\n15\n",
"56\n3\n8\n",
"29\n1\n0\n",
"10\n8\n2\n",
"44\n11\n0\n",
"0\n14\n2\n",
"12\n5\n6\n",
"12\n10\n6\n",
"0\n16\n3\n",
"20\n15\n8\n",
"3\n15\n0\n",
"24\n19\n1\n",
"40\n3\n27\n",
"44\n1\n0\n",
"28\n9\n1\n",
"0\n16\n0\n",
"51\n6\n4\n",
"44\n33\n9\n",
"15\n3\n0\n",
"3\n9\n6\n",
"12\n6\n5\n",
"3\n1\n8\n",
"22\n9\n3\n",
"9\n19\n15\n",
"56\n2\n8\n",
"8\n1\n0\n",
"0\n6\n2\n",
"20\n10\n8\n",
"3\n9\n0\n",
"16\n19\n1\n",
"28\n10\n1\n",
"51\n6\n3\n",
"44\n40\n9\n",
"3\n9\n27\n",
"12\n6\n0\n",
"3\n2\n8\n",
"56\n2\n24\n"
]
}
| 6AIZU
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
problem
Prepare the Othello board. The upper left is $ (1,1) $ and the lower right is $ (8,8) $. The board to be prepared here is $ (5,4) as follows. ) There is no $ black stone.
........
........
........
... ox ...
.... o ...
........
........
........
Kuroishi: x Shiraishi: o
8x8 board
From this state, Black starts Othello first.
AOR Ika-chan plays $ q $ times according to the following rules.
A rectangular area is given, with the upper left as the cell in the $ a $ and $ b $ columns, and the lower right as the cell in the $ c $ and $ d $ columns.
AOR Ika-chan puts black stones and white stones alternately according to the rules of Othello (reference: Wikipedia Othello) so as to maximize the number of stones contained in this rectangular area.
When no more stones can be placed (when both Shiraishi and Kuroishi have to pass or when all the boards are filled), the game ends.
In each game, output the number of stones when the number of stones contained in the area is maximized.
Since the number of inputs and outputs may increase, it is recommended to use high-speed functions for input and output.
output
In each game, output the number of stones in the area when the number of stones is maximized. Also, output a line break at the end.
Example
Input
3
1 1 8 8
2 4 3 8
8 8 8 8
Output
48
7
1
### Input:
3
1 1 8 8
2 4 3 8
8 8 8 8
### Output:
48
7
1
### Input:
3
1 1 8 8
2 4 3 8
8 3 8 8
### Output:
48
7
6
### Code:
q = int(input())
li = [input().split() for i in range(q)]
for i in li:
a, b, c, d = map(int, i)
ans = 0
for j in range(a, c+1):
for k in range(b, d+1):
ans += 0 if j%2 == 1 and k%2 == 0 else 1
print(ans)
|
p02325 Bitonic Traveling Salesman Problem_10746
|
For given $N$ points in the 2D Euclidean plane, find the distance of the shortest tour that meets the following criteria:
* Visit the points according to the following steps:
1. It starts from the leftmost point (starting point), goes strictly from left to right, and then visits the rightmost point (turn-around point).
2. Then it starts from the turn-around point, goes strictly from right to left, and then back to the starting point.
* Through the processes 1. 2., the tour must visit each point at least once.
Constraints
* $2 \leq N \leq 1000$
* $-1000 \leq x_i, y_i \leq 1000$
* $x_i$ differ from each other
* The given points are already sorted by x-coordinates
Input
The input data is given in the following format:
$N$
$x_1$ $y_1$
$x_2$ $y_2$
...
$x_N$ $y_N$
Output
Print the distance of the shortest tour in a line. The output should not have an error greater than 0.0001.
Examples
Input
3
0 0
1 1
2 0
Output
4.82842712
Input
4
0 1
1 2
2 0
3 1
Output
7.30056308
Input
5
0 0
1 2
2 1
3 2
4 0
Output
10.94427191
|
import math
pts = []
line = input()
N = int(line)
for _ in range(0, N):
line = input()
x, y = list(map(int, line.split()))
pts += [[x, y]]
def dist(i, j):
x1, y1 = pts[i]
x2, y2 = pts[j]
return math.sqrt((x1 - x2)**2 + (y1 - y2)**2)
def btsp():
dp = [ [0] * N for _ in range(0, N)]
for i in range(1, N):
dp[0][i] = dp[0][i - 1] + dist(i - 1, i)
for i in range(1, N):
for j in range(i, N):
if i == j - 1 or i == j:
m = 10 ** 10
for k in range(0, i):
m = min(m, dp[k][i] + dist(j, k))
dp[i][j] = m
else:
dp[i][j] = dp[i][j - 1] + dist(j - 1, j)
return dp[N - 1][N - 1]
print(btsp())
|
{
"input": [
"3\n0 0\n1 1\n2 0",
"5\n0 0\n1 2\n2 1\n3 2\n4 0",
"4\n0 1\n1 2\n2 0\n3 1",
"3\n0 -1\n1 1\n2 0",
"5\n-1 0\n1 2\n2 1\n3 2\n4 0",
"4\n0 1\n1 2\n3 0\n3 1",
"3\n0 -1\n1 2\n2 0",
"4\n0 1\n1 4\n3 0\n3 1",
"3\n0 -1\n1 0\n2 0",
"4\n0 0\n1 4\n3 0\n3 1",
"3\n0 -1\n1 0\n0 0",
"4\n0 0\n1 6\n3 0\n3 1",
"3\n0 0\n1 0\n0 0",
"4\n0 0\n1 6\n4 0\n3 1",
"3\n0 0\n0 0\n0 0",
"4\n0 0\n1 6\n4 0\n3 2",
"4\n-1 0\n1 6\n4 0\n3 2",
"4\n-2 0\n1 6\n4 0\n3 2",
"4\n-2 0\n1 6\n4 1\n3 2",
"4\n-2 1\n1 6\n4 1\n3 2",
"3\n-1 0\n1 0\n1 0",
"4\n-2 1\n2 6\n4 1\n3 2",
"3\n-1 -1\n1 0\n1 0",
"4\n-2 1\n2 6\n0 1\n3 2",
"4\n-2 1\n2 3\n0 1\n3 2",
"3\n-1 -1\n0 0\n1 -1",
"4\n0 1\n2 3\n0 1\n3 2",
"3\n-1 -1\n0 0\n2 -1",
"3\n-1 -1\n-1 0\n2 -1",
"3\n-1 0\n-1 0\n2 -1",
"3\n-1 0\n-1 0\n0 -1",
"3\n0 1\n-2 0\n0 -2",
"3\n0 1\n-2 0\n0 -4",
"3\n0 1\n0 0\n0 -4",
"3\n0 1\n1 0\n0 -4",
"3\n0 1\n4 0\n0 -4",
"3\n0 1\n4 0\n1 -4",
"3\n0 0\n4 0\n1 -4",
"3\n0 0\n2 0\n1 -4",
"3\n0 0\n2 0\n1 -5",
"3\n-1 1\n2 0\n1 0",
"3\n-1 1\n4 0\n1 0",
"3\n-1 1\n4 0\n2 0",
"3\n-1 1\n4 0\n4 0",
"3\n-1 1\n4 0\n4 1",
"3\n-1 1\n4 -1\n4 0",
"3\n-1 1\n4 0\n0 0",
"3\n-1 2\n4 0\n0 0",
"3\n-1 2\n4 0\n1 0",
"3\n-1 2\n4 -1\n1 0",
"3\n-1 2\n7 -1\n1 0",
"3\n-1 1\n7 -1\n1 0",
"3\n-1 1\n7 -1\n1 1",
"3\n-1 1\n11 -1\n1 1",
"3\n-2 1\n11 -1\n1 1",
"3\n-2 1\n11 -1\n1 0",
"3\n-2 1\n1 -1\n1 0",
"3\n-8 0\n1 -1\n1 0",
"3\n-13 0\n1 -1\n1 0",
"3\n-13 0\n1 -1\n2 0",
"3\n-13 -1\n1 -1\n2 0",
"3\n-13 -1\n1 0\n2 0",
"3\n-4 -1\n1 0\n2 -1",
"3\n-4 -1\n1 -1\n2 -1",
"3\n-4 -1\n0 0\n2 -1",
"3\n-4 -2\n0 0\n2 -1",
"3\n-4 -3\n0 0\n2 -1",
"3\n-4 -3\n0 -1\n2 -1",
"3\n-5 -3\n0 -1\n2 -1",
"3\n-5 -3\n0 -1\n4 -1",
"3\n-5 -3\n0 -1\n4 -2",
"3\n-7 -3\n0 -1\n4 -2",
"3\n-7 -3\n1 -1\n4 -2",
"3\n-7 -3\n-1 -1\n4 -2",
"3\n-7 -3\n-1 -1\n4 0",
"3\n-14 -3\n-1 -1\n4 0",
"3\n-14 0\n-1 -1\n4 0",
"3\n-14 0\n0 -1\n4 0",
"3\n-10 0\n0 -1\n4 0",
"3\n-10 0\n0 0\n4 0",
"3\n-10 -1\n0 0\n4 0",
"3\n-9 0\n0 0\n4 0",
"3\n-9 -1\n0 0\n4 0",
"3\n-9 -1\n0 0\n4 -1",
"3\n-9 -1\n1 0\n4 -1",
"3\n-13 -1\n1 0\n4 -1",
"3\n-13 -1\n0 0\n4 -1",
"3\n-13 0\n0 0\n5 -1",
"3\n-13 0\n0 0\n5 -2",
"3\n-13 -1\n0 0\n5 -2",
"3\n-13 -1\n0 0\n10 -2",
"3\n-13 -1\n0 -1\n10 -2",
"3\n-10 -1\n0 -1\n10 -2",
"3\n-1 -1\n0 -1\n10 -2",
"3\n-1 -1\n0 -1\n11 -2",
"3\n-1 -1\n0 0\n11 -2",
"3\n-2 -1\n0 0\n11 -2",
"3\n-4 -1\n0 0\n11 -2",
"3\n-4 -1\n0 0\n11 -4",
"3\n-4 -1\n0 0\n3 -4",
"3\n-4 -1\n-1 0\n3 -4",
"3\n-4 -1\n-1 0\n6 -4",
"3\n-4 -1\n-2 0\n6 -4"
],
"output": [
"4.82842712",
"10.94427191",
"7.30056308",
"5.886349517\n",
"12.462840740\n",
"7.812559200\n",
"7.634413615\n",
"10.930106596\n",
"4.650281540\n",
"11.728656901\n",
"3.414213562\n",
"15.467927337\n",
"2.000000000\n",
"16.882140900\n",
"0.000000000\n",
"16.790966463\n",
"18.032759253\n",
"19.416407865\n",
"18.677315980\n",
"17.717301412\n",
"4.000000000\n",
"17.940443425\n",
"4.472135955\n",
"15.688507523\n",
"11.048627178\n",
"4.828427125\n",
"7.404918347\n",
"6.650281540\n",
"7.162277660\n",
"6.324555320\n",
"2.828427125\n",
"8.064495102\n",
"11.708203932\n",
"10.000000000\n",
"10.537319188\n",
"14.779959875\n",
"14.222125139\n",
"13.123105626\n",
"10.246211251\n",
"12.198039027\n",
"6.398345638\n",
"10.335087491\n",
"10.261297174\n",
"10.198039027\n",
"11.099019514\n",
"11.484184321\n",
"10.513233076\n",
"11.621232785\n",
"11.213591932\n",
"11.821656680\n",
"17.455193400\n",
"16.565041759\n",
"16.570766572\n",
"24.363564088\n",
"26.350985465\n",
"26.365099719\n",
"7.767828936\n",
"19.055385138\n",
"29.035668848\n",
"30.449882410\n",
"30.447509941\n",
"30.068965226\n",
"12.513233076\n",
"12.000000000\n",
"12.359173603\n",
"12.790966463\n",
"13.560623298\n",
"12.796691275\n",
"14.665274696\n",
"18.604709264\n",
"18.563655571\n",
"22.448576532\n",
"22.453849929\n",
"22.468935851\n",
"22.825329085\n",
"36.500253542\n",
"36.137424324\n",
"36.158774473\n",
"28.172981247\n",
"28.000000000\n",
"28.085544469\n",
"26.000000000\n",
"26.093789949\n",
"26.178490764\n",
"26.212153281\n",
"34.197946508\n",
"34.161510436\n",
"36.126775891\n",
"36.495935083\n",
"36.451325995\n",
"46.258172704\n",
"46.071604488\n",
"40.074860016\n",
"22.095236638\n",
"24.086955596\n",
"24.636148029\n",
"26.454812675\n",
"30.336741891\n",
"31.124864077\n",
"16.738878731\n",
"16.434905016\n",
"21.664841917\n",
"21.620646396\n"
]
}
| 6AIZU
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
For given $N$ points in the 2D Euclidean plane, find the distance of the shortest tour that meets the following criteria:
* Visit the points according to the following steps:
1. It starts from the leftmost point (starting point), goes strictly from left to right, and then visits the rightmost point (turn-around point).
2. Then it starts from the turn-around point, goes strictly from right to left, and then back to the starting point.
* Through the processes 1. 2., the tour must visit each point at least once.
Constraints
* $2 \leq N \leq 1000$
* $-1000 \leq x_i, y_i \leq 1000$
* $x_i$ differ from each other
* The given points are already sorted by x-coordinates
Input
The input data is given in the following format:
$N$
$x_1$ $y_1$
$x_2$ $y_2$
...
$x_N$ $y_N$
Output
Print the distance of the shortest tour in a line. The output should not have an error greater than 0.0001.
Examples
Input
3
0 0
1 1
2 0
Output
4.82842712
Input
4
0 1
1 2
2 0
3 1
Output
7.30056308
Input
5
0 0
1 2
2 1
3 2
4 0
Output
10.94427191
### Input:
3
0 0
1 1
2 0
### Output:
4.82842712
### Input:
5
0 0
1 2
2 1
3 2
4 0
### Output:
10.94427191
### Code:
import math
pts = []
line = input()
N = int(line)
for _ in range(0, N):
line = input()
x, y = list(map(int, line.split()))
pts += [[x, y]]
def dist(i, j):
x1, y1 = pts[i]
x2, y2 = pts[j]
return math.sqrt((x1 - x2)**2 + (y1 - y2)**2)
def btsp():
dp = [ [0] * N for _ in range(0, N)]
for i in range(1, N):
dp[0][i] = dp[0][i - 1] + dist(i - 1, i)
for i in range(1, N):
for j in range(i, N):
if i == j - 1 or i == j:
m = 10 ** 10
for k in range(0, i):
m = min(m, dp[k][i] + dist(j, k))
dp[i][j] = m
else:
dp[i][j] = dp[i][j - 1] + dist(j - 1, j)
return dp[N - 1][N - 1]
print(btsp())
|
p02470 Euler's Phi Function_10750
|
For given integer n, count the totatives of n, that is, the positive integers less than or equal to n that are relatively prime to n.
Input
n
An integer n (1 ≤ n ≤ 1000000000).
Output
The number of totatives in a line.
Examples
Input
6
Output
2
Input
1000000
Output
400000
|
# https://tjkendev.github.io/procon-library/python/prime/eulers-totient-function.html
# https://qiita.com/drken/items/a14e9af0ca2d857dad23#%E5%95%8F%E9%A1%8C-6-%E3%82%AA%E3%82%A4%E3%83%A9%E3%83%BC%E9%96%A2%E6%95%B0
# オイラー関数
# 1,2,...,NのうちNと互いに素であるものの個数
# Python3 program to calculate
# Euler's Totient Function
def euler_phi(n):
# Initialize result as n
result = n;
# Consider all prime factors
# of n and subtract their
# multiples from result
p = 2;
while(p * p <= n):
# Check if p is a
# prime factor.
if (n % p == 0):
# If yes, then
# update n and result
while (n % p == 0):
n = int(n / p);
result -= int(result / p);
p += 1;
# If n has a prime factor
# greater than sqrt(n)
# (There can be at-most
# one such prime factor)
if (n > 1):
result -= int(result / n);
return result;
n=int(input())
print(euler_phi(n))
|
{
"input": [
"1000000",
"6",
"1000100",
"5",
"1000101",
"1000001",
"1000011",
"16",
"1010011",
"31",
"61",
"59",
"106",
"41",
"57",
"21",
"2",
"1100000",
"3",
"1000111",
"1001101",
"1010001",
"14",
"1001001",
"1100011",
"103",
"207",
"45",
"112",
"1100001",
"0000111",
"1001111",
"22",
"1101011",
"40",
"369",
"1001110",
"1100111",
"47",
"267",
"29",
"1000110",
"303",
"46",
"1010110",
"473",
"1010111",
"197",
"27",
"1110111",
"355",
"1111111",
"1101111",
"101",
"1001100",
"44",
"1010010",
"1110011",
"89",
"1100100",
"1010101",
"1001011",
"1011001",
"1100101",
"291",
"1101101",
"698",
"127",
"1001010",
"1110101",
"86",
"1010100",
"81",
"79",
"1011111",
"859",
"1011011",
"1110110",
"269",
"1011100",
"1011110",
"1111011",
"80",
"92",
"1110100",
"1011000",
"83",
"1111101",
"176",
"1281",
"133",
"175",
"1101010",
"1111100",
"67",
"1011101",
"211",
"481",
"1111001",
"1000010",
"107",
"97"
],
"output": [
"400000",
"2",
"391680\n",
"4\n",
"666732\n",
"990000\n",
"666672\n",
"8\n",
"976500\n",
"30\n",
"60\n",
"58\n",
"52\n",
"40\n",
"36\n",
"12\n",
"1\n",
"400000\n",
"2\n",
"857232\n",
"999100\n",
"673332\n",
"6\n",
"667332\n",
"999900\n",
"102\n",
"132\n",
"24\n",
"48\n",
"627984\n",
"72\n",
"995400\n",
"10\n",
"1084512\n",
"16\n",
"240\n",
"344160\n",
"1097712\n",
"46\n",
"176\n",
"28\n",
"239616\n",
"200\n",
"22\n",
"398848\n",
"420\n",
"1003752\n",
"196\n",
"18\n",
"705024\n",
"280\n",
"1106224\n",
"655200\n",
"100\n",
"257600\n",
"20\n",
"266240\n",
"951432\n",
"88\n",
"276480\n",
"979200\n",
"832000\n",
"1011000\n",
"1100100\n",
"192\n",
"1037232\n",
"348\n",
"126\n",
"262080\n",
"1107552\n",
"42\n",
"207360\n",
"54\n",
"78\n",
"644000\n",
"858\n",
"956032\n",
"429600\n",
"268\n",
"404400\n",
"404440\n",
"665600\n",
"32\n",
"44\n",
"417280\n",
"268800\n",
"82\n",
"691200\n",
"80\n",
"720\n",
"108\n",
"120\n",
"421168\n",
"432000\n",
"66\n",
"777600\n",
"210\n",
"432\n",
"1045632\n",
"363600\n",
"106\n",
"96\n"
]
}
| 6AIZU
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
For given integer n, count the totatives of n, that is, the positive integers less than or equal to n that are relatively prime to n.
Input
n
An integer n (1 ≤ n ≤ 1000000000).
Output
The number of totatives in a line.
Examples
Input
6
Output
2
Input
1000000
Output
400000
### Input:
1000000
### Output:
400000
### Input:
6
### Output:
2
### Code:
# https://tjkendev.github.io/procon-library/python/prime/eulers-totient-function.html
# https://qiita.com/drken/items/a14e9af0ca2d857dad23#%E5%95%8F%E9%A1%8C-6-%E3%82%AA%E3%82%A4%E3%83%A9%E3%83%BC%E9%96%A2%E6%95%B0
# オイラー関数
# 1,2,...,NのうちNと互いに素であるものの個数
# Python3 program to calculate
# Euler's Totient Function
def euler_phi(n):
# Initialize result as n
result = n;
# Consider all prime factors
# of n and subtract their
# multiples from result
p = 2;
while(p * p <= n):
# Check if p is a
# prime factor.
if (n % p == 0):
# If yes, then
# update n and result
while (n % p == 0):
n = int(n / p);
result -= int(result / p);
p += 1;
# If n has a prime factor
# greater than sqrt(n)
# (There can be at-most
# one such prime factor)
if (n > 1):
result -= int(result / n);
return result;
n=int(input())
print(euler_phi(n))
|
1019_A. Elections_10760
|
As you know, majority of students and teachers of Summer Informatics School live in Berland for the most part of the year. Since corruption there is quite widespread, the following story is not uncommon.
Elections are coming. You know the number of voters and the number of parties — n and m respectively. For each voter you know the party he is going to vote for. However, he can easily change his vote given a certain amount of money. In particular, if you give i-th voter c_i bytecoins you can ask him to vote for any other party you choose.
The United Party of Berland has decided to perform a statistical study — you need to calculate the minimum number of bytecoins the Party needs to spend to ensure its victory. In order for a party to win the elections, it needs to receive strictly more votes than any other party.
Input
The first line of input contains two integers n and m (1 ≤ n, m ≤ 3000) — the number of voters and the number of parties respectively.
Each of the following n lines contains two integers p_i and c_i (1 ≤ p_i ≤ m, 1 ≤ c_i ≤ 10^9) — the index of this voter's preferred party and the number of bytecoins needed for him to reconsider his decision.
The United Party of Berland has the index 1.
Output
Print a single number — the minimum number of bytecoins needed for The United Party of Berland to win the elections.
Examples
Input
1 2
1 100
Output
0
Input
5 5
2 100
3 200
4 300
5 400
5 900
Output
500
Input
5 5
2 100
3 200
4 300
5 800
5 900
Output
600
Note
In the first sample, The United Party wins the elections even without buying extra votes.
In the second sample, The United Party can buy the votes of the first and the fourth voter. This way The Party gets two votes, while parties 3, 4 and 5 get one vote and party number 2 gets no votes.
In the third sample, The United Party can buy the votes of the first three voters and win, getting three votes against two votes of the fifth party.
|
n, m = map(int, input().split())
pc = [(0, 0) for _ in range(n)]
party_votes = [0 for _ in range(m)]
for i in range(n):
p, c = map(int, input().split())
pc[i] = (p - 1, c)
party_votes[p - 1] += 1
pc.sort(key=lambda x: x[1])
min_cost = 10**20
for votes in range(n + 1):
_party_votes = party_votes[:]
dangerous = list(map(lambda party: _party_votes[party] >= votes, range(0, m)))
used = list(map(lambda i: pc[i][0] == 0, range(n)))
cur_cost = 0
for i in range(n):
if dangerous[pc[i][0]] and pc[i][0] != 0:
cur_cost += pc[i][1]
_party_votes[0] += 1
_party_votes[pc[i][0]] -= 1
dangerous[pc[i][0]] = _party_votes[pc[i][0]] >= votes
used[i] = True
for i in range(n):
if _party_votes[0] >= votes:
break
if not used[i]:
_party_votes[0] += 1
cur_cost += pc[i][1]
min_cost = min(min_cost, cur_cost)
print(min_cost)
|
{
"input": [
"1 2\n1 100\n",
"5 5\n2 100\n3 200\n4 300\n5 800\n5 900\n",
"5 5\n2 100\n3 200\n4 300\n5 400\n5 900\n",
"5 5\n2 5\n2 4\n2 1\n3 6\n3 7\n",
"1 3000\n918 548706881\n",
"1 3000\n2006 226621946\n",
"10 2\n1 1\n1 1\n1 1\n1 1\n1 1\n2 1\n2 1\n2 1\n2 1\n2 1\n",
"5 5\n1 3\n1 6\n5 4\n3 7\n2 10\n",
"10 10\n1 73\n2 8\n3 88\n1 5\n2 100\n1 29\n1 57\n3 37\n7 46\n3 21\n",
"5 5\n1 7\n3 3\n2 7\n2 4\n1 2\n",
"10 10\n5 81\n7 68\n7 48\n1 10\n5 37\n7 97\n8 54\n7 41\n7 56\n5 21\n",
"10 10\n7 29\n10 31\n9 40\n5 17\n5 30\n6 85\n2 53\n7 23\n4 57\n10 9\n",
"5 5\n2 5\n2 4\n2 1\n3 11\n3 7\n",
"5 5\n1 3\n1 6\n5 8\n3 7\n2 10\n",
"5 5\n1 7\n3 3\n3 7\n2 4\n1 2\n",
"10 10\n7 29\n10 31\n9 32\n5 17\n5 30\n6 85\n2 53\n7 23\n4 57\n10 9\n",
"5 5\n2 100\n5 200\n4 300\n5 800\n5 900\n",
"5 5\n4 100\n3 200\n4 300\n5 400\n5 900\n",
"5 5\n1 7\n3 2\n3 7\n2 4\n1 2\n",
"5 5\n2 100\n5 200\n4 175\n5 800\n5 900\n",
"5 5\n4 100\n3 200\n4 90\n5 400\n5 900\n",
"5 5\n4 100\n3 170\n4 90\n5 400\n5 900\n",
"5 6\n4 100\n3 170\n4 117\n5 400\n5 900\n",
"5 6\n4 100\n3 170\n4 117\n3 400\n5 900\n",
"5 6\n4 100\n3 45\n4 117\n3 400\n5 900\n",
"5 6\n3 100\n3 45\n4 117\n1 400\n5 900\n",
"5 6\n3 100\n3 77\n5 150\n1 400\n5 752\n",
"1 3000\n670 548706881\n",
"10 10\n5 81\n7 68\n7 48\n1 10\n5 37\n7 47\n8 54\n7 41\n7 56\n5 21\n",
"5 5\n2 9\n2 4\n2 1\n3 11\n3 7\n",
"5 5\n4 100\n3 200\n4 115\n5 400\n5 900\n",
"5 5\n2 5\n2 4\n3 1\n3 11\n3 0\n",
"5 5\n4 100\n3 170\n4 111\n5 400\n5 900\n",
"5 6\n4 100\n3 34\n4 117\n3 400\n5 900\n",
"5 6\n3 100\n3 45\n4 117\n5 400\n5 900\n",
"5 6\n3 100\n3 62\n5 219\n1 400\n5 752\n",
"1 3000\n670 141077449\n",
"5 5\n4 101\n3 170\n4 111\n5 400\n5 900\n",
"5 6\n4 100\n3 34\n4 45\n3 400\n5 900\n",
"5 9\n3 100\n3 45\n5 90\n1 400\n5 752\n",
"5 6\n3 100\n3 25\n5 219\n1 400\n5 752\n",
"1 3000\n670 56891830\n",
"10 10\n1 73\n2 8\n3 88\n1 5\n2 100\n1 29\n1 57\n3 37\n6 46\n3 21\n",
"5 5\n2 5\n2 4\n3 1\n3 11\n3 7\n",
"5 6\n4 100\n3 170\n4 90\n5 400\n5 900\n",
"5 6\n3 100\n3 45\n4 117\n3 400\n5 900\n",
"5 6\n3 100\n3 45\n4 150\n1 400\n5 900\n",
"5 6\n3 100\n3 45\n5 150\n1 400\n5 900\n",
"5 6\n3 100\n3 45\n5 150\n1 400\n5 752\n",
"5 6\n3 100\n3 77\n5 219\n1 400\n5 752\n",
"10 10\n1 73\n2 13\n3 88\n1 5\n2 100\n1 29\n1 57\n3 37\n7 46\n3 21\n",
"5 5\n1 7\n3 3\n1 7\n2 4\n1 2\n",
"5 5\n2 100\n3 200\n2 300\n5 800\n5 900\n",
"10 10\n1 73\n2 8\n3 88\n1 5\n2 100\n1 29\n1 57\n3 58\n6 46\n3 21\n",
"10 10\n7 29\n10 31\n9 32\n5 17\n5 30\n6 85\n2 53\n4 23\n4 57\n10 9\n",
"5 5\n1 7\n3 2\n3 9\n2 4\n1 2\n",
"5 5\n4 100\n3 200\n4 90\n5 421\n5 900\n",
"5 6\n4 100\n2 170\n4 117\n5 400\n5 900\n",
"5 6\n6 100\n3 45\n4 150\n1 400\n5 900\n",
"5 9\n3 100\n3 45\n5 150\n1 400\n5 752\n",
"5 5\n3 100\n3 77\n5 150\n1 400\n5 752\n",
"10 10\n1 73\n2 13\n3 88\n1 3\n2 100\n1 29\n1 57\n3 37\n7 46\n3 21\n",
"5 5\n1 7\n3 3\n1 7\n2 1\n1 2\n",
"5 5\n2 100\n3 200\n3 300\n5 800\n5 900\n",
"10 10\n1 73\n2 8\n5 88\n1 5\n2 100\n1 29\n1 57\n3 58\n6 46\n3 21\n",
"5 5\n4 100\n3 200\n4 115\n5 633\n5 900\n",
"5 5\n1 7\n3 2\n3 4\n2 4\n1 2\n",
"5 6\n3 100\n2 170\n4 117\n5 400\n5 900\n",
"5 6\n6 110\n3 45\n4 150\n1 400\n5 900\n"
],
"output": [
"0\n",
"600\n",
"500\n",
"10\n",
"548706881\n",
"226621946\n",
"1\n",
"0\n",
"0\n",
"3\n",
"110\n",
"49\n",
"10\n",
"0\n",
"3\n",
"49\n",
"600\n",
"500\n",
"2\n",
"475\n",
"390\n",
"360\n",
"387\n",
"270\n",
"145\n",
"45\n",
"177\n",
"548706881\n",
"109\n",
"12\n",
"415\n",
"5\n",
"381\n",
"134\n",
"262\n",
"162\n",
"141077449\n",
"382\n",
"79\n",
"135\n",
"125\n",
"56891830\n",
"0\n",
"10\n",
"360\n",
"145\n",
"45\n",
"145\n",
"145\n",
"177\n",
"0\n",
"0\n",
"600\n",
"0\n",
"49\n",
"2\n",
"390\n",
"387\n",
"45\n",
"145\n",
"177\n",
"0\n",
"0\n",
"600\n",
"0\n",
"415\n",
"2\n",
"387\n",
"45\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
As you know, majority of students and teachers of Summer Informatics School live in Berland for the most part of the year. Since corruption there is quite widespread, the following story is not uncommon.
Elections are coming. You know the number of voters and the number of parties — n and m respectively. For each voter you know the party he is going to vote for. However, he can easily change his vote given a certain amount of money. In particular, if you give i-th voter c_i bytecoins you can ask him to vote for any other party you choose.
The United Party of Berland has decided to perform a statistical study — you need to calculate the minimum number of bytecoins the Party needs to spend to ensure its victory. In order for a party to win the elections, it needs to receive strictly more votes than any other party.
Input
The first line of input contains two integers n and m (1 ≤ n, m ≤ 3000) — the number of voters and the number of parties respectively.
Each of the following n lines contains two integers p_i and c_i (1 ≤ p_i ≤ m, 1 ≤ c_i ≤ 10^9) — the index of this voter's preferred party and the number of bytecoins needed for him to reconsider his decision.
The United Party of Berland has the index 1.
Output
Print a single number — the minimum number of bytecoins needed for The United Party of Berland to win the elections.
Examples
Input
1 2
1 100
Output
0
Input
5 5
2 100
3 200
4 300
5 400
5 900
Output
500
Input
5 5
2 100
3 200
4 300
5 800
5 900
Output
600
Note
In the first sample, The United Party wins the elections even without buying extra votes.
In the second sample, The United Party can buy the votes of the first and the fourth voter. This way The Party gets two votes, while parties 3, 4 and 5 get one vote and party number 2 gets no votes.
In the third sample, The United Party can buy the votes of the first three voters and win, getting three votes against two votes of the fifth party.
### Input:
1 2
1 100
### Output:
0
### Input:
5 5
2 100
3 200
4 300
5 800
5 900
### Output:
600
### Code:
n, m = map(int, input().split())
pc = [(0, 0) for _ in range(n)]
party_votes = [0 for _ in range(m)]
for i in range(n):
p, c = map(int, input().split())
pc[i] = (p - 1, c)
party_votes[p - 1] += 1
pc.sort(key=lambda x: x[1])
min_cost = 10**20
for votes in range(n + 1):
_party_votes = party_votes[:]
dangerous = list(map(lambda party: _party_votes[party] >= votes, range(0, m)))
used = list(map(lambda i: pc[i][0] == 0, range(n)))
cur_cost = 0
for i in range(n):
if dangerous[pc[i][0]] and pc[i][0] != 0:
cur_cost += pc[i][1]
_party_votes[0] += 1
_party_votes[pc[i][0]] -= 1
dangerous[pc[i][0]] = _party_votes[pc[i][0]] >= votes
used[i] = True
for i in range(n):
if _party_votes[0] >= votes:
break
if not used[i]:
_party_votes[0] += 1
cur_cost += pc[i][1]
min_cost = min(min_cost, cur_cost)
print(min_cost)
|
1041_F. Ray in the tube_10764
|
You are given a tube which is reflective inside represented as two non-coinciding, but parallel to Ox lines. Each line has some special integer points — positions of sensors on sides of the tube.
You are going to emit a laser ray in the tube. To do so, you have to choose two integer points A and B on the first and the second line respectively (coordinates can be negative): the point A is responsible for the position of the laser, and the point B — for the direction of the laser ray. The laser ray is a ray starting at A and directed at B which will reflect from the sides of the tube (it doesn't matter if there are any sensors at a reflection point or not). A sensor will only register the ray if the ray hits exactly at the position of the sensor.
<image> Examples of laser rays. Note that image contains two examples. The 3 sensors (denoted by black bold points on the tube sides) will register the blue ray but only 2 will register the red.
Calculate the maximum number of sensors which can register your ray if you choose points A and B on the first and the second lines respectively.
Input
The first line contains two integers n and y_1 (1 ≤ n ≤ 10^5, 0 ≤ y_1 ≤ 10^9) — number of sensors on the first line and its y coordinate.
The second line contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ 10^9) — x coordinates of the sensors on the first line in the ascending order.
The third line contains two integers m and y_2 (1 ≤ m ≤ 10^5, y_1 < y_2 ≤ 10^9) — number of sensors on the second line and its y coordinate.
The fourth line contains m integers b_1, b_2, …, b_m (0 ≤ b_i ≤ 10^9) — x coordinates of the sensors on the second line in the ascending order.
Output
Print the only integer — the maximum number of sensors which can register the ray.
Example
Input
3 1
1 5 6
1 3
3
Output
3
Note
One of the solutions illustrated on the image by pair A_2 and B_2.
|
n, y1 = map(int, input().split())
a = list(map(int, input().split()))
m, y2 = map(int, input().split())
b = list(map(int, input().split()))
a_st, b_st = dict(), dict()
osn = 2 ** 30
k_a, k_b = set(), set()
for el in a:
try:
a_st[el % osn] += 1
except KeyError:
a_st[el % osn] = 1
finally:
k_a.add(el % osn)
for el in b:
try:
b_st[el % osn] += 1
except KeyError:
b_st[el % osn] = 1
finally:
k_b.add(el % osn)
ans = 2
for i in range(1, 31)[::-1]:
temp = 0
for el in k_a:
try:
temp = max(temp, a_st[el] + b_st[(el + osn // 2) % osn])
except KeyError:
temp = max(temp, a_st[el])
for el in k_b:
try:
temp = max(temp, b_st[el] + a_st[(el + osn // 2) % osn])
except KeyError:
temp = max(temp, b_st[el])
ans = max(ans, temp)
osn //= 2
k_ = set()
k_add = set()
for el in k_a:
if el >= osn:
try:
a_st[el - osn] += a_st[el]
except KeyError:
a_st[el - osn] = a_st[el]
finally:
del a_st[el]
k_add.add(el - osn)
k_.add(el)
for el in k_:
k_a.remove(el)
for el in k_add:
k_a.add(el)
k_ = set()
k_add = set()
for el in k_b:
if el >= osn:
try:
b_st[el - osn] += b_st[el]
except KeyError:
b_st[el - osn] = b_st[el]
finally:
del b_st[el]
k_add.add(el - osn)
k_.add(el)
for el in k_:
k_b.remove(el)
for el in k_add:
k_b.add(el)
print(ans)
|
{
"input": [
"3 1\n1 5 6\n1 3\n3\n",
"6 94192\n0 134217728 268435456 402653184 536870912 671088640\n6 435192\n67108864 201326592 335544320 469762048 603979776 738197504\n",
"8 896753688\n106089702 120543561 161218905 447312211 764275096 764710792 813135974 841008065\n8 933908609\n20162935 104158090 483658135 499325847 728277205 735070694 855995285 879244384\n",
"8 492203512\n98566550 171717746 339893791 370819580 755813098 774632721 775762385 997216159\n8 780893623\n126572826 185519858 200153392 395703045 594904233 795104446 848860665 987834782\n",
"1 0\n268435456\n2 1\n0 536870912\n",
"22 369666\n1 9 17 25 33 41 49 57 65 73 81 89 97 105 113 121 129 137 145 153 161 169\n16 492689\n5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65\n",
"8 252920536\n244638831 495795451 571294469 608283654 824658394 848820488 889026403 989575878\n8 536603650\n173809980 459083932 618916368 671025009 824972497 845836688 910492805 996913393\n",
"1 1\n0\n1 2\n0\n",
"8 670286936\n388336854 391155719 408017710 459915835 583763838 598232267 651837043 677546042\n8 739744483\n77918488 346255845 684268992 706730425 729280923 764781472 851729309 960597662\n",
"2 32871\n0 268435456\n2 244027\n134217728 402653184\n",
"8 13637560\n75803938 118458082 578587112 599074426 675903899 825712388 835922815 876673516\n8 823205164\n54450960 552515514 586968563 590678437 611812464 705676588 725408561 901537037\n",
"8 553403064\n90389644 110886835 224843533 416499061 494331076 500074828 631337283 827633884\n8 657307279\n149565245 163218715 233843732 346670915 508274748 782271108 878164651 972834939\n",
"5 999999999\n999999996 999999997 999999998 999999999 1000000000\n5 1000000000\n999999996 999999997 999999998 999999999 1000000000\n",
"2 0\n0 2\n4 1000000000\n0 2 4 6\n",
"1 828613\n0\n1 951087\n268435456\n",
"1 1\n1\n1 2\n1\n",
"13 968288\n0 67108864 134217728 201326592 268435456 335544320 402653184 469762048 536870912 603979776 671088640 738197504 805306368\n13 986214\n33554432 100663296 167772160 234881024 301989888 369098752 436207616 503316480 570425344 637534208 704643072 771751936 838860800\n",
"8 136036664\n126269260 262156105 282965964 352160984 697058273 782155472 852153700 917928159\n8 683144774\n61397867 113538443 319336093 384894230 392472203 597064745 621785013 743973848\n",
"1 1\n1\n1 3\n1\n",
"8 314120088\n96023745 125339289 248259794 279673378 308309305 545296057 624420255 846280440\n8 567898834\n218919064 398609068 402104390 521955395 551024729 612549267 863097158 874451603\n",
"1 2\n1\n1 3\n1\n",
"8 369804408\n295549995 297155803 364413607 495086842 522088849 729029685 791692715 987594669\n8 773248229\n167810330 261639682 321080432 453152328 502142334 643215633 657539609 917625873\n",
"8 934901355\n37124098 77222116 138199181 249214100 487897674 738878092 880827398 954080351\n8 945722121\n54836744 340149103 518507628 534560545 659693096 807080067 837037908 971967276\n",
"1 100\n0\n1 200\n0\n",
"6 94192\n0 134217728 268435456 402653184 536870912 671088640\n6 304400\n67108864 201326592 335544320 469762048 603979776 738197504\n",
"8 896753688\n106089702 95007271 161218905 447312211 764275096 764710792 813135974 841008065\n8 933908609\n20162935 104158090 483658135 499325847 728277205 735070694 855995285 879244384\n",
"22 369666\n0 9 17 25 33 41 49 57 65 73 81 89 97 105 113 121 129 137 145 153 161 169\n16 492689\n5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65\n",
"1 0\n0\n1 2\n0\n",
"8 670286936\n388336854 391155719 408017710 459915835 583763838 598232267 651837043 798399870\n8 739744483\n77918488 346255845 684268992 706730425 729280923 764781472 851729309 960597662\n",
"2 32871\n0 268435456\n2 214962\n134217728 402653184\n",
"8 13637560\n80088332 118458082 578587112 599074426 675903899 825712388 835922815 876673516\n8 823205164\n54450960 552515514 586968563 590678437 611812464 705676588 725408561 901537037\n",
"5 999999999\n999999996 999999997 999999998 1797296095 1000000000\n5 1000000000\n999999996 999999997 999999998 999999999 1000000000\n",
"2 0\n0 2\n4 1000000000\n0 2 7 6\n",
"8 136036664\n126269260 262156105 282965964 352160984 697058273 782155472 852153700 917928159\n8 683144774\n61397867 113538443 319336093 717161104 392472203 597064745 621785013 743973848\n",
"22 369666\n0 9 17 25 33 41 49 57 65 73 81 89 97 105 113 121 129 137 192 153 161 169\n16 492689\n5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65\n",
"22 369666\n0 9 17 25 33 41 49 57 65 73 81 89 97 105 113 11 129 137 192 153 161 169\n16 492689\n5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65\n",
"8 492203512\n98566550 171717746 339893791 370819580 755813098 774632721 775762385 997216159\n8 780893623\n126572826 185519858 200153392 109887577 594904233 795104446 848860665 987834782\n",
"8 553403064\n90389644 110886835 224843533 416499061 494331076 500074828 631337283 827633884\n8 657307279\n149565245 18937496 233843732 346670915 508274748 782271108 878164651 972834939\n",
"1 233830\n0\n1 951087\n268435456\n",
"1 0\n1\n1 2\n1\n",
"1 1\n1\n1 5\n1\n",
"8 314120088\n96023745 125339289 248259794 279673378 308309305 545296057 624420255 846280440\n8 567898834\n218919064 398609068 402104390 521955395 551024729 786298857 863097158 874451603\n",
"8 369804408\n295549995 297155803 364413607 495086842 522088849 729029685 791692715 987594669\n8 773248229\n167810330 261639682 321080432 365120020 502142334 643215633 657539609 917625873\n",
"8 934901355\n37124098 77222116 138199181 249214100 487897674 738878092 880827398 954080351\n8 945722121\n54836744 481733079 518507628 534560545 659693096 807080067 837037908 971967276\n",
"1 100\n0\n1 240\n0\n",
"3 1\n0 5 6\n1 3\n3\n",
"8 896753688\n106089702 95007271 161218905 447312211 764275096 764710792 813135974 841008065\n8 976764948\n20162935 104158090 483658135 499325847 728277205 735070694 855995285 879244384\n",
"8 492203512\n98566550 171717746 78309140 370819580 755813098 774632721 775762385 997216159\n8 780893623\n126572826 185519858 200153392 109887577 594904233 795104446 848860665 987834782\n",
"8 701640840\n388336854 391155719 408017710 459915835 583763838 598232267 651837043 798399870\n8 739744483\n77918488 346255845 684268992 706730425 729280923 764781472 851729309 960597662\n",
"2 32871\n0 268435456\n2 120395\n134217728 402653184\n",
"8 13637560\n80088332 116345018 578587112 599074426 675903899 825712388 835922815 876673516\n8 823205164\n54450960 552515514 586968563 590678437 611812464 705676588 725408561 901537037\n",
"8 553403064\n90389644 110886835 224843533 416499061 494331076 500074828 631337283 827633884\n8 657307279\n149565245 18937496 352622862 346670915 508274748 782271108 878164651 972834939\n",
"2 0\n0 2\n4 1000000000\n0 2 9 6\n",
"1 233830\n1\n1 951087\n268435456\n",
"1 -1\n1\n1 2\n1\n",
"8 136036664\n126269260 262156105 282965964 352160984 697058273 782155472 852153700 927769559\n8 683144774\n61397867 113538443 319336093 717161104 392472203 597064745 621785013 743973848\n",
"1 1\n1\n1 10\n1\n",
"8 314120088\n96023745 125339289 159261109 279673378 308309305 545296057 624420255 846280440\n8 567898834\n218919064 398609068 402104390 521955395 551024729 786298857 863097158 874451603\n",
"8 369804408\n295549995 297155803 530254556 495086842 522088849 729029685 791692715 987594669\n8 773248229\n167810330 261639682 321080432 365120020 502142334 643215633 657539609 917625873\n",
"8 934901355\n37124098 77222116 138199181 249214100 487897674 738878092 880827398 954080351\n8 945722121\n54836744 481733079 518507628 534560545 169210124 807080067 837037908 971967276\n",
"1 100\n0\n1 240\n1\n",
"3 1\n0 5 6\n1 3\n1\n",
"8 701640840\n388336854 391155719 408017710 459915835 583763838 598232267 651837043 412481814\n8 739744483\n77918488 346255845 684268992 706730425 729280923 764781472 851729309 960597662\n",
"2 25175\n0 268435456\n2 120395\n134217728 402653184\n",
"2 0\n0 2\n4 1000000000\n0 2 13 6\n",
"1 -1\n1\n1 4\n1\n",
"8 934901355\n37124098 77222116 138199181 249214100 487897674 738878092 880827398 31313517\n8 945722121\n54836744 481733079 518507628 534560545 169210124 807080067 837037908 971967276\n",
"1 000\n0\n1 240\n1\n",
"3 2\n0 5 6\n1 3\n1\n",
"22 369666\n0 9 17 25 33 41 49 57 65 73 81 89 97 105 113 11 129 137 192 153 161 169\n16 492689\n5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 74\n",
"8 1627911835\n37124098 77222116 138199181 249214100 487897674 738878092 880827398 31313517\n8 945722121\n54836744 481733079 518507628 534560545 169210124 807080067 837037908 971967276\n",
"8 1627911835\n37124098 77222116 138199181 249214100 487897674 738878092 880827398 31313517\n7 945722121\n54836744 481733079 518507628 534560545 169210124 807080067 837037908 971967276\n",
"6 94192\n0 134217728 268435456 402653184 536870912 1056090181\n6 435192\n67108864 201326592 335544320 469762048 603979776 738197504\n",
"8 896753688\n106089702 120543561 161218905 447312211 764275096 764710792 813135974 841008065\n8 856057048\n20162935 104158090 483658135 499325847 728277205 735070694 855995285 879244384\n",
"8 492203512\n98566550 313003560 339893791 370819580 755813098 774632721 775762385 997216159\n8 780893623\n126572826 185519858 200153392 395703045 594904233 795104446 848860665 987834782\n",
"22 369666\n1 9 17 25 33 41 49 86 65 73 81 89 97 105 113 121 129 137 145 153 161 169\n16 492689\n5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65\n"
],
"output": [
"3\n",
"12\n",
"9\n",
"9\n",
"3\n",
"30\n",
"8\n",
"2\n",
"8\n",
"4\n",
"10\n",
"9\n",
"5\n",
"4\n",
"2\n",
"2\n",
"26\n",
"11\n",
"2\n",
"9\n",
"2\n",
"12\n",
"9\n",
"2\n",
"12\n",
"9\n",
"29\n",
"2\n",
"8\n",
"4\n",
"10\n",
"5\n",
"3\n",
"11\n",
"28\n",
"27\n",
"9\n",
"8\n",
"2\n",
"2\n",
"2\n",
"9\n",
"12\n",
"9\n",
"2\n",
"3\n",
"9\n",
"8\n",
"8\n",
"4\n",
"10\n",
"8\n",
"3\n",
"2\n",
"2\n",
"11\n",
"2\n",
"10\n",
"11\n",
"9\n",
"2\n",
"3\n",
"8\n",
"4\n",
"3\n",
"2\n",
"9\n",
"2\n",
"3\n",
"27\n",
"9\n",
"9\n",
"11\n",
"9\n",
"9\n",
"29\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You are given a tube which is reflective inside represented as two non-coinciding, but parallel to Ox lines. Each line has some special integer points — positions of sensors on sides of the tube.
You are going to emit a laser ray in the tube. To do so, you have to choose two integer points A and B on the first and the second line respectively (coordinates can be negative): the point A is responsible for the position of the laser, and the point B — for the direction of the laser ray. The laser ray is a ray starting at A and directed at B which will reflect from the sides of the tube (it doesn't matter if there are any sensors at a reflection point or not). A sensor will only register the ray if the ray hits exactly at the position of the sensor.
<image> Examples of laser rays. Note that image contains two examples. The 3 sensors (denoted by black bold points on the tube sides) will register the blue ray but only 2 will register the red.
Calculate the maximum number of sensors which can register your ray if you choose points A and B on the first and the second lines respectively.
Input
The first line contains two integers n and y_1 (1 ≤ n ≤ 10^5, 0 ≤ y_1 ≤ 10^9) — number of sensors on the first line and its y coordinate.
The second line contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ 10^9) — x coordinates of the sensors on the first line in the ascending order.
The third line contains two integers m and y_2 (1 ≤ m ≤ 10^5, y_1 < y_2 ≤ 10^9) — number of sensors on the second line and its y coordinate.
The fourth line contains m integers b_1, b_2, …, b_m (0 ≤ b_i ≤ 10^9) — x coordinates of the sensors on the second line in the ascending order.
Output
Print the only integer — the maximum number of sensors which can register the ray.
Example
Input
3 1
1 5 6
1 3
3
Output
3
Note
One of the solutions illustrated on the image by pair A_2 and B_2.
### Input:
3 1
1 5 6
1 3
3
### Output:
3
### Input:
6 94192
0 134217728 268435456 402653184 536870912 671088640
6 435192
67108864 201326592 335544320 469762048 603979776 738197504
### Output:
12
### Code:
n, y1 = map(int, input().split())
a = list(map(int, input().split()))
m, y2 = map(int, input().split())
b = list(map(int, input().split()))
a_st, b_st = dict(), dict()
osn = 2 ** 30
k_a, k_b = set(), set()
for el in a:
try:
a_st[el % osn] += 1
except KeyError:
a_st[el % osn] = 1
finally:
k_a.add(el % osn)
for el in b:
try:
b_st[el % osn] += 1
except KeyError:
b_st[el % osn] = 1
finally:
k_b.add(el % osn)
ans = 2
for i in range(1, 31)[::-1]:
temp = 0
for el in k_a:
try:
temp = max(temp, a_st[el] + b_st[(el + osn // 2) % osn])
except KeyError:
temp = max(temp, a_st[el])
for el in k_b:
try:
temp = max(temp, b_st[el] + a_st[(el + osn // 2) % osn])
except KeyError:
temp = max(temp, b_st[el])
ans = max(ans, temp)
osn //= 2
k_ = set()
k_add = set()
for el in k_a:
if el >= osn:
try:
a_st[el - osn] += a_st[el]
except KeyError:
a_st[el - osn] = a_st[el]
finally:
del a_st[el]
k_add.add(el - osn)
k_.add(el)
for el in k_:
k_a.remove(el)
for el in k_add:
k_a.add(el)
k_ = set()
k_add = set()
for el in k_b:
if el >= osn:
try:
b_st[el - osn] += b_st[el]
except KeyError:
b_st[el - osn] = b_st[el]
finally:
del b_st[el]
k_add.add(el - osn)
k_.add(el)
for el in k_:
k_b.remove(el)
for el in k_add:
k_b.add(el)
print(ans)
|
1106_C. Lunar New Year and Number Division_10772
|
Lunar New Year is approaching, and Bob is struggling with his homework – a number division problem.
There are n positive integers a_1, a_2, …, a_n on Bob's homework paper, where n is always an even number. Bob is asked to divide those numbers into groups, where each group must contain at least 2 numbers. Suppose the numbers are divided into m groups, and the sum of the numbers in the j-th group is s_j. Bob's aim is to minimize the sum of the square of s_j, that is $$$∑_{j = 1}^{m} s_j^2.$$$
Bob is puzzled by this hard problem. Could you please help him solve it?
Input
The first line contains an even integer n (2 ≤ n ≤ 3 ⋅ 10^5), denoting that there are n integers on Bob's homework paper.
The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^4), describing the numbers you need to deal with.
Output
A single line containing one integer, denoting the minimum of the sum of the square of s_j, which is $$$∑_{i = j}^{m} s_j^2, where m$$$ is the number of groups.
Examples
Input
4
8 5 2 3
Output
164
Input
6
1 1 1 2 2 2
Output
27
Note
In the first sample, one of the optimal solutions is to divide those 4 numbers into 2 groups \{2, 8\}, \{5, 3\}. Thus the answer is (2 + 8)^2 + (5 + 3)^2 = 164.
In the second sample, one of the optimal solutions is to divide those 6 numbers into 3 groups \{1, 2\}, \{1, 2\}, \{1, 2\}. Thus the answer is (1 + 2)^2 + (1 + 2)^2 + (1 + 2)^2 = 27.
|
n = int(input())
a = [int(s) for s in input().split(" ")]
a.sort()
ans = 0
for i in range(n//2):
ans += (a[i]+a[n-i-1])**2
print(ans)
|
{
"input": [
"6\n1 1 1 2 2 2\n",
"4\n8 5 2 3\n",
"100\n28 27 23 6 23 11 25 20 28 15 29 23 20 2 8 24 8 9 30 8 8 1 11 7 6 17 17 27 26 30 12 22 17 22 9 25 4 26 9 26 10 30 13 4 16 12 23 19 10 22 12 20 3 16 10 4 29 11 15 4 5 7 29 16 3 1 7 16 26 14 28 1 15 19 30 28 5 22 14 28 13 12 11 30 3 4 7 10 22 8 4 10 22 12 17 27 23 11 18 7\n",
"4\n10000 10000 10000 10000\n",
"50\n9 16 3 3 12 2 9 13 6 11 18 15 6 20 14 13 20 5 19 4 10 2 10 19 20 3 15 3 9 1 9 4 16 3 19 14 12 13 12 5 9 16 4 1 8 20 8 2 11 5\n",
"8\n726 372 2425 5063 3153 1702 1658 4692\n",
"2\n4556 1770\n",
"50\n1321 1464 2036 1106 9084 9681 8004 2941 4653 6863 3870 6695 6163 7996 7749 2372 7339 9621 6688 3083 4373 2443 3513 296 4119 5189 5183 1532 5352 2733 3573 3528 4854 9807 2817 3830 8785 3229 9886 736 5389 733 394 55 2820 9417 2744 1517 7778 1118\n",
"4\n9540 7069 4914 2241\n",
"2\n1 1\n",
"10\n2978 1695 4979 2943 3114 9622 3446 4871 8308 5427\n",
"6\n7229 5073 766 748 4111 3544\n",
"2\n10000 10000\n",
"20\n8 10 10 1 1 5 9 2 1 5 4 3 4 4 2 10 3 9 9 4\n",
"100\n28 27 23 6 23 11 25 20 28 15 29 23 20 2 8 24 8 9 30 8 8 1 11 7 6 17 17 27 26 30 12 22 17 22 9 25 4 26 9 26 10 30 13 4 16 12 23 19 10 22 12 20 3 16 10 4 29 11 15 4 5 7 29 16 3 1 7 16 26 14 28 1 15 19 10 28 5 22 14 28 13 12 11 30 3 4 7 10 22 8 4 10 22 12 17 27 23 11 18 7\n",
"4\n10000 10100 10000 10000\n",
"50\n9 16 3 3 12 2 9 13 6 11 18 15 6 20 14 25 20 5 19 4 10 2 10 19 20 3 15 3 9 1 9 4 16 3 19 14 12 13 12 5 9 16 4 1 8 20 8 2 11 5\n",
"8\n726 372 2425 5063 3153 3061 1658 4692\n",
"2\n6582 1770\n",
"50\n1321 1464 2036 1106 9084 9681 8004 2941 4653 6863 3870 6695 6163 7996 7749 2372 7339 9621 6688 3083 4373 2443 3513 296 4119 5189 5183 1532 5352 2733 3573 3528 2356 9807 2817 3830 8785 3229 9886 736 5389 733 394 55 2820 9417 2744 1517 7778 1118\n",
"4\n9540 7069 3734 2241\n",
"2\n2 1\n",
"10\n2978 1695 4979 2943 3114 9622 3446 4511 8308 5427\n",
"6\n9449 5073 766 748 4111 3544\n",
"2\n10001 10000\n",
"20\n8 10 10 1 1 5 9 2 1 5 4 3 4 4 2 10 3 9 9 5\n",
"6\n0 1 1 2 2 2\n",
"4\n8 7 2 3\n",
"100\n28 27 23 6 23 11 25 20 28 15 29 23 20 2 8 24 8 9 30 8 8 1 11 7 6 17 17 27 26 30 12 22 17 22 9 25 4 26 9 26 10 30 13 4 16 12 23 19 10 22 12 20 3 16 10 4 29 11 15 4 5 7 29 16 3 1 1 16 26 14 28 1 15 19 10 28 5 22 14 28 13 12 11 30 3 4 7 10 22 8 4 10 22 12 17 27 23 11 18 7\n",
"4\n10000 10100 00000 10000\n",
"50\n9 16 3 3 12 2 9 13 6 11 18 15 6 20 14 25 20 5 19 4 10 2 10 19 20 3 15 3 9 1 9 4 16 3 19 14 12 13 12 5 9 16 4 1 8 20 8 3 11 5\n",
"8\n726 372 2425 5063 3153 3061 1658 8197\n",
"2\n6582 477\n",
"50\n1321 1464 2036 1106 9084 9681 8004 3683 4653 6863 3870 6695 6163 7996 7749 2372 7339 9621 6688 3083 4373 2443 3513 296 4119 5189 5183 1532 5352 2733 3573 3528 2356 9807 2817 3830 8785 3229 9886 736 5389 733 394 55 2820 9417 2744 1517 7778 1118\n",
"4\n17070 7069 3734 2241\n",
"2\n2 0\n",
"10\n2448 1695 4979 2943 3114 9622 3446 4511 8308 5427\n",
"6\n9449 5073 766 287 4111 3544\n",
"2\n00001 10000\n",
"20\n8 8 10 1 1 5 9 2 1 5 4 3 4 4 2 10 3 9 9 5\n",
"6\n0 1 1 2 2 4\n",
"4\n8 7 2 1\n",
"100\n28 27 23 6 23 11 25 20 28 15 29 23 20 2 8 24 8 9 30 8 8 1 11 7 6 17 17 27 26 30 12 22 17 22 9 25 4 26 9 26 10 30 13 4 16 12 23 19 10 22 12 20 3 16 10 4 29 11 15 4 5 7 29 16 3 1 1 16 26 14 28 1 15 19 10 28 5 22 14 28 13 12 11 30 3 4 7 10 22 8 4 10 22 12 17 27 23 11 36 7\n",
"4\n10000 10100 00000 11000\n",
"8\n726 372 2425 5063 4331 3061 1658 8197\n",
"2\n6582 75\n",
"50\n1321 1464 2036 1106 9084 9681 8004 3683 4653 6863 3870 6695 6163 7996 7749 2372 7339 9621 6688 3083 4373 2443 3513 296 4119 5189 5183 1532 5352 2733 3573 3528 2356 9807 2817 3830 8785 3229 9886 736 5740 733 394 55 2820 9417 2744 1517 7778 1118\n",
"4\n6699 7069 3734 2241\n",
"2\n0 0\n",
"10\n2448 1695 4979 2943 3114 9622 785 4511 8308 5427\n",
"6\n9449 9695 766 287 4111 3544\n",
"2\n00011 10000\n",
"20\n8 8 9 1 1 5 9 2 1 5 4 3 4 4 2 10 3 9 9 5\n",
"6\n0 1 0 2 2 4\n",
"4\n8 10 2 1\n",
"100\n28 27 23 6 23 11 25 20 28 15 29 23 20 2 8 24 8 9 30 8 8 1 11 7 6 17 17 27 26 30 12 22 17 22 9 25 4 26 9 26 10 30 13 4 16 12 23 19 10 22 12 20 6 16 10 4 29 11 15 4 5 7 29 16 3 1 1 16 26 14 28 1 15 19 10 28 5 22 14 28 13 12 11 30 3 4 7 10 22 8 4 10 22 12 17 27 23 11 36 7\n",
"4\n10001 10100 00000 11000\n",
"50\n9 16 3 3 12 2 9 13 6 11 18 15 6 20 14 25 20 5 19 4 10 2 10 19 20 0 15 3 9 1 9 4 16 3 19 14 12 13 12 5 9 16 4 1 8 20 8 3 11 5\n",
"8\n726 372 2425 5063 4331 3061 1658 432\n",
"2\n6582 28\n",
"50\n1321 1464 2036 1106 9084 9681 8004 3683 4653 6863 3870 6695 6163 7996 7749 2372 7339 9621 6688 5457 4373 2443 3513 296 4119 5189 5183 1532 5352 2733 3573 3528 2356 9807 2817 3830 8785 3229 9886 736 5740 733 394 55 2820 9417 2744 1517 7778 1118\n",
"4\n9840 7069 3734 2241\n",
"10\n2448 1695 4979 2943 3114 667 785 4511 8308 5427\n",
"6\n9449 4179 766 287 4111 3544\n",
"2\n00011 11000\n",
"20\n8 8 9 1 1 2 9 2 1 5 4 3 4 4 2 10 3 9 9 5\n",
"4\n8 10 4 1\n",
"100\n28 27 23 6 23 11 25 20 28 15 29 23 20 2 8 24 8 9 30 8 8 1 11 7 6 17 17 27 26 30 12 22 17 22 9 25 4 26 9 26 10 30 13 4 16 12 23 19 10 22 12 20 6 16 10 4 29 11 15 4 5 7 29 16 3 1 1 16 26 14 28 1 15 19 2 28 5 22 14 28 13 12 11 30 3 4 7 10 22 8 4 10 22 12 17 27 23 11 36 7\n",
"4\n10001 10100 00100 11000\n",
"50\n9 16 3 3 12 2 9 13 6 11 18 15 6 20 14 25 20 5 19 4 10 2 10 19 32 0 15 3 9 1 9 4 16 3 19 14 12 13 12 5 9 16 4 1 8 20 8 3 11 5\n",
"8\n229 372 2425 5063 4331 3061 1658 432\n",
"2\n1203 28\n",
"50\n1321 1464 2036 1106 9084 9681 8004 3683 4653 6863 3870 6695 6163 7996 7749 2372 1586 9621 6688 5457 4373 2443 3513 296 4119 5189 5183 1532 5352 2733 3573 3528 2356 9807 2817 3830 8785 3229 9886 736 5740 733 394 55 2820 9417 2744 1517 7778 1118\n",
"4\n9840 7069 3156 2241\n",
"10\n2448 1695 4979 2943 3114 667 785 4511 16045 5427\n",
"6\n9449 4179 766 287 6742 3544\n",
"2\n10011 11000\n",
"20\n8 8 9 1 1 2 9 2 1 2 4 3 4 4 2 10 3 9 9 5\n",
"6\n0 2 0 2 2 0\n",
"4\n8 10 6 1\n",
"100\n28 27 23 6 23 11 25 20 28 15 29 23 20 2 8 24 8 9 30 8 8 1 11 7 6 17 17 27 26 30 12 22 17 22 9 25 4 26 9 26 10 30 13 4 16 12 23 19 10 22 12 20 6 16 10 4 29 11 15 4 5 0 29 16 3 1 1 16 26 14 28 1 15 19 2 28 5 22 14 28 13 12 11 30 3 4 7 10 22 8 4 10 22 12 17 27 23 11 36 7\n",
"4\n00001 10100 00100 11000\n",
"50\n9 16 3 3 12 2 9 13 6 11 18 15 6 20 14 25 20 5 19 4 10 2 10 19 32 0 15 3 9 1 9 4 16 3 19 14 12 13 12 5 9 16 4 1 8 20 8 3 11 6\n",
"8\n229 372 3182 5063 4331 3061 1658 432\n",
"2\n1203 34\n",
"50\n1321 1464 2036 1106 9084 9681 8004 3683 4653 6863 3870 6695 6163 7996 7749 2372 1586 9621 6688 5457 4373 2443 3513 296 4119 5189 5183 1532 5352 2733 3573 3528 2356 9807 2817 3830 10006 3229 9886 736 5740 733 394 55 2820 9417 2744 1517 7778 1118\n",
"4\n9840 7069 535 2241\n",
"10\n2448 1695 4979 2943 1811 667 785 4511 16045 5427\n",
"6\n9449 7732 766 287 6742 3544\n",
"2\n10011 10000\n",
"20\n8 8 9 1 1 2 4 2 1 2 4 3 4 4 2 10 3 9 9 5\n",
"6\n0 2 0 3 2 0\n",
"4\n8 10 5 1\n",
"100\n28 27 23 6 23 11 25 20 28 15 29 23 20 2 8 24 8 9 30 8 8 1 11 7 4 17 17 27 26 30 12 22 17 22 9 25 4 26 9 26 10 30 13 4 16 12 23 19 10 22 12 20 6 16 10 4 29 11 15 4 5 0 29 16 3 1 1 16 26 14 28 1 15 19 2 28 5 22 14 28 13 12 11 30 3 4 7 10 22 8 4 10 22 12 17 27 23 11 36 7\n",
"4\n00001 11100 00100 11000\n",
"50\n9 16 3 3 12 2 7 13 6 11 18 15 6 20 14 25 20 5 19 4 10 2 10 19 32 0 15 3 9 1 9 4 16 3 19 14 12 13 12 5 9 16 4 1 8 20 8 3 11 6\n",
"8\n229 372 3972 5063 4331 3061 1658 432\n",
"2\n669 34\n",
"50\n1321 1464 2036 1106 9084 9681 8004 3683 4653 6863 3870 6695 6163 7996 7749 2372 1586 9621 6688 5457 4373 2443 3513 296 4119 5189 5183 1532 4354 2733 3573 3528 2356 9807 2817 3830 10006 3229 9886 736 5740 733 394 55 2820 9417 2744 1517 7778 1118\n",
"4\n8694 7069 535 2241\n",
"10\n2448 1695 2199 2943 1811 667 785 4511 16045 5427\n",
"6\n9449 7732 766 287 6074 3544\n",
"2\n10011 10010\n",
"20\n8 8 9 1 1 2 4 2 1 2 4 3 4 4 2 10 3 0 9 5\n",
"4\n8 10 5 0\n",
"100\n28 27 23 6 23 11 25 20 28 15 29 23 20 2 8 24 8 9 30 8 8 1 11 7 4 17 17 27 26 30 12 22 17 22 9 25 4 26 9 46 10 30 13 4 16 12 23 19 10 22 12 20 6 16 10 4 29 11 15 4 5 0 29 16 3 1 1 16 26 14 28 1 15 19 2 28 5 22 14 28 13 12 11 30 3 4 7 10 22 8 4 10 22 12 17 27 23 11 36 7\n",
"4\n00000 10100 00100 11000\n",
"50\n9 16 3 3 12 2 7 13 6 11 18 15 6 20 14 25 20 5 19 4 10 2 10 19 32 0 15 3 9 1 9 4 16 3 19 14 12 13 12 5 9 16 4 1 8 20 12 3 11 6\n",
"8\n229 372 3972 5063 4331 3061 919 432\n",
"2\n669 52\n",
"50\n1321 1464 2036 1106 9084 9681 8004 3683 4653 6863 3870 6695 6163 7996 7749 2372 1586 9621 6688 5457 4373 2443 3513 296 4119 5189 5183 1532 4354 2733 3573 3528 2356 9807 2817 3830 10006 3229 9886 736 5740 733 394 55 2820 9417 5169 1517 7778 1118\n",
"4\n8694 7069 535 4319\n",
"10\n2448 1695 2199 2943 1811 667 785 4511 16045 555\n",
"6\n9449 7732 1236 287 6074 3544\n"
],
"output": [
"27\n",
"164\n",
"48573\n",
"800000000\n",
"10075\n",
"99071799\n",
"40018276\n",
"2069788730\n",
"282384250\n",
"4\n",
"459972653\n",
"156325475\n",
"400000000\n",
"1096\n",
"47353\n",
"804010000\n",
"10591\n",
"112135866\n",
"69755904\n",
"2029620256\n",
"255496770\n",
"9\n",
"454114013\n",
"196671755\n",
"400040001\n",
"1113\n",
"22\n",
"200\n",
"46973\n",
"502010000\n",
"10636\n",
"160182199\n",
"49829481\n",
"2041164246\n",
"489619530\n",
"4\n",
"442633423\n",
"187482642\n",
"100020001\n",
"1069\n",
"34\n",
"162\n",
"48131\n",
"525010000\n",
"172904599\n",
"44315649\n",
"2046996813\n",
"195523589\n",
"0\n",
"391279992\n",
"262585574\n",
"100220121\n",
"1048\n",
"29\n",
"221\n",
"48324\n",
"525050201\n",
"10497\n",
"83237652\n",
"43692100\n",
"2085111149\n",
"262655370\n",
"248796775\n",
"177841746\n",
"121242121\n",
"993\n",
"265\n",
"47814\n",
"527260201\n",
"11131\n",
"78995411\n",
"1515361\n",
"1988193080\n",
"250501186\n",
"447537094\n",
"210804489\n",
"441462121\n",
"940\n",
"12\n",
"317\n",
"47361\n",
"225062001\n",
"11170\n",
"85453430\n",
"1530169\n",
"2013089555\n",
"194316725\n",
"431452729\n",
"272807496\n",
"400440121\n",
"853\n",
"17\n",
"290\n",
"47235\n",
"246442201\n",
"11090\n",
"91787650\n",
"494209\n",
"1997543685\n",
"171850541\n",
"400589449\n",
"259511624\n",
"400840441\n",
"700\n",
"269\n",
"48715\n",
"225040000\n",
"11250\n",
"85359089\n",
"519841\n",
"2035543686\n",
"214860985\n",
"349514217\n",
"267720644\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Lunar New Year is approaching, and Bob is struggling with his homework – a number division problem.
There are n positive integers a_1, a_2, …, a_n on Bob's homework paper, where n is always an even number. Bob is asked to divide those numbers into groups, where each group must contain at least 2 numbers. Suppose the numbers are divided into m groups, and the sum of the numbers in the j-th group is s_j. Bob's aim is to minimize the sum of the square of s_j, that is $$$∑_{j = 1}^{m} s_j^2.$$$
Bob is puzzled by this hard problem. Could you please help him solve it?
Input
The first line contains an even integer n (2 ≤ n ≤ 3 ⋅ 10^5), denoting that there are n integers on Bob's homework paper.
The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^4), describing the numbers you need to deal with.
Output
A single line containing one integer, denoting the minimum of the sum of the square of s_j, which is $$$∑_{i = j}^{m} s_j^2, where m$$$ is the number of groups.
Examples
Input
4
8 5 2 3
Output
164
Input
6
1 1 1 2 2 2
Output
27
Note
In the first sample, one of the optimal solutions is to divide those 4 numbers into 2 groups \{2, 8\}, \{5, 3\}. Thus the answer is (2 + 8)^2 + (5 + 3)^2 = 164.
In the second sample, one of the optimal solutions is to divide those 6 numbers into 3 groups \{1, 2\}, \{1, 2\}, \{1, 2\}. Thus the answer is (1 + 2)^2 + (1 + 2)^2 + (1 + 2)^2 = 27.
### Input:
6
1 1 1 2 2 2
### Output:
27
### Input:
4
8 5 2 3
### Output:
164
### Code:
n = int(input())
a = [int(s) for s in input().split(" ")]
a.sort()
ans = 0
for i in range(n//2):
ans += (a[i]+a[n-i-1])**2
print(ans)
|
1133_D. Zero Quantity Maximization_10776
|
You are given two arrays a and b, each contains n integers.
You want to create a new array c as follows: choose some real (i.e. not necessarily integer) number d, and then for every i ∈ [1, n] let c_i := d ⋅ a_i + b_i.
Your goal is to maximize the number of zeroes in array c. What is the largest possible answer, if you choose d optimally?
Input
The first line contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the number of elements in both arrays.
The second line contains n integers a_1, a_2, ..., a_n (-10^9 ≤ a_i ≤ 10^9).
The third line contains n integers b_1, b_2, ..., b_n (-10^9 ≤ b_i ≤ 10^9).
Output
Print one integer — the maximum number of zeroes in array c, if you choose d optimally.
Examples
Input
5
1 2 3 4 5
2 4 7 11 3
Output
2
Input
3
13 37 39
1 2 3
Output
2
Input
4
0 0 0 0
1 2 3 4
Output
0
Input
3
1 2 -1
-6 -12 6
Output
3
Note
In the first example, we may choose d = -2.
In the second example, we may choose d = -1/13.
In the third example, we cannot obtain any zero in array c, no matter which d we choose.
In the fourth example, we may choose d = 6.
|
from fractions import Fraction
n = int(input())
A = list(map(int, input().split()))
B = list(map(int, input().split()))
count = {}
ans = 0
zeros = 0
for i in range(n):
if A[i] == 0 and B[i] != 0:
continue
elif A[i] == 0 and B[i] == 0:
zeros += 1
else:
temp = Fraction(abs(B[i]), abs(A[i]))
if A[i] > 0 and B[i] > 0:
temp *= -1
elif A[i] < 0 and B[i] < 0:
temp *= -1
temp = str(temp)
if temp not in count:
count[temp] = 1
else:
count[temp] += 1
ans = max(ans, count[temp])
print(ans + zeros)
# for i in range(n):
# if A[i] == 0 and B[i] != 0:
# continue
# elif A[i] == 0 and B[i] == 0:
# temp = 0
# else:
# temp = Fraction(abs(B[i]), abs(A[i]))
# if A[i] > 0 and B[i] < 0:
# pass
# elif A[i] < 0 and B[i] < 0:
# temp *= -1
# elif A[i] > 0 and B[i] > 0:
# temp *= -1
# elif A[i] > 0 and B[i] < 0:
# pass
# temp = str(temp)
# if temp not in count:
# count[temp] = 1
# else:
# count[temp] += 1
# ans = max(ans, count[temp])
|
{
"input": [
"4\n0 0 0 0\n1 2 3 4\n",
"5\n1 2 3 4 5\n2 4 7 11 3\n",
"3\n13 37 39\n1 2 3\n",
"3\n1 2 -1\n-6 -12 6\n",
"5\n-2 2 1 0 2\n0 0 2 -1 -2\n",
"4\n0 1 2 3\n0 0 0 3\n",
"2\n0 1000000000\n0 0\n",
"3\n999999999 999999998 999999999\n999999998 999999997 999999998\n",
"2\n0 0\n0 0\n",
"2\n999999999 1000000000\n999999998 999999999\n",
"3\n0 5 7\n0 10 13\n",
"14\n1 1 1 1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
"2\n1 13\n1 3\n",
"5\n-999999999 999999999 999999999 999999998 -999999999\n-999999999 -1000000000 -1000000000 -999999999 1000000000\n",
"2\n999999998 999999999\n999999999 1000000000\n",
"5\n-2 2 1 0 2\n0 0 2 -1 -4\n",
"4\n0 1 2 3\n0 0 0 6\n",
"2\n999999999 1000001000\n999999998 999999999\n",
"14\n1 2 1 1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
"14\n1 2 1 1 1 1 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1 1 0 1\n",
"14\n1 2 1 1 1 2 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1 1 0 1\n",
"14\n2 2 1 1 1 2 1 1 1 1 1 1 1 1\n1 1 1 1 1 1 1 1 1 1 1 1 0 1\n",
"14\n2 2 1 1 1 2 1 1 1 1 1 1 1 1\n1 1 2 1 1 1 1 1 1 1 1 1 0 1\n",
"2\n0 1000000100\n0 0\n",
"3\n999999999 999999998 999999999\n999999998 523253279 999999998\n",
"2\n0 1\n0 0\n",
"3\n0 5 5\n0 10 13\n",
"2\n1 13\n1 0\n",
"5\n-999999999 999999999 1252085585 999999998 -999999999\n-999999999 -1000000000 -1000000000 -999999999 1000000000\n",
"2\n999999998 999999999\n928229923 1000000000\n",
"4\n1 0 0 0\n1 2 3 4\n",
"5\n1 2 3 4 5\n2 4 7 9 3\n",
"3\n13 37 37\n1 2 3\n",
"3\n1 2 -1\n-6 -10 6\n",
"5\n-2 2 1 0 0\n0 0 2 -1 -4\n",
"4\n0 1 2 3\n1 0 0 6\n",
"2\n0 1000000100\n0 -1\n",
"3\n999999999 999999998 999999999\n999999998 523253279 99403329\n",
"2\n0 1\n1 0\n",
"2\n831730402 1000001000\n999999998 999999999\n",
"3\n0 5 5\n0 10 18\n",
"2\n1 13\n2 0\n",
"5\n-999999999 999999999 1252085585 999999998 -414067761\n-999999999 -1000000000 -1000000000 -999999999 1000000000\n",
"2\n999999998 999999999\n769727702 1000000000\n",
"4\n1 0 0 0\n1 2 3 2\n",
"5\n1 2 3 8 5\n2 4 7 9 3\n",
"3\n13 47 37\n1 2 3\n",
"3\n1 2 -1\n-6 -1 6\n",
"5\n-2 2 1 0 0\n0 1 2 -1 -4\n",
"4\n0 0 2 3\n1 0 0 6\n",
"2\n0 1000010100\n0 -1\n",
"3\n999999999 999999998 999999999\n1603544893 523253279 99403329\n",
"2\n1 1\n1 0\n",
"2\n585720637 1000001000\n999999998 999999999\n",
"3\n0 5 7\n0 10 18\n",
"2\n0 13\n2 0\n",
"5\n-999999999 999999999 1252085585 999999998 -414067761\n-1011239935 -1000000000 -1000000000 -999999999 1000000000\n",
"2\n1727030919 999999999\n769727702 1000000000\n",
"4\n1 0 1 0\n1 2 3 2\n",
"5\n1 2 3 8 5\n2 4 7 9 6\n",
"3\n6 47 37\n1 2 3\n",
"3\n1 1 -1\n-6 -1 6\n",
"5\n-2 2 1 0 0\n0 1 3 -1 -4\n",
"4\n0 -1 2 3\n1 0 0 6\n",
"2\n0 0000010100\n0 -1\n",
"3\n999999999 999999998 999999999\n1603544893 886927161 99403329\n",
"2\n0 0\n-1 0\n",
"2\n963878744 1000001000\n999999998 999999999\n",
"3\n0 5 7\n0 8 18\n",
"2\n0 13\n4 0\n",
"5\n-999999999 999999999 1252085585 999999998 -414067761\n-1011239935 -1000000000 -1000000000 -999999999 1010000000\n",
"2\n1727030919 999999999\n769727702 1000010000\n",
"4\n1 0 2 0\n1 2 3 2\n",
"5\n1 2 3 8 5\n2 0 7 9 6\n",
"3\n3 47 37\n1 2 3\n",
"3\n1 1 -1\n-6 -2 6\n",
"5\n-2 2 1 0 0\n0 1 4 -1 -4\n",
"4\n0 -1 2 3\n1 0 -1 6\n",
"2\n0 0000010100\n1 -1\n",
"3\n999999999 999999998 999999999\n1603544893 50160751 99403329\n",
"2\n0 0\n-2 0\n",
"2\n907238052 1000001000\n999999998 999999999\n",
"3\n0 5 7\n-1 8 18\n",
"14\n2 2 1 1 1 2 1 1 1 1 1 1 1 1\n1 1 1 1 1 0 1 1 1 1 1 1 0 1\n",
"2\n0 13\n8 0\n",
"5\n-999999999 999999999 1252085585 999999998 -414067761\n-1011239935 -1000000000 -1000000000 -1397885361 1010000000\n",
"2\n1727030919 999999999\n1260882446 1000010000\n",
"4\n1 0 2 0\n1 3 3 2\n",
"5\n1 2 3 8 5\n2 1 7 9 6\n",
"3\n3 47 37\n1 2 4\n",
"3\n1 0 -1\n-6 -2 6\n",
"5\n-2 3 1 0 0\n0 1 4 -1 -4\n",
"4\n0 -2 2 3\n1 0 -1 6\n",
"2\n0 0000010100\n1 0\n",
"3\n999999999 999999998 1521845320\n1603544893 50160751 99403329\n",
"2\n0 0\n-4 0\n",
"2\n907238052 1000101000\n999999998 999999999\n",
"3\n0 3 7\n-1 8 18\n",
"2\n0 13\n8 1\n",
"5\n-999999999 999999999 1252085585 999999998 -421666581\n-1011239935 -1000000000 -1000000000 -1397885361 1010000000\n",
"2\n1727030919 187724555\n1260882446 1000010000\n"
],
"output": [
"0\n",
"2\n",
"2\n",
"3\n",
"2\n",
"3\n",
"2\n",
"2\n",
"2\n",
"1\n",
"2\n",
"14\n",
"1\n",
"3\n",
"1\n",
"2\n",
"3\n",
"1\n",
"13\n",
"12\n",
"11\n",
"10\n",
"9\n",
"2\n",
"2\n",
"2\n",
"2\n",
"1\n",
"2\n",
"1\n",
"1\n",
"2\n",
"1\n",
"2\n",
"2\n",
"2\n",
"2\n",
"1\n",
"1\n",
"1\n",
"2\n",
"1\n",
"1\n",
"1\n",
"1\n",
"2\n",
"1\n",
"2\n",
"1\n",
"2\n",
"2\n",
"1\n",
"1\n",
"1\n",
"2\n",
"1\n",
"1\n",
"1\n",
"1\n",
"2\n",
"1\n",
"2\n",
"1\n",
"2\n",
"2\n",
"1\n",
"1\n",
"1\n",
"2\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"2\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"10\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"2\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n",
"1\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You are given two arrays a and b, each contains n integers.
You want to create a new array c as follows: choose some real (i.e. not necessarily integer) number d, and then for every i ∈ [1, n] let c_i := d ⋅ a_i + b_i.
Your goal is to maximize the number of zeroes in array c. What is the largest possible answer, if you choose d optimally?
Input
The first line contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the number of elements in both arrays.
The second line contains n integers a_1, a_2, ..., a_n (-10^9 ≤ a_i ≤ 10^9).
The third line contains n integers b_1, b_2, ..., b_n (-10^9 ≤ b_i ≤ 10^9).
Output
Print one integer — the maximum number of zeroes in array c, if you choose d optimally.
Examples
Input
5
1 2 3 4 5
2 4 7 11 3
Output
2
Input
3
13 37 39
1 2 3
Output
2
Input
4
0 0 0 0
1 2 3 4
Output
0
Input
3
1 2 -1
-6 -12 6
Output
3
Note
In the first example, we may choose d = -2.
In the second example, we may choose d = -1/13.
In the third example, we cannot obtain any zero in array c, no matter which d we choose.
In the fourth example, we may choose d = 6.
### Input:
4
0 0 0 0
1 2 3 4
### Output:
0
### Input:
5
1 2 3 4 5
2 4 7 11 3
### Output:
2
### Code:
from fractions import Fraction
n = int(input())
A = list(map(int, input().split()))
B = list(map(int, input().split()))
count = {}
ans = 0
zeros = 0
for i in range(n):
if A[i] == 0 and B[i] != 0:
continue
elif A[i] == 0 and B[i] == 0:
zeros += 1
else:
temp = Fraction(abs(B[i]), abs(A[i]))
if A[i] > 0 and B[i] > 0:
temp *= -1
elif A[i] < 0 and B[i] < 0:
temp *= -1
temp = str(temp)
if temp not in count:
count[temp] = 1
else:
count[temp] += 1
ans = max(ans, count[temp])
print(ans + zeros)
# for i in range(n):
# if A[i] == 0 and B[i] != 0:
# continue
# elif A[i] == 0 and B[i] == 0:
# temp = 0
# else:
# temp = Fraction(abs(B[i]), abs(A[i]))
# if A[i] > 0 and B[i] < 0:
# pass
# elif A[i] < 0 and B[i] < 0:
# temp *= -1
# elif A[i] > 0 and B[i] > 0:
# temp *= -1
# elif A[i] > 0 and B[i] < 0:
# pass
# temp = str(temp)
# if temp not in count:
# count[temp] = 1
# else:
# count[temp] += 1
# ans = max(ans, count[temp])
|
1154_A. Restoring Three Numbers_10780
|
Polycarp has guessed three positive integers a, b and c. He keeps these numbers in secret, but he writes down four numbers on a board in arbitrary order — their pairwise sums (three numbers) and sum of all three numbers (one number). So, there are four numbers on a board in random order: a+b, a+c, b+c and a+b+c.
You have to guess three numbers a, b and c using given numbers. Print three guessed integers in any order.
Pay attention that some given numbers a, b and c can be equal (it is also possible that a=b=c).
Input
The only line of the input contains four positive integers x_1, x_2, x_3, x_4 (2 ≤ x_i ≤ 10^9) — numbers written on a board in random order. It is guaranteed that the answer exists for the given number x_1, x_2, x_3, x_4.
Output
Print such positive integers a, b and c that four numbers written on a board are values a+b, a+c, b+c and a+b+c written in some order. Print a, b and c in any order. If there are several answers, you can print any. It is guaranteed that the answer exists.
Examples
Input
3 6 5 4
Output
2 1 3
Input
40 40 40 60
Output
20 20 20
Input
201 101 101 200
Output
1 100 100
|
x,y,z,w = (int(i) for i in input().split())
s = (x+y+z+w)//3
for i in x,y,z,w:
temp = s - i
if s - i > 0:
print(s-i, end=' ')
|
{
"input": [
"40 40 40 60\n",
"201 101 101 200\n",
"3 6 5 4\n",
"500000000 500000001 999999999 1000000000\n",
"3 999999990 999999991 999999992\n",
"600000000 900000000 500000000 1000000000\n",
"1000000000 666666667 666666667 666666666\n",
"10101000 101000 10001000 10100000\n",
"2 2 3 2\n",
"3 6 5 4\n",
"3 3 5 4\n",
"4 6 7 4\n",
"3 4 5 6\n",
"198 101 101 200\n",
"3 7 5 6\n",
"40 70 40 60\n",
"3 4 3 2\n",
"2 4 5 4\n",
"4 6 4 4\n",
"206 101 111 200\n",
"3 6 8 7\n",
"4 5 7 8\n",
"4 6 6 8\n",
"3 5 3 4\n",
"3 5 6 4\n",
"4 6 4 7\n",
"3 2 3 4\n",
"6 3 5 4\n",
"4 4 6 4\n",
"4 7 6 4\n",
"3 3 2 4\n",
"3 6 5 7\n",
"7 6 4 4\n",
"3 4 3 5\n",
"3 4 5 3\n",
"3 4 2 3\n",
"5 3 6 4\n",
"6 4 4 4\n",
"6 7 4 4\n"
],
"output": [
"20 20 20\n",
"100 100 1 ",
"3 1 2\n",
"500000000 499999999 1 ",
"999999989 2 1 ",
"400000000 100000000 500000000\n",
"333333333 333333333 333333334\n",
"10000000 100000 1000 ",
"1 1 1\n",
"3 1 2\n",
"2 2 1\n",
"3 3 1\n",
"3 2 1\n",
"99 99 2\n",
"4 2 1\n",
"30 30 10\n",
"2 1 1\n",
"3 1 1\n",
"2 2 2\n",
"105 95 6\n",
"5 2 1\n",
"4 3 1\n",
"4 2 2\n",
"2 2 1\n",
"3 2 1\n",
"3 3 1\n",
"2 1 1\n",
"3 2 1\n",
"2 2 2\n",
"3 3 1\n",
"2 1 1\n",
"4 2 1\n",
"3 3 1\n",
"2 2 1\n",
"2 2 1\n",
"2 1 1\n",
"3 2 1\n",
"2 2 2\n",
"3 3 1\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Polycarp has guessed three positive integers a, b and c. He keeps these numbers in secret, but he writes down four numbers on a board in arbitrary order — their pairwise sums (three numbers) and sum of all three numbers (one number). So, there are four numbers on a board in random order: a+b, a+c, b+c and a+b+c.
You have to guess three numbers a, b and c using given numbers. Print three guessed integers in any order.
Pay attention that some given numbers a, b and c can be equal (it is also possible that a=b=c).
Input
The only line of the input contains four positive integers x_1, x_2, x_3, x_4 (2 ≤ x_i ≤ 10^9) — numbers written on a board in random order. It is guaranteed that the answer exists for the given number x_1, x_2, x_3, x_4.
Output
Print such positive integers a, b and c that four numbers written on a board are values a+b, a+c, b+c and a+b+c written in some order. Print a, b and c in any order. If there are several answers, you can print any. It is guaranteed that the answer exists.
Examples
Input
3 6 5 4
Output
2 1 3
Input
40 40 40 60
Output
20 20 20
Input
201 101 101 200
Output
1 100 100
### Input:
40 40 40 60
### Output:
20 20 20
### Input:
201 101 101 200
### Output:
100 100 1
### Code:
x,y,z,w = (int(i) for i in input().split())
s = (x+y+z+w)//3
for i in x,y,z,w:
temp = s - i
if s - i > 0:
print(s-i, end=' ')
|
1175_F. The Number of Subpermutations_10783
|
You have an array a_1, a_2, ..., a_n.
Let's call some subarray a_l, a_{l + 1}, ... , a_r of this array a subpermutation if it contains all integers from 1 to r-l+1 exactly once. For example, array a = [2, 2, 1, 3, 2, 3, 1] contains 6 subarrays which are subpermutations: [a_2 ... a_3], [a_2 ... a_4], [a_3 ... a_3], [a_3 ... a_5], [a_5 ... a_7], [a_7 ... a_7].
You are asked to calculate the number of subpermutations.
Input
The first line contains one integer n (1 ≤ n ≤ 3 ⋅ 10^5).
The second line contains n integers a_1, a_2, ... , a_n (1 ≤ a_i ≤ n).
This array can contain the same integers.
Output
Print the number of subpermutations of the array a.
Examples
Input
8
2 4 1 3 4 2 1 2
Output
7
Input
5
1 1 2 1 2
Output
6
Note
There are 7 subpermutations in the first test case. Their segments of indices are [1, 4], [3, 3], [3, 6], [4, 7], [6, 7], [7, 7] and [7, 8].
In the second test case 6 subpermutations exist: [1, 1], [2, 2], [2, 3], [3, 4], [4, 4] and [4, 5].
|
#import sys
import math
#input=sys.stdin.readline
#sys.setrecursionlimit(1000000)
mod=int(1000000007)
i=lambda :map(int,input().split())
n=int(input())
a=[int(x) for x in input().split()]
t=[[0]*21 for i in range(300005)]
for i in range(n):
t[i][0]=a[i]
def build(n):
for j in range(1,20):
for i in range(n):
if i+(1<<j)-1>n-1:
break;
t[i][j]=max(t[i][j-1],t[i+(1<<(j-1))][j-1])
def query(p,q):
p,q=int(p),int(q)
log=int(math.log2(q-p+1))
m=t[p][log]
n=t[q-(1<<log)+1][log]
return max(m,n)
b=[-1]*(n+2)
build(n)
max1=-1
ans=0
for i in range(n):
max1=max(max1,b[a[i]])
b[a[i]]=i
x=b[1]
while x>max1:
if x<=max1:
break
p=query(x,i)
if p==i-x+1:
ans+=1
x=b[p+1]
else:
x=i-p+1
print(ans)
|
{
"input": [
"8\n2 4 1 3 4 2 1 2\n",
"5\n1 1 2 1 2\n",
"98\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98\n",
"99\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99\n",
"99\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 6 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99\n",
"8\n2 4 1 3 4 3 1 2\n",
"8\n2 7 1 3 4 3 1 2\n",
"8\n2 8 2 3 4 3 1 2\n",
"98\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 61 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98\n",
"99\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 40 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99\n",
"8\n2 8 1 3 4 6 1 2\n",
"98\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 1 35 36 37 38 39 40 61 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98\n",
"99\n1 2 3 4 5 6 7 8 9 19 11 12 13 14 15 16 17 18 19 20 21 22 23 24 40 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99\n",
"99\n1 2 3 4 5 6 7 8 9 10 11 12 13 12 15 6 17 18 19 20 21 22 23 24 33 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99\n",
"8\n2 4 1 3 4 6 2 2\n",
"8\n4 4 1 3 4 6 2 2\n",
"98\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 7 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98\n",
"98\n1 2 3 4 5 6 7 13 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 61 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98\n",
"8\n2 8 1 3 4 3 1 2\n",
"99\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 6 17 18 19 20 21 22 23 24 33 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99\n",
"8\n2 4 1 3 4 6 1 2\n",
"8\n2 3 1 3 4 6 1 2\n",
"98\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 1 35 36 37 38 39 40 61 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 15 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98\n",
"99\n1 2 3 4 5 6 7 8 9 19 11 12 13 14 15 16 17 18 19 20 21 22 23 24 40 26 27 28 29 30 31 32 33 34 35 36 37 38 33 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99\n",
"99\n1 2 3 4 5 6 7 8 9 10 11 12 13 12 15 6 17 18 19 20 21 22 23 24 33 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 99 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99\n",
"8\n2 6 1 3 4 6 1 2\n",
"99\n1 2 3 4 5 6 7 8 9 10 11 12 13 12 15 6 17 18 19 20 21 22 23 24 33 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 54 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 99 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99\n",
"8\n4 4 1 3 1 6 2 2\n",
"8\n2 6 1 4 4 6 1 2\n",
"99\n1 2 3 4 5 6 3 8 9 10 11 12 13 12 15 6 17 18 19 20 21 22 23 24 33 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 54 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 99 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99\n",
"99\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 44 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99\n",
"8\n2 4 1 3 4 1 1 2\n",
"99\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 6 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 89 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99\n",
"8\n2 4 1 3 4 3 2 2\n",
"8\n2 7 1 3 4 3 1 4\n",
"99\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 6 17 13 19 20 21 22 23 24 33 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99\n",
"8\n2 1 1 3 4 6 1 2\n",
"8\n2 8 1 1 4 6 1 2\n",
"98\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 1 35 36 37 38 39 40 61 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 38 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98\n",
"99\n1 2 3 4 5 6 7 8 9 19 11 12 13 14 15 16 17 18 19 20 21 22 23 24 40 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 36 88 89 90 91 92 93 94 95 96 97 98 99\n",
"99\n1 2 3 4 5 6 7 8 9 10 11 12 13 12 15 6 17 18 19 20 21 22 23 24 33 26 6 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99\n",
"8\n2 4 1 5 4 6 2 2\n",
"8\n2 3 2 3 4 6 1 2\n",
"98\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 1 35 36 37 38 39 40 61 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 15 68 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98\n",
"99\n1 2 3 4 5 6 7 8 9 10 11 12 13 12 15 6 17 18 19 20 21 22 23 24 33 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 71 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 99 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99\n"
],
"output": [
"7\n",
"6\n",
"98\n",
"99\n",
"15\n",
"6\n",
"5\n",
"4\n",
"40\n",
"24\n",
"3\n",
"35\n",
"9\n",
"13\n",
"2\n",
"1\n",
"71\n",
"7\n",
"5\n",
"15\n",
"4\n",
"4\n",
"35\n",
"9\n",
"13\n",
"3\n",
"13\n",
"2\n",
"3\n",
"6\n",
"35\n",
"5\n",
"15\n",
"2\n",
"2\n",
"15\n",
"5\n",
"4\n",
"35\n",
"9\n",
"13\n",
"1\n",
"2\n",
"35\n",
"13\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You have an array a_1, a_2, ..., a_n.
Let's call some subarray a_l, a_{l + 1}, ... , a_r of this array a subpermutation if it contains all integers from 1 to r-l+1 exactly once. For example, array a = [2, 2, 1, 3, 2, 3, 1] contains 6 subarrays which are subpermutations: [a_2 ... a_3], [a_2 ... a_4], [a_3 ... a_3], [a_3 ... a_5], [a_5 ... a_7], [a_7 ... a_7].
You are asked to calculate the number of subpermutations.
Input
The first line contains one integer n (1 ≤ n ≤ 3 ⋅ 10^5).
The second line contains n integers a_1, a_2, ... , a_n (1 ≤ a_i ≤ n).
This array can contain the same integers.
Output
Print the number of subpermutations of the array a.
Examples
Input
8
2 4 1 3 4 2 1 2
Output
7
Input
5
1 1 2 1 2
Output
6
Note
There are 7 subpermutations in the first test case. Their segments of indices are [1, 4], [3, 3], [3, 6], [4, 7], [6, 7], [7, 7] and [7, 8].
In the second test case 6 subpermutations exist: [1, 1], [2, 2], [2, 3], [3, 4], [4, 4] and [4, 5].
### Input:
8
2 4 1 3 4 2 1 2
### Output:
7
### Input:
5
1 1 2 1 2
### Output:
6
### Code:
#import sys
import math
#input=sys.stdin.readline
#sys.setrecursionlimit(1000000)
mod=int(1000000007)
i=lambda :map(int,input().split())
n=int(input())
a=[int(x) for x in input().split()]
t=[[0]*21 for i in range(300005)]
for i in range(n):
t[i][0]=a[i]
def build(n):
for j in range(1,20):
for i in range(n):
if i+(1<<j)-1>n-1:
break;
t[i][j]=max(t[i][j-1],t[i+(1<<(j-1))][j-1])
def query(p,q):
p,q=int(p),int(q)
log=int(math.log2(q-p+1))
m=t[p][log]
n=t[q-(1<<log)+1][log]
return max(m,n)
b=[-1]*(n+2)
build(n)
max1=-1
ans=0
for i in range(n):
max1=max(max1,b[a[i]])
b[a[i]]=i
x=b[1]
while x>max1:
if x<=max1:
break
p=query(x,i)
if p==i-x+1:
ans+=1
x=b[p+1]
else:
x=i-p+1
print(ans)
|
1234_A. Equalize Prices Again_10789
|
You are both a shop keeper and a shop assistant at a small nearby shop. You have n goods, the i-th good costs a_i coins.
You got tired of remembering the price of each product when customers ask for it, thus you decided to simplify your life. More precisely you decided to set the same price for all n goods you have.
However, you don't want to lose any money so you want to choose the price in such a way that the sum of new prices is not less than the sum of the initial prices. It means that if you sell all n goods for the new price, you will receive at least the same (or greater) amount of money as if you sell them for their initial prices.
On the other hand, you don't want to lose customers because of big prices so among all prices you can choose you need to choose the minimum one.
So you need to find the minimum possible equal price of all n goods so if you sell them for this price, you will receive at least the same (or greater) amount of money as if you sell them for their initial prices.
You have to answer q independent queries.
Input
The first line of the input contains one integer q (1 ≤ q ≤ 100) — the number of queries. Then q queries follow.
The first line of the query contains one integer n (1 ≤ n ≤ 100) — the number of goods. The second line of the query contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^7), where a_i is the price of the i-th good.
Output
For each query, print the answer for it — the minimum possible equal price of all n goods so if you sell them for this price, you will receive at least the same (or greater) amount of money as if you sell them for their initial prices.
Example
Input
3
5
1 2 3 4 5
3
1 2 2
4
1 1 1 1
Output
3
2
1
|
import math
for _ in range(int(input())):
k=int(input())
l=list(map(int,input().split()))
k=sum(l)/k
print(math.ceil(k))
|
{
"input": [
"3\n5\n1 2 3 4 5\n3\n1 2 2\n4\n1 1 1 1\n",
"3\n5\n1 2 3 4 5\n3\n1 2 3\n2\n777 778\n",
"1\n2\n777 778\n",
"1\n2\n777 1\n",
"1\n1\n2441139\n",
"3\n5\n1 2 3 4 5\n3\n1 4 3\n2\n777 778\n",
"1\n2\n777 144\n",
"1\n2\n386 1\n",
"3\n5\n1 2 3 4 5\n3\n1 2 2\n4\n2 1 1 1\n",
"1\n2\n391 144\n",
"1\n2\n665 1\n",
"3\n5\n1 2 3 4 5\n3\n1 2 4\n4\n2 1 1 1\n",
"1\n2\n449 1\n",
"3\n5\n1 3 3 4 5\n3\n1 2 3\n2\n777 778\n",
"1\n2\n327 1\n",
"1\n1\n1775901\n",
"3\n5\n1 2 3 4 5\n3\n1 2 0\n4\n1 1 1 1\n",
"3\n5\n1 2 3 4 5\n3\n1 4 6\n2\n777 778\n",
"1\n2\n577 1\n",
"3\n5\n1 2 3 4 5\n3\n1 2 4\n4\n2 1 1 0\n",
"1\n2\n314 1\n",
"1\n2\n552 1\n",
"1\n1\n85479\n",
"3\n5\n1 2 3 4 5\n3\n1 2 0\n4\n1 1 1 2\n",
"1\n2\n632 1\n",
"3\n5\n1 2 6 4 5\n3\n1 2 4\n4\n2 1 1 0\n",
"1\n2\n554 1\n",
"1\n1\n15826\n",
"1\n1\n14343\n",
"3\n5\n1 2 3 4 5\n3\n1 2 3\n2\n777 1089\n",
"1\n2\n1160 778\n",
"1\n2\n777 2\n",
"1\n2\n386 0\n",
"1\n2\n578 144\n",
"1\n2\n665 2\n",
"3\n5\n1 2 3 4 0\n3\n1 2 4\n4\n2 1 1 1\n",
"1\n1\n2397558\n",
"3\n5\n1 2 3 6 5\n3\n1 2 0\n4\n1 1 1 1\n",
"1\n2\n407 1\n",
"1\n2\n601 2\n",
"1\n2\n552 0\n",
"1\n2\n314 0\n",
"1\n1\n25761\n",
"3\n5\n1 2 0 2 5\n3\n2 2 1\n4\n3 1 1 1\n",
"3\n5\n1 2 6 4 5\n3\n1 2 3\n2\n777 1089\n",
"1\n2\n1251 778\n",
"1\n2\n75 2\n",
"1\n2\n578 65\n",
"1\n2\n1075 2\n",
"1\n2\n282 0\n",
"1\n2\n514 2\n",
"3\n5\n0 3 3 8 5\n3\n2 2 3\n2\n777 778\n",
"3\n5\n1 3 3 4 5\n3\n1 2 0\n4\n1 1 2 2\n",
"1\n2\n65 0\n",
"1\n1\n20164\n",
"3\n5\n1 2 6 4 5\n3\n1 2 3\n2\n777 2131\n",
"1\n2\n1385 778\n",
"1\n2\n332 2\n",
"1\n2\n282 1\n",
"3\n5\n0 3 3 16 5\n3\n2 2 3\n2\n777 778\n",
"3\n5\n1 2 3 4 5\n3\n1 2 1\n4\n2 1 1 1\n",
"3\n5\n1 3 3 8 5\n3\n1 2 3\n2\n777 778\n",
"3\n5\n1 2 1 4 5\n3\n1 4 6\n2\n777 778\n",
"3\n5\n1 2 0 4 5\n3\n1 2 1\n4\n2 1 1 1\n",
"1\n2\n314 2\n",
"3\n5\n1 2 3 4 5\n3\n1 1 0\n4\n1 1 1 2\n",
"3\n5\n1 2 0 4 5\n3\n2 2 1\n4\n2 1 1 1\n",
"3\n5\n1 2 0 4 5\n3\n2 2 1\n4\n3 1 1 1\n",
"3\n5\n2 2 0 4 5\n3\n2 2 1\n4\n3 1 1 1\n",
"3\n5\n2 2 0 4 5\n3\n2 3 1\n4\n3 1 1 1\n",
"3\n5\n1 2 3 4 5\n3\n1 0 2\n4\n1 1 1 1\n",
"3\n5\n1 2 3 4 5\n3\n1 2 2\n4\n2 2 1 1\n",
"3\n5\n1 3 3 4 5\n3\n0 2 3\n2\n777 778\n",
"1\n2\n327 0\n",
"3\n5\n1 2 0 4 5\n3\n1 4 6\n2\n777 778\n",
"3\n5\n1 2 3 4 5\n3\n1 0 1\n4\n2 1 1 1\n",
"3\n5\n1 2 3 4 5\n3\n2 2 4\n4\n2 1 1 0\n",
"3\n5\n0 3 3 8 5\n3\n1 2 3\n2\n777 778\n",
"3\n5\n1 2 3 4 5\n3\n1 2 0\n4\n1 1 2 2\n",
"3\n5\n1 2 0 4 5\n3\n1 2 1\n4\n3 1 1 1\n",
"3\n5\n1 2 6 4 5\n3\n1 2 5\n4\n2 1 1 0\n",
"1\n2\n554 0\n",
"3\n5\n1 2 3 4 5\n3\n1 1 0\n4\n1 1 1 0\n",
"3\n5\n1 2 0 4 5\n3\n3 2 1\n4\n2 1 1 1\n",
"3\n5\n2 2 0 4 5\n3\n2 3 1\n4\n3 2 1 1\n",
"3\n5\n1 2 3 4 5\n3\n0 2 2\n4\n2 2 1 1\n",
"3\n5\n1 2 3 4 0\n3\n1 3 4\n4\n2 1 1 1\n",
"3\n5\n1 3 3 4 7\n3\n0 2 3\n2\n777 778\n",
"3\n5\n1 2 3 6 3\n3\n1 2 0\n4\n1 1 1 1\n",
"3\n5\n1 2 0 5 5\n3\n1 4 6\n2\n777 778\n",
"3\n5\n1 2 3 4 5\n3\n1 0 1\n4\n2 2 1 1\n",
"3\n5\n1 2 3 4 5\n3\n2 2 4\n4\n2 0 1 0\n",
"3\n5\n1 2 1 4 5\n3\n1 2 1\n4\n3 1 1 1\n",
"3\n5\n1 2 3 7 5\n3\n1 1 0\n4\n1 1 1 0\n",
"3\n5\n2 2 0 4 5\n3\n3 2 1\n4\n2 1 1 1\n",
"3\n5\n1 2 0 2 5\n3\n2 2 1\n4\n3 0 1 1\n",
"3\n5\n1 5 3 4 7\n3\n0 2 3\n2\n777 778\n",
"3\n5\n1 2 3 6 3\n3\n1 2 0\n4\n1 1 2 1\n",
"3\n5\n1 4 3 4 5\n3\n1 0 1\n4\n2 2 1 1\n",
"3\n5\n1 2 3 4 5\n3\n2 2 4\n4\n3 0 1 0\n",
"3\n5\n1 3 3 4 5\n3\n0 2 0\n4\n1 1 2 2\n",
"3\n5\n1 2 1 4 5\n3\n0 2 1\n4\n3 1 1 1\n"
],
"output": [
"3\n2\n1\n",
"3\n2\n778\n",
"778\n",
"389\n",
"2441139\n",
"3\n3\n778\n",
"461\n",
"194\n",
"3\n2\n2\n",
"268\n",
"333\n",
"3\n3\n2\n",
"225\n",
"4\n2\n778\n",
"164\n",
"1775901\n",
"3\n1\n1\n",
"3\n4\n778\n",
"289\n",
"3\n3\n1\n",
"158\n",
"277\n",
"85479\n",
"3\n1\n2\n",
"317\n",
"4\n3\n1\n",
"278\n",
"15826\n",
"14343\n",
"3\n2\n933\n",
"969\n",
"390\n",
"193\n",
"361\n",
"334\n",
"2\n3\n2\n",
"2397558\n",
"4\n1\n1\n",
"204\n",
"302\n",
"276\n",
"157\n",
"25761\n",
"2\n2\n2\n",
"4\n2\n933\n",
"1015\n",
"39\n",
"322\n",
"539\n",
"141\n",
"258\n",
"4\n3\n778\n",
"4\n1\n2\n",
"33\n",
"20164\n",
"4\n2\n1454\n",
"1082\n",
"167\n",
"142\n",
"6\n3\n778\n",
"3\n2\n2\n",
"4\n2\n778\n",
"3\n4\n778\n",
"3\n2\n2\n",
"158\n",
"3\n1\n2\n",
"3\n2\n2\n",
"3\n2\n2\n",
"3\n2\n2\n",
"3\n2\n2\n",
"3\n1\n1\n",
"3\n2\n2\n",
"4\n2\n778\n",
"164\n",
"3\n4\n778\n",
"3\n1\n2\n",
"3\n3\n1\n",
"4\n2\n778\n",
"3\n1\n2\n",
"3\n2\n2\n",
"4\n3\n1\n",
"277\n",
"3\n1\n1\n",
"3\n2\n2\n",
"3\n2\n2\n",
"3\n2\n2\n",
"2\n3\n2\n",
"4\n2\n778\n",
"3\n1\n1\n",
"3\n4\n778\n",
"3\n1\n2\n",
"3\n3\n1\n",
"3\n2\n2\n",
"4\n1\n1\n",
"3\n2\n2\n",
"2\n2\n2\n",
"4\n2\n778\n",
"3\n1\n2\n",
"4\n1\n2\n",
"3\n3\n1\n",
"4\n1\n2\n",
"3\n1\n2\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You are both a shop keeper and a shop assistant at a small nearby shop. You have n goods, the i-th good costs a_i coins.
You got tired of remembering the price of each product when customers ask for it, thus you decided to simplify your life. More precisely you decided to set the same price for all n goods you have.
However, you don't want to lose any money so you want to choose the price in such a way that the sum of new prices is not less than the sum of the initial prices. It means that if you sell all n goods for the new price, you will receive at least the same (or greater) amount of money as if you sell them for their initial prices.
On the other hand, you don't want to lose customers because of big prices so among all prices you can choose you need to choose the minimum one.
So you need to find the minimum possible equal price of all n goods so if you sell them for this price, you will receive at least the same (or greater) amount of money as if you sell them for their initial prices.
You have to answer q independent queries.
Input
The first line of the input contains one integer q (1 ≤ q ≤ 100) — the number of queries. Then q queries follow.
The first line of the query contains one integer n (1 ≤ n ≤ 100) — the number of goods. The second line of the query contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^7), where a_i is the price of the i-th good.
Output
For each query, print the answer for it — the minimum possible equal price of all n goods so if you sell them for this price, you will receive at least the same (or greater) amount of money as if you sell them for their initial prices.
Example
Input
3
5
1 2 3 4 5
3
1 2 2
4
1 1 1 1
Output
3
2
1
### Input:
3
5
1 2 3 4 5
3
1 2 2
4
1 1 1 1
### Output:
3
2
1
### Input:
3
5
1 2 3 4 5
3
1 2 3
2
777 778
### Output:
3
2
778
### Code:
import math
for _ in range(int(input())):
k=int(input())
l=list(map(int,input().split()))
k=sum(l)/k
print(math.ceil(k))
|
1296_E1. String Coloring (easy version)_10795
|
This is an easy version of the problem. The actual problems are different, but the easy version is almost a subtask of the hard version. Note that the constraints and the output format are different.
You are given a string s consisting of n lowercase Latin letters.
You have to color all its characters one of the two colors (each character to exactly one color, the same letters can be colored the same or different colors, i.e. you can choose exactly one color for each index in s).
After coloring, you can swap any two neighboring characters of the string that are colored different colors. You can perform such an operation arbitrary (possibly, zero) number of times.
The goal is to make the string sorted, i.e. all characters should be in alphabetical order.
Your task is to say if it is possible to color the given string so that after coloring it can become sorted by some sequence of swaps. Note that you have to restore only coloring, not the sequence of swaps.
Input
The first line of the input contains one integer n (1 ≤ n ≤ 200) — the length of s.
The second line of the input contains the string s consisting of exactly n lowercase Latin letters.
Output
If it is impossible to color the given string so that after coloring it can become sorted by some sequence of swaps, print "NO" (without quotes) in the first line.
Otherwise, print "YES" in the first line and any correct coloring in the second line (the coloring is the string consisting of n characters, the i-th character should be '0' if the i-th character is colored the first color and '1' otherwise).
Examples
Input
9
abacbecfd
Output
YES
001010101
Input
8
aaabbcbb
Output
YES
01011011
Input
7
abcdedc
Output
NO
Input
5
abcde
Output
YES
00000
|
# ------------------- fast io --------------------
import os
import sys
from io import BytesIO, IOBase
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
# ------------------- fast io --------------------
n = int(input())
s = input()
indexes = [[] for i in range(26)]
for i in range(len(s)):
indexes[ord(s[i])-97] += [i]
#print(indexes)
order = [0]*n
count = 1
for each in indexes:
incount = False
for k in each:
incount=True
order[k] = count
if incount:
count += 1
coloring = ['']*n
opposites = [[] for i in range(n+1)]
#print(order, opposites)
for i in range(n):
for j in range(i+1, n):
if order[i] > order[j]:
#print(i, j)
for k in range(i, j):
opposites[j] += [i]
opposites[i] += [j]
coloring[0] = '0'
def opp(x): return '0' if x == '1' else '1'
poss = True
for i in range(n):
if not coloring[i]:
coloring[i] = '0'
for k in opposites[i]:
#print(i, k, coloring)
if coloring[k] == '':
coloring[k] = opp(coloring[i])
else:
if coloring[k] != opp(coloring[i]):
poss = False
break
if poss:
print('YES')
print(''.join(coloring))
else:
print('NO')
|
{
"input": [
"7\nabcdedc\n",
"9\nabacbecfd\n",
"5\nabcde\n",
"8\naaabbcbb\n",
"6\nqdlrhw\n",
"500\nxwxpgalijfbdbdmluuaubobxztpkfnuparzxczfzchinxdtaevbepdxlouzfzaizkinuaufhckjvydmgnkuaneqohcqocfrsbmmohgpoacnqlgspppfogdkkbrkrhdpdlnknjyeccbqssqtaqmyamtkedlhpbjmchfnmwhxepzfrfmlrxrirbvvlryzmulxqjlthclocmiudxbtqpihlnielggjxjmvqjbeozjpskenampuszybcorplicekprqbsdkidwpgwkrpvbpcsdcngawcgeyxsjimalrrwttjjualmhypzrmyauvtothnermlednvjbpgkehxbtbpxolmaapmlcuetghikbgtaspqesjkqwxtvccphjdqpuairsaypfudwvelmupbzhxwuchnfumcxmhflkpyzeppddtczbcjrookncgtojmujyvponennuudppqwwjtnwpgapokwzvbxohrdcvcckzbcrwwvfqlbnwbnmmvh\n",
"200\naadfgghjjjkmnpqqtuuwwxyzaaaaaaaabbbbbbbbcccccddddeeeeeeeeeffgggghhhhhhiiiiiiiijjjjjjjjkkkkklllllmmmmmmmmmmmnnnnnoooooppppppppqqqqqqqqrrrrrrrrrrrssssstttttttttuuuuuuuuvvvvvvvwwwwwwxxxxxxxyyyyyzzzzzzzzz\n",
"4\nzcza\n",
"200\naaaaabbbbbbbbbbbccccccdddddddddeeeeeefffffffffggggggggggggggghhhhhhhhhiiiiijjjjjjjjjjjkkkkkklllllllmmmmmmmmmnnnnnnnnnnoooooppppppqqqqqqqrrrrrssssssstttttuuuuuuuuvvvvwwwwwwwwwwwwxxxxxxyyyyyyzzzzzzzzzmu\n",
"1\nr\n",
"200\naaaaaabbbbbbbbbbbbbccccccccccccdddeeeeeeffffggghhhhhhhhhiiiiiiiijjjjjjjjjjkkkkklllllmmmmmmmmmnnnnnnnoooooooppppppppqqqqqqrrrrrrrrrsssssssttttttttuuuuuuuuvvvvvvvvwwwwwwxxxxxxxyyyyyyyyyyzzzzzzzzzzzeinuy\n",
"200\naaaaaaabcbbbbcccccdccdcdddddeeddeeeeeeeeeefffffffggghgghghhhhhhhihhhiiiiiiiijijijjjjkjkkkkkkkklkkllllllllmmmmmmmmmmmnnnnnnnnoooppnqnnqoqroooorsoppqqstttqruuurruvrrvvtvttvvtuwvwwwwxxxwxyzzxzzyyzzyyzzzz\n",
"200\ntoimpgygoklxroowdhpacrtrrwmkhcgcpidapeyxrjmiqgilveimnazyydvnujtqpenfkeqdbylfdinompxupfwvirxohaampqihjueasygkucweptgcowjibgnwyqetynykgoujeargnhjbmntfovwusqavpdwtpnpqpkcgaxbhgdxloyealksmgkxprtpfugixdyfn\n",
"5\nadcbz\n",
"200\nraaaaabbbccccccccccdddddeeeeeeeeeeeeeeffffffffffggggggggghhhhhiiiiiiiiijjjjkkkkkkkkkkllllllllmmmmmmmmnnnnnnnooooooooppppppqqqqqqqqqqrrrrrrrrssssttttttttttuuuuuuuuvvvvvvwwwwwwxxxxxxxyyyyyyyzzzzzzzzzzzz\n",
"200\naaaaaadeafgibbbbbbjbjlncpccccsdsdddtdtdtdeetuevwwezzefffffgggghhhhhhhiijjjjjjjjkkklllllllmmmmmmmmmmmmmnnnnnnnooooooooopppppppppppppqqqqrrrrrrsssssssttttttttttuuuuuuuuuvvvvvvvwwwwwwxxxxxyyyyyyyyyzzzzzz\n",
"200\nftiqlgirbkmlpzkthoivcifhflyietxsfiwiojenqgxrnetzutdsyfuhrbfpedyksfzuvnqonbyydogbrwsfuuivboanufitbjngppagzfgqwyroaofcdgrwoxwfpvcgzdnkhnwtlavnoppdbddpfpcaaipdcqskcqtccrrspvjyqpvjwziexnmmnlqvacdpgnzzhude\n",
"200\nazaaaaaabbbbbbbcccccccccdeeeeeeefffffffgggggggghhhhhhiijjjjjkkkkkkkkkllllllmmmmmmmmmmmmnnnnnnoooooopppppppppppqqqqqrrrrrrrrrrrrrssssssssssstttttttttttuuuuuuuuvvvvvvvwwwwwwwwwxxxxxxxyyyyyyyyyyyyzzzzzzz\n",
"100\neivzgzvqvlgzdltwjcmpublpvopzxylucxhrrltwmizxtdxdrnmuivvcewvaunkqmnjgqgcwdphbvapebhkltmkfcslvgmnqoseu\n",
"3\nedc\n",
"30\nlpxzyiymhgfemqbhburdctevpybxlv\n",
"200\naaaaeillaoobbwbbxbzbbcccccccdddddddddeeeeeeeffffffffggggghhhhhiiiijjjjjjjkkkkklllllmmmmmmmmmnnnnnnnnnnnnnooooooooppppqqqqqqqqqqrrrrrrrrrrrsssssssssttttttttttuuuuuuuvvvvvvvwwwwwwwxxxxxxyyyyzzzzzzzzzzzz\n",
"37\nxxxxxxxxxxxxxaaaaaaaaaaaccccccccccacx\n",
"4\nhcha\n",
"100\nyojtyktazyfegvnnsexxiosqxdlpdwlyojsghpvjpavnvjvttbylqcdabyhleltltzalmgoelxdalcbjejsjxnfebzsxusnujdyk\n",
"8\naaabbcbb\n",
"30\nxsvbtliwvggtjbvdebjwcirlfnnuio\n",
"200\naaaabbbbcceefffgghhhhijjllnnnnopqrrsstuuvvvwwxxyyyaaaabbbbbbbbcccdddddeeeeeefffffggggghhhhhhhhhiiiiiiiiijjjjkkkkkkllllllmmmmmmmnnnnnoooooooopppppppqqqrrrrrrsssssstttttuuuuuuuvvvvvwwwxxxxxyyyyzzzzzzzzz\n",
"200\nfhrvyaaaaaaaaabbbbbbbccccccccccdddddeeeeeeeeeeeeefffffggggggghhiiiiiiiiiiiijjjjjkkkklllllllmmmmmmmmnnnnnoooooppppppppqqqrrrrrrrrrrsssssssstttttttttttttuuuuuuuvvvvvvwwwwwwwwwwwwwwxxxxxxyyyyyyyyzzzzzzzz\n",
"200\njaaaabbbbbbccccccccccccdddddddddddeeeeeeffffffggggghhhhhhhiiiijjjjjjjjjkkkkkkkkkkkllllllllllllmmmmmmmmmmmnnnooooppppppqqqqqqqqqqqqqqrrrrrrrrrrrrsssssttttttuuuuuuuvvvvvwwwwwwwwwwwwxxxxxxxyyyyyyyyzzzzzz\n",
"4\ncbca\n",
"200\naaaabbbbbbcccccdddddeeeeeeeffffggggggggghhhhhiiiiijjjjjjjkkkkkkkkllmmmmmmmmmmnnoooooppppqqqqqrrrrrrsssssttttttttttttuuuvvvvvwwwwwwxxxxxxxxyyyzzzzzzzzzaccddddeeffgjjjjkkklllllmmmmnnooppqrrsssttwwxyyzzz\n",
"500\ndqkumomydseavvuukspjmbvtwbtsaquomfojmvcmzokytzyhbhsmhwonrqnuocadbwvpdwtxvanwiacyijmdjbwpgvkllzrpgbuyekvmkmzwnnvetlrodcxaitkrsakkaxuajkhdmmjqtpehyyzelygbdzsauqgnnvveoeulmufgeqxqfiqxuckbbbyxinwtbtewhvycarhunsebyznqxskdqvwtvdelnpmhfagvmouidoytfwnpxjnmgabudblycswciftoeeuxpnyicfibfutvnadvretbunshkdpaxtzzyxbpyzyxynyjjhgwyshjkksvbcffveldqwqevmpnemtzxuomtewvsrqdrmqmbkruartebmvjqaksbhotfbysoorthvattezazpvxrytlzurpfkjscnkitkjvhlirzbnsoujicmrvaecespknvkjufsudkiznsyatgbtkebqpycukbcdqxdwqicrhphbiiesxftkicwsx\n",
"200\naaabbsbbbbbbbbbbbbbcccccccccdddddddddddddeeeeeeeeffffffffgggggggggghhhhhhhhhhhhijjjjjjjjjjkkkkkkllllmmmmmnnnnnnoooooooppppppqqqqqqqqqqqqrrrrrsssssssssttttttuuuuuuvvvvvvvvvwwwwwwxxxxxxyyyyyyzzzzzzzzzzz\n",
"6\ncbaabc\n",
"200\nbdimoqrstvaaaaaaaaabbbbbbbbbbcccccddddddeeeeeeeeeeeeeeeffffffgggggggghhhhhhhhhiiiiiiiijjjjjjjjjjjjkkkkkkkklllllllllmmmmmmmmnnnnnoooooooppppppqqqqqqrrrrrrrrssssssstttttuuvvvvvvwwwwwwwwxxxxxxxyyyyyyyzzz\n",
"5\ncbbda\n",
"200\naaaabccccdddddddeefffffffgghhhiiiiiijjjjjjjkkkkkllllmmmmnnnnnoooooooppqqqqqrrrrsssttuuuuuvwwxxyyyzzzaaaaaabbbbbccccddddddeefffffffggghhiiiikkllmmnnnnnnoooooppppqqqqrrrrsttttuuuuuvvvvwwwwwwxxxxyyyzzzzz\n",
"200\naaaaaaaaabbbbcccccccccccdddeeeeeeeefffgggghhhhhhhhiiiiiiijjjjjjjkkklllmmmmmnnnnnnnoooooppppppppqqqqrrrrrrrssssssttttuuuuuuvvvvvwwwwxxxxxxyyyyyzzzzzzzzaabbbcccdeeefggggghhhhiijjjjkllnpqqqrrsssstuuvwyzz\n",
"4\ndcda\n",
"200\naaaaaaaaaabbbbbbccccccddddddddddddeeeeeeeeeeffffffffggggghhhhhhiiijjjjjjkkkkkklllllllllllllmmmmmmmnnnnnooooooooooppppppppppqqqqqqqqqrrrrrrrrsssssstttttttttuuuuvvvvvvwwwwwwwwwwwxxxxxyyyyyyyyyyzzzzzzzzw\n",
"200\naaaabbbbbbccccddddefffffgghhhiiiiiiiiijjjjjkkklmmmmnnnnnnooopppppppprrrstuuuuuuvvvvvvvwwxxxxyyyyyyzzaabbbbbbcccdddddddddeffggggghhhhhhiiijjjjjjkkkkllllmmmnnnoopqqqrrssssttttuuuvvvvvwwwwwxxxxyyyyyzzzzz\n",
"9\nbefblmbhg\n",
"200\naaaaaaabbbbbbcccccccccdddddddeeeeffffffggggghhhhhiiiiiiiijjjjkkkkkllllllllmmmmmmmmmnnnnnnnnnooooooooopppppppppqqqqqqqqrrrrrrrrrrrsssssssttttuuvvvvvvvvvvwwwwwwwxxxxxxyyyyyyzzzzzbceghhhijjjmmooqrrttvvwx\n",
"200\nndwpatpnvwldptairxlxqmzzysfvglpjkwbebtosqvfnoebfvxfpupvohcaazsjbdshoducigmfoqzltdgvmdmputqmoaqscilmtafqrxdunwnijhrtbwonpvpeouednmjswhauahmgyozmbiilxxflkkmwywvuojbrwwbkyhxtdywiktkfcsmozklhrwlwyajekejrx\n",
"200\naaaaaaaaaabbbbbccccccccccccccdddddddddeeeeeeefffffffffgggggghhhhhhiiiiiiijjjjjjjjjjkkkkkkllllllllmmmmmmmmnnnnnnoooooooppppppqqqqqqqqqqqrrrrrrsssssssttttttttuuuuuuvvvvvwwwwwxxxyyyyzzzzzzzzzzzcddddjksvw\n",
"1\na\n",
"100\nkshxumdmoygtdgjkwmpsiffhoswmapcogjkngvcznwhtufgjstqrbgwjtxrnoevhwaoaxporxbnrijtwkqnteergtvvwkxvbvwch\n",
"200\nzywmerhahxlqsjekpqsdqxnjiduyjrytswiweohctztgpiorwimhjmdfofqynyggcrtzslbyvkuvqrsgwyacyvcuathplliwwshusluiqwuhutnzwvuchfedhwwfdzizltdxibtsaocpnqezstblgkfdcvfsjjyzwalkksumsaljqljmmkcyejwwdkolmcgmodoiclte\n",
"500\nlbwrbavuwfcryqijwcsoafplpiafchmfrrrfagmracruvzendlvjbhqvgskhjtksnjbglefsqmwmwleturpkutdqyxunrkzznfrlnzlvijntlckzaleovnsvpksawjlqndzoixhmjbuysxbffcimcorlndwxowittgtyiomqewnkmxkpdunvnynoybqtdunavsjhgkmtdwugqmaqnduocxzpeqimjguwnjbkvmstekjpppwcuhabmdemqskzrgorgfbuxlsccxsmsrtxgeppwenecutwhxxfevjtxipmsbymvjsprftfqqndumwtissszzzewtbwyeijkvcifexnuzjmtgrilojhrtdaefhwumwafcujhrqlntzqoubqazzmfsbwlvkqijfahdgokzyuskplbkzgomdweqttoqduzurxnslagqgmgywbojnfjuiiattdmuxqmtgrkypqhpxszroffmimhbheasenpvzerzpzamhbealj\n",
"200\naaawaaaabbbbccccccccddddddddddeeeeeeeffffffffffgggggggggghhhhhhhhiiiiiiiiijjjjjjjkkkkkkkkklllllllmmmmmmmmnnnnnnooooooooppppppppqqqqrrrrrrrsssssssttttttuuuuuuuuuvvvvvvvvvwwwwwwwxxxxxxxyyyyyyyzzzzzzzzzz\n",
"200\naaaabccdeffgghhijklllmnnnoopqrrrrssssssttuuvvvwxyyaaaabbbcccccddddddeeeeeeffffgggggghhhhiiiiiiiiiiijjjjjjjjjkkkkllmmmmmmmmnnoooooooooooppppppppppqqqqqqrrrsssstttttuuuuvvvvwwwwwwwxxxxxxxxxyyyyyyyyyyzzz\n",
"500\ndhlmtnvecsbwbycahddxnvwpsxwxgfmidfetpkpeevpjzfbgfafbjpyuevupuptoxutnketcxwrllooyxtxjzwxpzcbpiqzeiplcqvdxyyznjxgkwstpxogdihsamoqhyspbjlelxpbarzqawsgidjtmnpmmupohnslirorliapvntasudhpuuxynyoipuqxdiysbyctpmfpbxqfdlmlsmsvtbxoypkbhwrtpwbsbcdhypsbqhqpdlilquppdwsszrpavcowudreygmpwckbzlpnxxqxjdpqmtidjatvgcbxjrpqqxhhsvlpyxxkoqxutsvebrlxqeggvsnshetkpnfygpwbmnuujfvqnlgavwppufxadhxtffsrdknfmqbsjjegcwokbauzivhnldkvykkytkyrwhimmkznkkofcuioqmpbshskvdhsetyidubcgvuerbozqfbkcmaguaszaivtuswzmtnqcpoiqlvronibiqyeoqms\n",
"200\naaaabbbbabcaccaadbebfbbbfgbbggchhcccchhhcccicjdkkldldddldmdenoeeooffpppfqrfffuuufggguvgggvggwghhxhyyyhhhhzhiiiiiiijjjjjjjkkkllmmmnnnooooppppppppppppqqqqrssssttttttuuuvvvvwwwwwwwwxxxxxxxxyyyyzzzzzzzzzz\n",
"200\ncnaaaaaabbbbbccccdddddddddddddeeeeeeeeefffffffgggggggggghhhhhhhhhiiijjjjjkkkkkkklllllllmmmmmmmnnnnnnnnnooooooooooooppppppppqqqqqqqqqqqrrrssssssstuuuuuuuuvvvvvvvvvvvvwwwwwwxxxxxxxxyyyyyyyzzzzzzzzzzzzzz\n",
"2\ntj\n",
"200\naacdaeabblbxbbbbbbcccccdddddeeeeeeefffffffggggggghhhhhhhhhiiiiiiiiiijjjjjjjkkkkkkkklllllllllmmmmmmmmnnnoooooooopppppqqqqqqqqqqqrrrrrrrrrrsstttttttttuuuuuuuvvvvvvvvvvwwwwwwwxxxxxxxxxxxyyyyyyyyyzzzzzzzz\n",
"8\nenjmfmcb\n",
"100\nyvharmmxcxhibqfixtjmhurxchhkvhubxjcveajrkssbsbrxpijxolrtmvanzyybzbdpgzocicakipmkpxhcjtegksbvabfghpfg\n",
"30\ndcjajwrqosgljwltqlozqmldwuukkg\n",
"30\nrzlwlvhfatfwmlpvndtgrxyphfjnnm\n",
"500\nrmjqqncoqtblylyxilxrmkjdgmivdwdywfwbnqvwatarwbntepxhwrteyteseixiyvhatntnjyceluhldcssemkppagowvhjuiqbypzeffzqlrbuhnsnovopvabjdtoxzjezilgtgpfjsiycjhquudzuvhbshdkwaspsbxeyxxxowezqafmtgxrauahozegjponudxakgchruhxdcgaohdpzslxexkhflfpmjxduthxwbowjkqnobxxlylvddkoinqgonrssasszuxrmnevcopeqrniwarejpcafknswomzypuhpikqojrdzfooqsrddoogmojvpedirgvplnvemknzzprrgbwuunxswpxyglqeglmwopxjnlpnqchnlvwaeyyjysvuoxpjartofbbdcncngzlqtzlwkoydrxyyzzlxepqmrlxsbkqqxleqxadfxsttdofvteonpqtjumaduagibkxnhsysrshowpiyzywnaueeuhgcv\n",
"9\nabcabcabc\n",
"30\nrhkegyacbthzhghossgtqdxtmjfhhx\n",
"200\naaaaabbaaaaabcbebebbccecccffgjklccmcmnccoccooddoqqqdddqderreerrsfffsfsfghuuhhhvhhhhvviwixixixxixijjjxjyjzzjzkkklllllmmmmmmmnnnnnnnoooooppppppppppppqqqqqrrrrrrrsssssstttuuuvvvvvvvwwwwwwxxxyyyyyyyyyzzzz\n",
"200\naaaaaaaaaaaabbbbccccccdddddddeeeeeeffgggggggggggghhhhhhiiiiiiiiiiiijjjjjjjjjkkkkklllllllmmmmmmmmnnnnnnnnoooooooopppppppppqqqqqrrrrrrrrrssssssssssttuuuuuuuvvvvvvvvvvwwwwwwwwxxxxxxxyyyyyyyyzzzzzzzzzzzzw\n",
"100\nqdvwjzmgfmgngaxzgvuuukxyfzecafuflxpkvemenkorwhmnsxuoxsatlymyjugwjmutfxcksnwhxrwruyqbouyflxhwqhflczzx\n",
"8\nhinzrvgh\n",
"6\nwhrldq\n",
"4\nczza\n",
"1\ns\n",
"3\ncde\n",
"4\nahch\n",
"8\naaabbcab\n",
"200\njaaaabbbbbbccccccccccccdddddddddddeeeeeeffffffggggghhhhhhhiiiijjjjjjjjjkkkkkkkkkkkllllllllllllmmmmmmmmmmmnnnooooppppppqqqqqqqqqqqqqqrrrrrrrrrrrrsssssttttttuuuuuuuvvvvvwwwwwwwwwwwwxxxxxxxyyyyyyyxzzzzzz\n",
"200\naaabbsbbbbbbbbbbbbbcccccccccdddddddddddddeeeeeeeeffffffffgggggggggghhhhhhhhhhhhijjjjjjjjjjkkkkkkllllmmmmmnnnnnnoooooooppppppqqqqqqqqqqqqrrrrrsssssstssttttttuuuuuuvvvvvvvvvwwwwwwxxxxxxyyyyyyzzzzzzzzzzz\n",
"5\nadbbc\n",
"2\njt\n",
"5\nabdde\n",
"8\naaabacbb\n",
"3\ndce\n",
"500\nxwxpgalijfbdbdmluuaubobxztpkfnuparzxczfzchinxdtaevbepdxlouzfzaizkinuaufhckjvydmgnkuaneqohcqocfrsbmmohgpoacnqlgspppfogdkkbrkrhdpdlnknjyeccbqssqtaqmyamtkedlhpbjmchfnmwhxepzfrfmlrxrirbvvlryzmulxqjlthclocmiudxbtqpihlnielggjxjmvqjbeozjpskenampuszybcorplibekprqbsdkidwpgwkrpvbpcsdcngawcgeyxsjimalrrwttjjualmhypzrmyauvtothnermlednvjbpgkehxbtbpxolmaapmlcuetghikbgtaspqesjkqwxtvccphjdqpuairsaypfudwvelmupbzhxwuchnfumcxmhflkpyzeppddtczbcjrookncgtojmujyvponennuudppqwwjtnwpgapokwzvbxohrdcvcckzbcrwwvfqlbnwbnmmvh\n",
"200\naadagghjjjkmnpqqtuuwwxyzaaafaaaabbbbbbbbcccccddddeeeeeeeeeffgggghhhhhhiiiiiiiijjjjjjjjkkkkklllllmmmmmmmmmmmnnnnnoooooppppppppqqqqqqqqrrrrrrrrrrrssssstttttttttuuuuuuuuvvvvvvvwwwwwwxxxxxxxyyyyyzzzzzzzzz\n",
"200\naaaaabbbbbbbbbbbccccccdddddddddeeeeeefffffffffggggggggggggggghhhhhhhhhiiiiijjjjjjjjjjjkkkkkklllllllmmmmmmmmmnnnnnnnnnnoooooppppppqqqqqqqrrrrrssssssstutttuuuuuuuuvvvvwwwwwwwwwwwwxxxxxxyyyyyyzzzzzzzzzmu\n",
"200\naaaaaabbbbbbbbbbbbbccccccccccccdddeeeeeeffffggghhhhhhhhhiiiiiiiijjjjjjjjjjkkkkkllllqmmmmmmmmmnnnnnnnoooooooppppppppqlqqqqrrrrrrrrrsssssssttttttttuuuuuuuuvvvvvvvvwwwwwwxxxxxxxyyyyyyyyyyzzzzzzzzzzzeinuy\n",
"200\nzzzzyyzzyyzzxzzyxwxxxwwwwvwutvvttvtvvrrvurruuurqtttsqqpposroooorqoqnnqnppooonnnnnnnnmmmmmmmmmmmllllllllkklkkkkkkkkjkjjjjijijiiiiiiiihhhihhhhhhhghgghgggfffffffeeeeeeeeeeddeedddddcdccdcccccbbbbcbaaaaaaa\n",
"200\nnfydxigufptrpxkgmsklaeyolxdghbxagckpqpnptwdpvaqsuwvoftnmbjhngraejuogkynyteqywngbijwocgtpewcukgysaeujhiqpmaahoxrivwfpuxpmonidflybdqekfnepqtjunvdyyzanmievligqimjrxyepadipcgchkmwrrtrcaphdwoorxlkogygpmiot\n",
"5\nzbcda\n",
"200\nraaaaabbbczccccccccdddddeeeeeeeeeeeeeeffffffffffggggggggghhhhhiiiiiiiiijjjjkkkkkkkkkkllllllllmmmmmmmmnnnnnnnooooooooppppppqqqqqqqqqqrrrrrrrrssssttttttttttuuuuuuuuvvvvvvwwwwwwxxxxxxxyyyyyyyzzzzczzzzzzz\n",
"200\nzzzzzzyyyyyyyyyxxxxxwwwwwwvvvvvvvuuuuuuuuuttttttttttsssssssrrrrrrqqqqpppppppppppppooooooooonnnnnnnmmmmmmmmmmmmmlllllllkkkjjjjjjjjiihhhhhhhggggfffffezzewwveuteedtdtdtdddsdsccccpcnljbjbbbbbbigfaedaaaaaa\n",
"200\nfthqlgirbkmlpzkthoivcifhflyietxsfiwiojenqgxrnetzutdsyfuhrbfpedyksfzuvnqonbyydogbrwsfuuivboanufitbjngppagzfgqwyroaofcdgrwoxwfpvcgzdnkhnwtlavnoppdbddpfpcaaipdcqskcqtccrrspvjyqpvjwziexnmmnlqvacdpgnzzhude\n",
"200\nzzzzzzzyyyyyyyyyyyyxxxxxxxwwwwwwwwwvvvvvvvuuuuuuuutttttttttttsssssssssssrrrrrrrrrrrrrqqqqqpppppppppppoooooonnnnnnmmmmmmmmmmmmllllllkkkkkkkkkjjjjjiihhhhhhggggggggfffffffeeeeeeedcccccccccbbbbbbbaaaaaaza\n",
"100\neivzgzvqwlgzdltwjcmpublpvopzxylucxhrrltwmizxtdxdrnmuivvcewvaunkqmnjgqgcwdphbvapebhkltmkfcslvgmnqoseu\n",
"30\nloxzyiymhgfemqbhburdctevpybxlv\n",
"200\naaaaeillaoobbwbbxbzbbcccccccdddddddddeeeeeeefffeffffggggghhhhhiiiijjjjjjjkkkkklllllmmmmmmmmmnnnnnnnnnnnnnooooooooppppqqqqqqqqqqrrrrrrrrrrrsssssssssttttttttttuuuuuuuvvvvvvvwwwwwwwxxxxxxyyyyzzzzzzzzzzzz\n",
"37\nxcaccccccccccaaaaaaaaaaaxxxxxxxxxxxxx\n",
"100\nyojtyktazyfegvnnpexxiosqxdlpdwlyojsghsvjpavnvjvttbylqcdabyhleltltzalmgoelxdalcbjejsjxnfebzsxusnujdyk\n",
"30\noiunnflricwjbedvbjtggvwiltbvsx\n",
"200\naaaabbbbcceefffgghhhhijjllnnnnopqrrsstuuvvvwwxxyyyaaaabbbbbbbbcccdddddeeeeeefffffggggghhhhhhhhhiiiiiiiiijjjjkkkkkkllllllmmnmmmmnnnnnoooooooopppppppqqqrrrrrrsssssstttttuuuuuuuvvvvvwwwxxxxxyyyyzzzzzzzzz\n",
"200\nzzzzzzzzyyyyyyyyxxxxxxwwwwwwwwwwwwwwvvvvvvuuuuuuutttttttttttttssssssssrrrrrrrrrrqqqppppppppooooonnnnnmmmmmmmmlllllllkkkkjjjjjiiiiiiiiiiiihhgggggggfffffeeeeeeeeeeeeedddddccccccccccbbbbbbbaaaaaaaaayvrhf\n",
"4\nccba\n",
"200\naaaabbbbbbcccccdddddeeeeeeeffffggggggggghhhhhiiiiijjjjjjjkkkkkkkkllmmmmmmmmmmnnoooooppppqqqqqrrrrrrsssssttttttttttttuuuvvvvvwwwwwwxxxxxxxxyyyzzzzzzzzzaccddddeeffgjjjjkkklllllmmmmonooppqrrsssttwwxyyzzz\n",
"500\nxswciktfxseiibhphrciqwdxqdcbkucypqbektbgtaysnzikdusfujkvnkpseceavrmcijuosnbzrilhvjktikncsjkfpruzltyrxvpzazettavhtroosybftohbskaqjvmbetraurkbmqmrdqrsvwetmouxztmenpmveqwqdlevffcbvskkjhsywghjjynyxyzypbxyzztxapdkhsnubtervdanvtufbifciynpxueeotficwscylbdubagmnjxpnwftyodiuomvgafhmpnledvtwvqdksxqnzybesnuhracyvhwetbtwnixybbbkcuxqifqxqegfumlueoevvnngquaszdbgylezyyheptqjmmdhkjauxakkasrktiaxcdorltevnnwzmkmvkeyubgprzllkvgpwbjdmjiycaiwnavxtwdpvwbdacounqrnowhmshbhyztykozmcvmjofmouqastbwtvbmjpskuuvvaesdymomukqd\n",
"200\nbdimmqrstvaaaaaaaaabbbbbbbbbbcccccddddddeeeeeeeeeeeeeeeffffffgggggggghhhhhhhhhiiiiiiiijjjjjjjjjjjjkkkkkkkklllllllllmmommmmmnnnnnoooooooppppppqqqqqqrrrrrrrrssssssstttttuuvvvvvvwwwwwwwwxxxxxxxyyyyyyyzzz\n",
"200\naaaabccccdddddddeefffffffgghhhiiiiiijjjkjjjkkkkkllllmmmmnnnnnoooooooppqqqqqrrrrsssttuuuuuvwwxxyyyzzzaaaaaabbbbbccccddddddeefffffffggghhiiiikkllmmnnnnnnoooooppppqqqqrrrrsttttuuuuuvvvvwwwwwwxxxxyyyzzzzz\n",
"200\nzzywvuutssssrrqqqpnllkjjjjiihhhhgggggfeeedcccbbbaazzzzzzzzyyyyyxxxxxxwwwwvvvvvuuuuuuttttssssssrrrrrrrqqqqppppppppooooonnnnnnnmmmmmlllkkkjjjjjjjiiiiiiihhhhhhhhggggfffeeeeeeeedddcccccccccccbbbbaaaaaaaaa\n",
"200\nwzzzzzzzzyyyyyyyyyyxxxxxwwwwwwwwwwwvvvvvvuuuutttttttttssssssrrrrrrrrqqqqqqqqqppppppppppoooooooooonnnnnmmmmmmmlllllllllllllkkkkkkjjjjjjiiihhhhhhgggggffffffffeeeeeeeeeeddddddddddddccccccbbbbbbaaaaaaaaaa\n",
"200\naaaabbbbbbccccddddefffffgghhhiiiiiiijijjjjjkkklmmmmnnnnnnooopppppppprrrstuuuuuuvvvvvvvwwxxxxyyyyyyzzaabbbbbbcccdddddddddeffggggghhhhhhiiijjjjjjkkkkllllmmmnnnoopqqqrrssssttttuuuvvvvvwwwwwxxxxyyyyyzzzzz\n",
"9\naefblmbhg\n",
"200\naaaaaaabbbbbbcccccccccdddddddeeeeffffffggggghhhhhiiiiiiiijjjjkkkkkllllllllmmmmmmmmmnnnnnnnnnooooooooopppppppppqqqqqqqqrrrrrrrrrrrsssssssttttuuvvvvvvvvvvwwwwwwwxxxxxxyyyyyyzzyzzbceghhhijjjmmooqrrttvvwx\n",
"200\nndwpatpnvwldptairxlxqbzzysfvglpjkwbemtosqvfnoebfvxfpupvohcaazsjbdshoducigmfoqzltdgvmdmputqmoaqscilmtafqrxdunwnijhrtbwonpvpeouednmjswhauahmgyozmbiilxxflkkmwywvuojbrwwbkyhxtdywiktkfcsmozklhrwlwyajekejrx\n",
"200\nwvskjddddczzzzzzzzzzzyyyyxxxwwwwwvvvvvuuuuuuttttttttsssssssrrrrrrqqqqqqqqqqqppppppooooooonnnnnnmmmmmmmmllllllllkkkkkkjjjjjjjjjjiiiiiiihhhhhhggggggfffffffffeeeeeeedddddddddccccccccccccccbbbbbaaaaaaaaaa\n",
"1\nb\n",
"100\nkshxumdmoygtdgjkwmpsiffhoswmapcogikngvcznwhtufgjstqrbgwjtxrnoevhwaoaxporxbnrijtwkqnteergtvvwkxvbvwch\n",
"200\netlciodomgcmlokdwwjeyckmmjlqjlasmuskklawzyjjsfvcdfkglbtszeqnpcoastbixdtlzizdfwwhdefhcuvwzntuhuwqiulsuhswwillphtaucvycaywgsrqvukvyblsztrcggynyqfofdmjhmiwroipgtztchoewiwstyrjyudijnxqdsqpkejsqlxhahremwyz\n",
"500\nlbwrbavuwfcryqijwcsoafplpiaechmfrrrfagmracruvzendlvjbhqvgskhjtksnjbglefsqmwmwleturpkutdqyxunrkzznfrlnzlvijntlckzaleovnsvpksawjlqndzoixhmjbuysxbffcimcorlndwxowittgtyiomqewnkmxkpdunvnynoybqtdunavsjhgkmtdwugqmaqnduocxzpeqimjguwnjbkvmstekjpppwcuhabmdemqskzrgorgfbuxlsccxsmsrtxgeppwenecutwhxxfevjtxipmsbymvjsprftfqqndumwtissszzzewtbwyeijkvcifexnuzjmtgrilojhrtdaefhwumwafcujhrqlntzqoubqazzmfsbwlvkqijfahdgokzyuskplbkzgomdweqttoqduzurxnslagqgmgywbojnfjuiiattdmuxqmtgrkypqhpxszroffmimhbheasenpvzerzpzamhbealj\n",
"200\naaawaaaabbbbccccccccddddddddddeeeeeeeffffffffffgggggggggghhhhhhhhiiiiiiiiljjjjjjjkkkkkkkkkllllillmmmmmmmmnnnnnnooooooooppppppppqqqqrrrrrrrsssssssttttttuuuuuuuuuvvvvvvvvvwwwwwwwxxxxxxxyyyyyyyzzzzzzzzzz\n",
"200\nzzzyyyyyyyyyyxxxxxxxxxwwwwwwwvvvvuuuutttttssssrrrqqqqqqppppppppppooooooooooonnmmmmmmmmllkkkkjjjjjjjjjiiiiiiiiiiihhhhggggggffffeeeeeeddddddcccccbbbaaaayyxwvvvuuttssssssrrrrqpoonnnmlllkjihhggffedccbaaaa\n",
"500\ndhlmtnvecsbwbycahddxnvwpsxwxgfmidfetpkpeevpjzfbgfafbjpyuevusuptoxutnketcxwrllooyxtxjzwxpzcbpiqzeiplcqvdxyyznjxgkwstpxogdihsamoqhyspbjlelxpbarzqawsgidjtmnpmmupohnslirorliapvntasudhpuuxynyoipuqxdiysbyctpmfpbxqfdlmlsmsvtbxoypkbhwrtpwbsbcdhyppbqhqpdlilquppdwsszrpavcowudreygmpwckbzlpnxxqxjdpqmtidjatvgcbxjrpqqxhhsvlpyxxkoqxutsvebrlxqeggvsnshetkpnfygpwbmnuujfvqnlgavwppufxadhxtffsrdknfmqbsjjegcwokbauzivhnldkvykkytkyrwhimmkznkkofcuioqmpbshskvdhsetyidubcgvuerbozqfbkcmaguaszaivtuswzmtnqcpoiqlvronibiqyeoqms\n",
"200\nzzzzzzzzzzyyyyxxxxxxxxwwwwwwwwvvvvuuuttttttssssrqqqqppppppppppppoooonnnmmmllkkkjjjjjjjiiiiiiihzhhhhyyyhxhhgwggvgggvugggfuuufffrqfpppffooeeonedmdldddldlkkdjciccchhhcccchhcggbbgfbbbfbebdaaccacbabbbbaaaa\n",
"200\nzzzzzzzzyyyyyyyyyxxxxxxxxxxxwwwwwwwvvvvvvvvvvuuuuuuutttttttttssrrrrrrrrrrqqqqqqqqqqqpppppoooooooonnnmmmmmmmmlllllllllkkkkkkkkjjjjjjjiiiiiiiiiihhhhhhhhhgggggggfffffffeeeeeeedddddcccccbbbbbbxblbbaeadcaa\n",
"8\nenjlfmcb\n",
"100\nyvharmmxcxhibqfixtjmhurxchhkvhubxjcveajrkssbsbrxpijxolrtmvanzyybzbdpgzocicakipmkpxhcjtegjsbvabfghpfg\n",
"30\ndcjakwrqosgljwltqlozqmldwuukkg\n",
"30\njzlwlvhfatfwmlpvndtgrxyphfrnnm\n",
"500\nvcghueeuanwyzyipwohsrsyshnxkbigaudamujtqpnoetvfodttsxfdaxqelxqqkbsxlrmqpexlzzyyxrdyokwlztqlzgncncdbbfotrajpxouvsyjyyeawvlnhcqnplnjxpowmlgeqlgyxpwsxnuuwbgrrpzznkmevnlpvgridepvjomgooddrsqoofzdrjoqkiphupyzmowsnkfacpjerawinrqepocvenmrxuzssassrnogqniokddvlylxxbonqkjwobwxhtudxjmpflfhkxexlszpdhoagcdxhurhcgkaxdunopjgezohauarxgtmfaqzewoxxxyexbspsawkdhsbhvuzduuqhjcyisjfpgtglizejzxotdjbavpovonsnhubrlqzffezpybqiujhvwogappkmesscdlhulecyjntntahvyixiesetyetrwhxpetnbwratawvqnbwfwydwdvimgdjkmrxlixylylbtqocnqqjmr\n",
"9\ncbacbacba\n",
"30\nrhkegyacbthzhghossgtqdxtmjfhgx\n",
"200\nzzzzyyyyyyyyyxxxwwwwwwvvvvvvvuuutttssssssrrrrrrrqqqqqppppppppppppooooonnnnnnnmmmmmmmlllllkkkzjzzjyjxjjjixixxixixiwivvhhhhvhhhuuhgfsfsfffsrreerredqdddqqqoddooccoccnmcmcclkjgffccceccbbebebcbaaaaabbaaaaa\n",
"200\nwzzzzzzzzzzzzyyyyyyyyxxxxxxxwwwwwwwwvvvvvvvvvvuuuuuuuttssssssssssrrrrrrrrrqqqqqpppppppppoooooooonnnnnnnnmmmmmmmmlllllllkkkkkjjjjjjjjjiiiiiiiiiiiihhhhhhggggggggggggffeeeeeedddddddccccccbbbbaaaaaaaaaaaa\n",
"100\nqdvwjzmgfmgngaxzgvuuukxyfzecmfuflxpkveaenkorwhmnsxuoxsatlymyjugwjmutfxcksnwhxrwruyqbouyflxhwqhflczzx\n",
"7\nabdcedc\n",
"9\ndfcebcaba\n",
"6\nxhrldq\n",
"500\nhvmmnbwnblqfvwwrcbzkccvcdrhoxbvzwkopagpwntjwwqppduunnenopvyjumjotgcnkoorjcbzctddppezypklfhmxcmufnhcuwxhzbpumlevwdufpyasriaupqdjhpccvtxwqkjseqpsatgbkihgteuclmpaamloxpbtbxhekgpbjvndelmrenhtotvuaymrzpyhmlaujjttwrrlamijsxyegcwagncdscpbvprkwgpwdikdsbqrpkebilprocbyzsupmanekspjzoebjqvmjxjggleinlhipqtbxduimcolchtljqxlumzyrlvvbrirxrlmfrfzpexhwmnfhcmjbphldektmaymqatqssqbcceyjnknldpdhrkrbkkdgofpppsglqncaopghommbsrfcoqchoqenaukngmdyvjkchfuaunikziazfzuolxdpebveatdxnihczfzcxzrapunfkptzxbobuauulmdbdbfjilagpxwx\n",
"200\naadagghjjjkmnpqqttuwwxyzaaafaaaabbbbbbbbcccccddddeeeeeeeeeffgggghhhhhhiiiiiiiijjjjjjjjkkkkklllllmmmmmmmmmmmnnnnnoooooppppppppqqqqqqqqrrrrrrrrrrrssssstttttttttuuuuuuuuvvvvvvvwwwwwwxxxxxxxyyyyyzzzzzzzzz\n",
"4\nczzb\n",
"200\naaaaabbbbbbbbbbbccccccdddddddddeeeeeefffffffffhgggggggggggggghhhhhhhhhiiiiijjjjjjjjjjjkkkkkklllllllmmmmmmmmmnnnnnnnnnnoooooppppppqqqqqqqrrrrrssssssstutttuuuuuuuuvvvvwwwwwwwwwwwwxxxxxxyyyyyyzzzzzzzzzmu\n",
"1\nt\n",
"200\naaaaaabbbbbbbbbbbbbcccyccccccccdddeeeeeeffffggghhhhhhhhhiiiiiiiijjjjjjjjjjkkkkkllllqmmmmmmmmmnnnnnnnoooooooppppppppqlqqqqrrrrrrrrrsssssssttttttttuuuuuuuuvvvvvvvvwwwwwwxxxxxxxyyyyyyycyyzzzzzzzzzzzeinuy\n",
"200\nzzzzyyzzyyzzxzzyxwxxxwwwwvwutvvttvtvvrrvurruuurqdttsqqpposroooorqoqnnqnppooonnnnnnnnmmmmmmmmmmmllllllllkklkkkkkkkkjkjjjjijijiiiiiiiihhhihhhhhhhghgghgggfffffffeeeeeeeeeeddeedtdddcdccdcccccbbbbcbaaaaaaa\n",
"200\ntoimpgygoklxroowdhpacrtrrwmkhcgcpidapeyxrjmiqgilveimnazyydvnujtqpenfkeqdbylfdinompxupfwvirxohaamoqihjueasygkucweptgcowjibgnwyqetynykgoujeargnhjbmntfovwusqavpdwtpnpqpkcgaxbhgdxloyealksmgkxprtpfugixdyfn\n",
"5\nzbdda\n",
"200\nzzzzzzyyyyyyyyyxxxxxwwwwwwvvvvvvvuuuuuuuuuttttttttttsssssssrrrrrrqqqqpppppppppppppooooooooonnnnnnnmmmmmlmmmmmmmlllllllkkkjjjjjjjjiihhhhhhhggggfffffezzewwveuteedtdtdtdddsdsccccpcnljbjbbbbbbigfaedaaaaaa\n",
"200\neduhzzngpdcavqlnmmnxeizwjvpqyjvpsrrcctqcksqcdpiaacpfpddbdpponvaltwnhkndzgcvpfwxowrgdcfoaorywqgfzgappgnjbtifunaobviuufswrbgodyybnoqnvuzfskydepfbrhufysdtuztenrxgqnejoiwifsxteiylfhficviohtkzplmkbriglqhtf\n",
"200\nzzzzzzzyyyyyyyyyyyyxxxxxxxwwwwwwwwwvvvvvvvuuuuuuuutttttttttttsssssssssssrrrrrrrrrrrrrqqqqqpppppppppppoooooonnmnnnnmmmmmmmmmmmllllllkkkkkkkkkjjjjjiihhhhhhggggggggfffffffeeeeeeedcccccccccbbbbbbbaaaaaaza\n",
"100\neivzgzvqwlgzdltwjcmpublpvopzxylucxhqrltwmizxtdxdrnmuivvcewvaunkqmnjgqgcwdphbvapebhkltmkfcslvgmnqoseu\n",
"30\nloxzyiymhgfemqbhburdctevpyaxlv\n",
"200\naaaaeillaoobbwbbxbzbbcccccccdddddddddeeeeeeefffeffffggggghhhhhiiiijjjjjjjkkkkklllllmmmmmlmmmnnnnnnnnnnnnnooooooooppppqqqqqqqqqqrrrrrrrrrrrsssssssssttttttttttuuuuuuuvvvvvvvwwwwwwwxxxxxxyyyyzzzzzzzzzzzz\n",
"37\nxcaccccccccccaaaaaaaaaaaxxxxxxxxxyxxx\n",
"4\nchah\n",
"100\nyojtcktazyfegvnnpexxiosqxdlpdwlyojsghsvjpavnvjvttbylqydabyhleltltzalmgoelxdalcbjejsjxnfebzsxusnujdyk\n",
"8\naaaabcab\n",
"30\noiunnflricwjbedvbjsggvwiltbvtx\n"
],
"output": [
"NO\n",
"YES\n001010101\n",
"YES\n00000\n",
"YES\n00000011\n",
"NO\n",
"NO\n",
"YES\n00000000000000000000000011111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111000000000\n",
"NO\n",
"YES\n00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011\n",
"YES\n0\n",
"YES\n00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011111\n",
"YES\n00000000011110000001101000000011000000000000000000000110100000000111000000000101000001000000000110000000000000000000000000000000010110100111100111110000110001100110010110011010000000100001001100110000\n",
"NO\n",
"NO\n",
"YES\n01111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111100000000000000000000000000000000000000000000000000000000000000000000\n",
"YES\n00000000100011111101000101111010111010101110010001001111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111000000\n",
"NO\n",
"YES\n00111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111110000000\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n00000000100110110101111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111000000000000\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n00000011\n",
"NO\n",
"YES\n00000000000000000000000000000000000000000000000000111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111110000000000000\n",
"YES\n00000111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111110000000000000000\n",
"YES\n01111111111111111111111111111111111111111111111111111111111111000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\n",
"NO\n",
"YES\n00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011111111111111111111111111111111111111111111111000\n",
"NO\n",
"YES\n00000011111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111100000000000000000000000000000000000000000000000000000000000\n",
"NO\n",
"YES\n00000000001111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111110000000000000000000000000000000\n",
"NO\n",
"YES\n00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111100000\n",
"YES\n00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000011111111111111111111111111111111111111111111111100\n",
"NO\n",
"YES\n00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001\n",
"YES\n00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111100000\n",
"NO\n",
"YES\n00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000111111111111111111111111\n",
"NO\n",
"YES\n00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001111111111\n",
"YES\n0\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n00001111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111110000000000000000000000000000000\n",
"YES\n00000000000000000000000000000000000000000000000000111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111110000000000000\n",
"NO\n",
"YES\n00000000100100110101011100110010011110001110101000101110101100110011000100111000111100111011011101000111101111111111111111111111111111111111111111111111111111111111111111111111111111111111110000000000\n",
"YES\n00111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111110000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\n",
"YES\n01\n",
"YES\n00001011101011111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111110000000000000000000000000000\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n00000001111100101011110111000000110100110110011000011101100110001110101110011101111001010101001011110101001011111111111111111111111111111111111111111111111111111111111111111111111111111111111111110000\n",
"YES\n00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n0001\n",
"YES\n0\n",
"YES\n000\n",
"YES\n0010\n",
"YES\n00000011\n",
"YES\n01111111111111111111111111111111111111111111111111111111111111000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001000000\n",
"YES\n00000011111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111100000001100000000000000000000000000000000000000000000000000\n",
"YES\n00111\n",
"YES\n00\n",
"YES\n00000\n",
"YES\n00001011\n",
"YES\n010\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n0\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n0001\n",
"NO\n",
"YES\n0\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n0010\n",
"NO\n",
"YES\n00000011\n",
"NO\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
This is an easy version of the problem. The actual problems are different, but the easy version is almost a subtask of the hard version. Note that the constraints and the output format are different.
You are given a string s consisting of n lowercase Latin letters.
You have to color all its characters one of the two colors (each character to exactly one color, the same letters can be colored the same or different colors, i.e. you can choose exactly one color for each index in s).
After coloring, you can swap any two neighboring characters of the string that are colored different colors. You can perform such an operation arbitrary (possibly, zero) number of times.
The goal is to make the string sorted, i.e. all characters should be in alphabetical order.
Your task is to say if it is possible to color the given string so that after coloring it can become sorted by some sequence of swaps. Note that you have to restore only coloring, not the sequence of swaps.
Input
The first line of the input contains one integer n (1 ≤ n ≤ 200) — the length of s.
The second line of the input contains the string s consisting of exactly n lowercase Latin letters.
Output
If it is impossible to color the given string so that after coloring it can become sorted by some sequence of swaps, print "NO" (without quotes) in the first line.
Otherwise, print "YES" in the first line and any correct coloring in the second line (the coloring is the string consisting of n characters, the i-th character should be '0' if the i-th character is colored the first color and '1' otherwise).
Examples
Input
9
abacbecfd
Output
YES
001010101
Input
8
aaabbcbb
Output
YES
01011011
Input
7
abcdedc
Output
NO
Input
5
abcde
Output
YES
00000
### Input:
7
abcdedc
### Output:
NO
### Input:
9
abacbecfd
### Output:
YES
001010101
### Code:
# ------------------- fast io --------------------
import os
import sys
from io import BytesIO, IOBase
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
# ------------------- fast io --------------------
n = int(input())
s = input()
indexes = [[] for i in range(26)]
for i in range(len(s)):
indexes[ord(s[i])-97] += [i]
#print(indexes)
order = [0]*n
count = 1
for each in indexes:
incount = False
for k in each:
incount=True
order[k] = count
if incount:
count += 1
coloring = ['']*n
opposites = [[] for i in range(n+1)]
#print(order, opposites)
for i in range(n):
for j in range(i+1, n):
if order[i] > order[j]:
#print(i, j)
for k in range(i, j):
opposites[j] += [i]
opposites[i] += [j]
coloring[0] = '0'
def opp(x): return '0' if x == '1' else '1'
poss = True
for i in range(n):
if not coloring[i]:
coloring[i] = '0'
for k in opposites[i]:
#print(i, k, coloring)
if coloring[k] == '':
coloring[k] = opp(coloring[i])
else:
if coloring[k] != opp(coloring[i]):
poss = False
break
if poss:
print('YES')
print(''.join(coloring))
else:
print('NO')
|
131_E. Yet Another Task with Queens_10799
|
A queen is the strongest chess piece. In modern chess the queen can move any number of squares in any horizontal, vertical or diagonal direction (considering that there're no other pieces on its way). The queen combines the options given to the rook and the bishop.
There are m queens on a square n × n chessboard. You know each queen's positions, the i-th queen is positioned in the square (ri, ci), where ri is the board row number (numbered from the top to the bottom from 1 to n), and ci is the board's column number (numbered from the left to the right from 1 to n). No two queens share the same position.
For each queen one can count w — the number of other queens that the given queen threatens (attacks). For a fixed attack direction only the first queen in this direction is under attack if there are many queens are on the ray of the attack. Obviously, for any queen w is between 0 and 8, inclusive.
Print the sequence t0, t1, ..., t8, where ti is the number of queens that threaten exactly i other queens, i.e. the number of queens that their w equals i.
Input
The first line of the input contains a pair of integers n, m (1 ≤ n, m ≤ 105), where n is the size of the board and m is the number of queens on the board. Then m following lines contain positions of the queens, one per line. Each line contains a pair of integers ri, ci (1 ≤ ri, ci ≤ n) — the queen's position. No two queens stand on the same square.
Output
Print the required sequence t0, t1, ..., t8, separating the numbers with spaces.
Examples
Input
8 4
4 3
4 8
6 5
1 6
Output
0 3 0 1 0 0 0 0 0
Input
10 3
1 1
1 2
1 3
Output
0 2 1 0 0 0 0 0 0
|
#Code by Sounak, IIESTS
#------------------------------warmup----------------------------
import os
import sys
import math
from io import BytesIO, IOBase
from fractions import Fraction
import collections
from itertools import permutations
from collections import defaultdict
from collections import deque
import threading
#sys.setrecursionlimit(300000)
#threading.stack_size(10**8)
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
#-------------------------------------------------------------------------
#mod = 9223372036854775807
class SegmentTree:
def __init__(self, data, default=10**10, func=lambda a, b: min(a,b)):
"""initialize the segment tree with data"""
self._default = default
self._func = func
self._len = len(data)
self._size = _size = 1 << (self._len - 1).bit_length()
self.data = [default] * (2 * _size)
self.data[_size:_size + self._len] = data
for i in reversed(range(_size)):
self.data[i] = func(self.data[i + i], self.data[i + i + 1])
def __delitem__(self, idx):
self[idx] = self._default
def __getitem__(self, idx):
return self.data[idx + self._size]
def __setitem__(self, idx, value):
idx += self._size
self.data[idx] = value
idx >>= 1
while idx:
self.data[idx] = self._func(self.data[2 * idx], self.data[2 * idx + 1])
idx >>= 1
def __len__(self):
return self._len
def query(self, start, stop):
if start == stop:
return self.__getitem__(start)
stop += 1
start += self._size
stop += self._size
res = self._default
while start < stop:
if start & 1:
res = self._func(res, self.data[start])
start += 1
if stop & 1:
stop -= 1
res = self._func(res, self.data[stop])
start >>= 1
stop >>= 1
return res
def __repr__(self):
return "SegmentTree({0})".format(self.data)
MOD=10**9+7
class Factorial:
def __init__(self, MOD):
self.MOD = MOD
self.factorials = [1, 1]
self.invModulos = [0, 1]
self.invFactorial_ = [1, 1]
def calc(self, n):
if n <= -1:
print("Invalid argument to calculate n!")
print("n must be non-negative value. But the argument was " + str(n))
exit()
if n < len(self.factorials):
return self.factorials[n]
nextArr = [0] * (n + 1 - len(self.factorials))
initialI = len(self.factorials)
prev = self.factorials[-1]
m = self.MOD
for i in range(initialI, n + 1):
prev = nextArr[i - initialI] = prev * i % m
self.factorials += nextArr
return self.factorials[n]
def inv(self, n):
if n <= -1:
print("Invalid argument to calculate n^(-1)")
print("n must be non-negative value. But the argument was " + str(n))
exit()
p = self.MOD
pi = n % p
if pi < len(self.invModulos):
return self.invModulos[pi]
nextArr = [0] * (n + 1 - len(self.invModulos))
initialI = len(self.invModulos)
for i in range(initialI, min(p, n + 1)):
next = -self.invModulos[p % i] * (p // i) % p
self.invModulos.append(next)
return self.invModulos[pi]
def invFactorial(self, n):
if n <= -1:
print("Invalid argument to calculate (n^(-1))!")
print("n must be non-negative value. But the argument was " + str(n))
exit()
if n < len(self.invFactorial_):
return self.invFactorial_[n]
self.inv(n) # To make sure already calculated n^-1
nextArr = [0] * (n + 1 - len(self.invFactorial_))
initialI = len(self.invFactorial_)
prev = self.invFactorial_[-1]
p = self.MOD
for i in range(initialI, n + 1):
prev = nextArr[i - initialI] = (prev * self.invModulos[i % p]) % p
self.invFactorial_ += nextArr
return self.invFactorial_[n]
class Combination:
def __init__(self, MOD):
self.MOD = MOD
self.factorial = Factorial(MOD)
def ncr(self, n, k):
if k < 0 or n < k:
return 0
k = min(k, n - k)
f = self.factorial
return f.calc(n) * f.invFactorial(max(n - k, k)) * f.invFactorial(min(k, n - k)) % self.MOD
mod=10**9+7
omod=998244353
#-------------------------------------------------------------------------
n,m=list(map(int,input().split()))
f=[]
maxx=[-999999999]*n
minx=[999999999]*n
maxy=[-999999999]*n
miny=[999999999]*n
maxm=[-999999999]*(2*n-1)
minm=[999999999]*(2*n-1)
maxs=[-999999999]*(2*n-1)
mins=[999999999]*(2*n-1)
r=[0 for i in range(9)]
for i in range(m):
y,x=list(map(int,input().split()))
a,b,c,d=y-1,x-1,y+x-2,y-x+n-1
f.append((a,b,c,d))
if a>maxx[b]:maxx[b]=a
if a<minx[b]:minx[b]=a
if x-1>maxy[a]:maxy[a]=x-1
if x-1<miny[a]:miny[a]=x-1
if c>maxs[d]:maxs[d]=c
if c<mins[d]:mins[d]=c
if d>maxm[c]:maxm[c]=d
if d<minm[c]:minm[c]=d
for i in f:
k=0
if i[0]<maxx[i[1]]:k+=1
if i[0]>minx[i[1]]:k+=1
if i[1]<maxy[i[0]]:k+=1
if i[1]>miny[i[0]]:k+=1
if i[2]<maxs[i[3]]:k+=1
if i[2]>mins[i[3]]:k+=1
if i[3]<maxm[i[2]]:k+=1
if i[3]>minm[i[2]]:k+=1
r[k]+=1
print(*r)
|
{
"input": [
"10 3\n1 1\n1 2\n1 3\n",
"8 4\n4 3\n4 8\n6 5\n1 6\n",
"10 10\n6 5\n3 5\n3 4\n6 10\n3 10\n4 6\n6 2\n7 5\n1 8\n2 2\n",
"10 20\n6 10\n3 10\n10 4\n5 3\n9 4\n10 1\n10 3\n10 7\n8 5\n7 2\n4 7\n5 1\n2 9\n5 5\n6 6\n9 8\n2 10\n9 10\n1 4\n7 4\n",
"2 1\n1 1\n",
"10 4\n5 6\n4 8\n8 4\n7 4\n",
"10 5\n2 3\n1 3\n3 3\n2 1\n2 5\n",
"2 2\n1 1\n1 2\n",
"8 8\n8 3\n3 7\n7 1\n4 4\n1 6\n1 7\n3 3\n2 1\n",
"1 1\n1 1\n",
"2 4\n2 1\n1 2\n2 2\n1 1\n",
"100 10\n97 5\n53 35\n92 86\n54 95\n98 13\n36 23\n55 56\n96 94\n25 96\n49 31\n",
"10 5\n2 3\n1 6\n3 3\n2 1\n2 5\n",
"16 8\n8 3\n3 7\n7 1\n4 4\n1 6\n1 7\n3 3\n2 1\n",
"100 10\n97 5\n53 35\n92 86\n54 75\n98 13\n36 23\n55 56\n96 94\n25 96\n49 31\n",
"8 4\n4 3\n8 8\n6 5\n1 6\n",
"100 10\n97 5\n53 35\n92 86\n54 75\n7 13\n36 23\n55 56\n96 94\n25 96\n49 31\n",
"8 4\n1 3\n8 8\n6 5\n1 6\n",
"100 10\n97 5\n53 35\n92 86\n54 75\n7 13\n36 23\n55 27\n96 94\n25 96\n49 24\n",
"100 10\n97 3\n53 35\n92 86\n54 34\n7 6\n43 23\n55 27\n96 94\n25 96\n49 24\n",
"10 5\n2 3\n1 3\n3 3\n2 1\n1 5\n",
"20 3\n1 1\n1 2\n1 3\n",
"10 5\n2 3\n1 6\n3 3\n2 1\n2 8\n",
"16 8\n8 3\n3 7\n7 1\n4 4\n1 6\n1 7\n3 3\n1 1\n",
"8 4\n4 2\n8 8\n6 5\n1 6\n",
"10 4\n5 8\n4 9\n8 4\n7 4\n",
"16 8\n8 3\n3 7\n7 1\n8 4\n1 6\n1 7\n3 3\n1 1\n",
"10 5\n1 3\n1 6\n3 3\n2 1\n2 6\n",
"16 8\n8 3\n3 7\n7 1\n8 4\n1 6\n1 7\n3 3\n1 2\n",
"100 10\n97 5\n53 35\n92 86\n54 75\n7 13\n36 23\n55 27\n96 94\n25 96\n49 31\n",
"100 10\n97 5\n53 35\n92 86\n54 75\n7 6\n36 23\n55 27\n96 94\n25 96\n49 24\n",
"100 10\n97 3\n53 35\n92 86\n54 75\n7 6\n36 23\n55 27\n96 94\n25 96\n49 24\n",
"100 10\n97 3\n53 35\n92 86\n54 34\n7 6\n36 23\n55 27\n96 94\n25 96\n49 24\n",
"100 10\n97 3\n53 35\n92 86\n89 34\n7 6\n43 23\n55 27\n96 94\n25 96\n49 24\n",
"100 10\n97 3\n53 35\n9 86\n89 34\n7 6\n43 23\n55 27\n96 94\n25 96\n49 24\n",
"100 10\n97 3\n53 36\n9 86\n89 34\n7 6\n43 23\n55 27\n96 94\n25 96\n49 24\n",
"100 10\n97 3\n53 44\n9 86\n89 34\n7 6\n43 23\n55 27\n96 94\n25 96\n49 24\n",
"10 4\n5 6\n4 9\n8 4\n7 4\n",
"8 4\n2 3\n8 8\n6 5\n1 6\n",
"100 10\n97 5\n53 35\n92 86\n54 75\n1 13\n36 23\n55 27\n96 94\n25 96\n49 31\n",
"100 10\n97 5\n53 35\n92 86\n54 75\n7 13\n36 23\n55 27\n53 94\n25 96\n49 24\n",
"100 10\n97 5\n34 35\n92 86\n54 75\n7 6\n36 23\n55 27\n96 94\n25 96\n49 24\n",
"100 10\n97 3\n53 35\n92 86\n54 35\n7 6\n36 23\n55 27\n96 94\n25 96\n49 24\n",
"100 10\n97 3\n53 35\n92 86\n54 34\n7 6\n36 2\n55 27\n96 94\n25 96\n49 24\n",
"100 10\n97 3\n53 9\n92 86\n54 34\n7 6\n43 23\n55 27\n96 94\n25 96\n49 24\n",
"110 10\n97 3\n53 35\n92 86\n89 34\n7 6\n43 23\n55 27\n96 94\n25 96\n49 24\n",
"100 10\n97 3\n53 35\n12 86\n89 34\n7 6\n43 23\n55 27\n96 94\n25 96\n49 24\n",
"100 10\n97 3\n53 44\n9 86\n89 34\n7 6\n43 23\n55 27\n96 94\n38 96\n49 24\n",
"38 3\n1 1\n1 2\n1 3\n",
"10 5\n2 3\n1 6\n3 3\n2 1\n2 6\n",
"8 4\n4 2\n8 8\n6 5\n2 6\n",
"100 10\n72 5\n53 35\n92 86\n54 75\n1 13\n36 23\n55 27\n96 94\n25 96\n49 31\n",
"100 10\n97 5\n53 35\n92 86\n54 75\n7 13\n49 23\n55 27\n53 94\n25 96\n49 24\n",
"100 10\n97 5\n34 53\n92 86\n54 75\n7 6\n36 23\n55 27\n96 94\n25 96\n49 24\n",
"100 10\n97 3\n53 35\n92 86\n54 35\n7 6\n36 23\n55 27\n96 94\n25 96\n84 24\n",
"110 10\n97 3\n53 35\n92 86\n54 34\n7 6\n36 2\n55 27\n96 94\n25 96\n49 24\n",
"100 10\n97 3\n53 11\n92 86\n54 34\n7 6\n43 23\n55 27\n96 94\n25 96\n49 24\n",
"110 10\n97 3\n53 35\n92 86\n89 34\n7 6\n43 37\n55 27\n96 94\n25 96\n49 24\n",
"100 10\n97 3\n53 38\n12 86\n89 34\n7 6\n43 23\n55 27\n96 94\n25 96\n49 24\n",
"100 10\n97 3\n22 44\n9 86\n89 34\n7 6\n43 23\n55 27\n96 94\n38 96\n49 24\n",
"8 4\n4 2\n8 8\n6 5\n3 6\n",
"100 10\n97 5\n53 35\n92 86\n54 75\n7 13\n9 23\n55 27\n53 94\n25 96\n49 24\n"
],
"output": [
"0 2 1 0 0 0 0 0 0\n",
"0 3 0 1 0 0 0 0 0\n",
"0 5 1 2 1 1 0 0 0\n",
"0 0 4 9 4 1 2 0 0\n",
"1 0 0 0 0 0 0 0 0\n",
"0 2 2 0 0 0 0 0 0\n",
"0 4 0 0 1 0 0 0 0\n",
"0 2 0 0 0 0 0 0 0\n",
"0 3 2 3 0 0 0 0 0\n",
"1 0 0 0 0 0 0 0 0\n",
"0 0 0 4 0 0 0 0 0\n",
"6 4 0 0 0 0 0 0 0\n",
"0 3 1 1 0 0 0 0 0\n",
"0 3 2 3 0 0 0 0 0\n",
"6 4 0 0 0 0 0 0 0\n",
"1 2 1 0 0 0 0 0 0\n",
"8 2 0 0 0 0 0 0 0\n",
"2 2 0 0 0 0 0 0 0\n",
"10 0 0 0 0 0 0 0 0\n",
"7 2 1 0 0 0 0 0 0\n",
"0 1 3 1 0 0 0 0 0\n",
"0 2 1 0 0 0 0 0 0\n",
"1 3 0 1 0 0 0 0 0\n",
"0 1 3 3 1 0 0 0 0\n",
"4 0 0 0 0 0 0 0 0\n",
"0 4 0 0 0 0 0 0 0\n",
"0 1 4 3 0 0 0 0 0\n",
"0 2 3 0 0 0 0 0 0\n",
"0 3 4 1 0 0 0 0 0\n",
"8 2 0 0 0 0 0 0 0\n",
"10 0 0 0 0 0 0 0 0\n",
"10 0 0 0 0 0 0 0 0\n",
"8 2 0 0 0 0 0 0 0\n",
"10 0 0 0 0 0 0 0 0\n",
"10 0 0 0 0 0 0 0 0\n",
"10 0 0 0 0 0 0 0 0\n",
"10 0 0 0 0 0 0 0 0\n",
"1 2 1 0 0 0 0 0 0\n",
"4 0 0 0 0 0 0 0 0\n",
"8 2 0 0 0 0 0 0 0\n",
"8 2 0 0 0 0 0 0 0\n",
"10 0 0 0 0 0 0 0 0\n",
"8 2 0 0 0 0 0 0 0\n",
"8 2 0 0 0 0 0 0 0\n",
"8 2 0 0 0 0 0 0 0\n",
"10 0 0 0 0 0 0 0 0\n",
"10 0 0 0 0 0 0 0 0\n",
"10 0 0 0 0 0 0 0 0\n",
"0 2 1 0 0 0 0 0 0\n",
"0 3 1 1 0 0 0 0 0\n",
"4 0 0 0 0 0 0 0 0\n",
"8 2 0 0 0 0 0 0 0\n",
"6 4 0 0 0 0 0 0 0\n",
"10 0 0 0 0 0 0 0 0\n",
"8 2 0 0 0 0 0 0 0\n",
"8 2 0 0 0 0 0 0 0\n",
"8 2 0 0 0 0 0 0 0\n",
"8 2 0 0 0 0 0 0 0\n",
"10 0 0 0 0 0 0 0 0\n",
"8 2 0 0 0 0 0 0 0\n",
"4 0 0 0 0 0 0 0 0\n",
"8 2 0 0 0 0 0 0 0\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
A queen is the strongest chess piece. In modern chess the queen can move any number of squares in any horizontal, vertical or diagonal direction (considering that there're no other pieces on its way). The queen combines the options given to the rook and the bishop.
There are m queens on a square n × n chessboard. You know each queen's positions, the i-th queen is positioned in the square (ri, ci), where ri is the board row number (numbered from the top to the bottom from 1 to n), and ci is the board's column number (numbered from the left to the right from 1 to n). No two queens share the same position.
For each queen one can count w — the number of other queens that the given queen threatens (attacks). For a fixed attack direction only the first queen in this direction is under attack if there are many queens are on the ray of the attack. Obviously, for any queen w is between 0 and 8, inclusive.
Print the sequence t0, t1, ..., t8, where ti is the number of queens that threaten exactly i other queens, i.e. the number of queens that their w equals i.
Input
The first line of the input contains a pair of integers n, m (1 ≤ n, m ≤ 105), where n is the size of the board and m is the number of queens on the board. Then m following lines contain positions of the queens, one per line. Each line contains a pair of integers ri, ci (1 ≤ ri, ci ≤ n) — the queen's position. No two queens stand on the same square.
Output
Print the required sequence t0, t1, ..., t8, separating the numbers with spaces.
Examples
Input
8 4
4 3
4 8
6 5
1 6
Output
0 3 0 1 0 0 0 0 0
Input
10 3
1 1
1 2
1 3
Output
0 2 1 0 0 0 0 0 0
### Input:
10 3
1 1
1 2
1 3
### Output:
0 2 1 0 0 0 0 0 0
### Input:
8 4
4 3
4 8
6 5
1 6
### Output:
0 3 0 1 0 0 0 0 0
### Code:
#Code by Sounak, IIESTS
#------------------------------warmup----------------------------
import os
import sys
import math
from io import BytesIO, IOBase
from fractions import Fraction
import collections
from itertools import permutations
from collections import defaultdict
from collections import deque
import threading
#sys.setrecursionlimit(300000)
#threading.stack_size(10**8)
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
#-------------------------------------------------------------------------
#mod = 9223372036854775807
class SegmentTree:
def __init__(self, data, default=10**10, func=lambda a, b: min(a,b)):
"""initialize the segment tree with data"""
self._default = default
self._func = func
self._len = len(data)
self._size = _size = 1 << (self._len - 1).bit_length()
self.data = [default] * (2 * _size)
self.data[_size:_size + self._len] = data
for i in reversed(range(_size)):
self.data[i] = func(self.data[i + i], self.data[i + i + 1])
def __delitem__(self, idx):
self[idx] = self._default
def __getitem__(self, idx):
return self.data[idx + self._size]
def __setitem__(self, idx, value):
idx += self._size
self.data[idx] = value
idx >>= 1
while idx:
self.data[idx] = self._func(self.data[2 * idx], self.data[2 * idx + 1])
idx >>= 1
def __len__(self):
return self._len
def query(self, start, stop):
if start == stop:
return self.__getitem__(start)
stop += 1
start += self._size
stop += self._size
res = self._default
while start < stop:
if start & 1:
res = self._func(res, self.data[start])
start += 1
if stop & 1:
stop -= 1
res = self._func(res, self.data[stop])
start >>= 1
stop >>= 1
return res
def __repr__(self):
return "SegmentTree({0})".format(self.data)
MOD=10**9+7
class Factorial:
def __init__(self, MOD):
self.MOD = MOD
self.factorials = [1, 1]
self.invModulos = [0, 1]
self.invFactorial_ = [1, 1]
def calc(self, n):
if n <= -1:
print("Invalid argument to calculate n!")
print("n must be non-negative value. But the argument was " + str(n))
exit()
if n < len(self.factorials):
return self.factorials[n]
nextArr = [0] * (n + 1 - len(self.factorials))
initialI = len(self.factorials)
prev = self.factorials[-1]
m = self.MOD
for i in range(initialI, n + 1):
prev = nextArr[i - initialI] = prev * i % m
self.factorials += nextArr
return self.factorials[n]
def inv(self, n):
if n <= -1:
print("Invalid argument to calculate n^(-1)")
print("n must be non-negative value. But the argument was " + str(n))
exit()
p = self.MOD
pi = n % p
if pi < len(self.invModulos):
return self.invModulos[pi]
nextArr = [0] * (n + 1 - len(self.invModulos))
initialI = len(self.invModulos)
for i in range(initialI, min(p, n + 1)):
next = -self.invModulos[p % i] * (p // i) % p
self.invModulos.append(next)
return self.invModulos[pi]
def invFactorial(self, n):
if n <= -1:
print("Invalid argument to calculate (n^(-1))!")
print("n must be non-negative value. But the argument was " + str(n))
exit()
if n < len(self.invFactorial_):
return self.invFactorial_[n]
self.inv(n) # To make sure already calculated n^-1
nextArr = [0] * (n + 1 - len(self.invFactorial_))
initialI = len(self.invFactorial_)
prev = self.invFactorial_[-1]
p = self.MOD
for i in range(initialI, n + 1):
prev = nextArr[i - initialI] = (prev * self.invModulos[i % p]) % p
self.invFactorial_ += nextArr
return self.invFactorial_[n]
class Combination:
def __init__(self, MOD):
self.MOD = MOD
self.factorial = Factorial(MOD)
def ncr(self, n, k):
if k < 0 or n < k:
return 0
k = min(k, n - k)
f = self.factorial
return f.calc(n) * f.invFactorial(max(n - k, k)) * f.invFactorial(min(k, n - k)) % self.MOD
mod=10**9+7
omod=998244353
#-------------------------------------------------------------------------
n,m=list(map(int,input().split()))
f=[]
maxx=[-999999999]*n
minx=[999999999]*n
maxy=[-999999999]*n
miny=[999999999]*n
maxm=[-999999999]*(2*n-1)
minm=[999999999]*(2*n-1)
maxs=[-999999999]*(2*n-1)
mins=[999999999]*(2*n-1)
r=[0 for i in range(9)]
for i in range(m):
y,x=list(map(int,input().split()))
a,b,c,d=y-1,x-1,y+x-2,y-x+n-1
f.append((a,b,c,d))
if a>maxx[b]:maxx[b]=a
if a<minx[b]:minx[b]=a
if x-1>maxy[a]:maxy[a]=x-1
if x-1<miny[a]:miny[a]=x-1
if c>maxs[d]:maxs[d]=c
if c<mins[d]:mins[d]=c
if d>maxm[c]:maxm[c]=d
if d<minm[c]:minm[c]=d
for i in f:
k=0
if i[0]<maxx[i[1]]:k+=1
if i[0]>minx[i[1]]:k+=1
if i[1]<maxy[i[0]]:k+=1
if i[1]>miny[i[0]]:k+=1
if i[2]<maxs[i[3]]:k+=1
if i[2]>mins[i[3]]:k+=1
if i[3]<maxm[i[2]]:k+=1
if i[3]>minm[i[2]]:k+=1
r[k]+=1
print(*r)
|
1339_B. Sorted Adjacent Differences_10803
|
You have array of n numbers a_{1}, a_{2}, …, a_{n}.
Rearrange these numbers to satisfy |a_{1} - a_{2}| ≤ |a_{2} - a_{3}| ≤ … ≤ |a_{n-1} - a_{n}|, where |x| denotes absolute value of x. It's always possible to find such rearrangement.
Note that all numbers in a are not necessarily different. In other words, some numbers of a may be same.
You have to answer independent t test cases.
Input
The first line contains a single integer t (1 ≤ t ≤ 10^{4}) — the number of test cases.
The first line of each test case contains single integer n (3 ≤ n ≤ 10^{5}) — the length of array a. It is guaranteed that the sum of values of n over all test cases in the input does not exceed 10^{5}.
The second line of each test case contains n integers a_{1}, a_{2}, …, a_{n} (-10^{9} ≤ a_{i} ≤ 10^{9}).
Output
For each test case, print the rearranged version of array a which satisfies given condition. If there are multiple valid rearrangements, print any of them.
Example
Input
2
6
5 -2 4 8 6 5
4
8 1 4 2
Output
5 5 4 6 8 -2
1 2 4 8
Note
In the first test case, after given rearrangement, |a_{1} - a_{2}| = 0 ≤ |a_{2} - a_{3}| = 1 ≤ |a_{3} - a_{4}| = 2 ≤ |a_{4} - a_{5}| = 2 ≤ |a_{5} - a_{6}| = 10. There are other possible answers like "5 4 5 6 -2 8".
In the second test case, after given rearrangement, |a_{1} - a_{2}| = 1 ≤ |a_{2} - a_{3}| = 2 ≤ |a_{3} - a_{4}| = 4. There are other possible answers like "2 4 8 1".
|
for _ in range(int(input())):
n = int(input())
ls = sorted(list(map(int, input().split())))
mid = n // 2
if n % 2 == 0:
mid -= 1
i = mid - 1
turn = True
j = mid + 1
ar = []
ar.append(ls[mid])
while i >= 0 or j < n:
if turn and j < n:
ar.append(ls[j])
j += 1
elif not turn and i >= 0:
ar.append(ls[i])
i -= 1
turn = not turn
print(*ar)
|
{
"input": [
"2\n6\n5 -2 4 8 6 5\n4\n8 1 4 2\n",
"1\n29\n31 16383 15 127 255 3 4095 536870911 7 63 262143 2097151 1 16777215 134217727 524287 511 8388607 67108863 1023 8191 2047 32767 33554431 268435455 65535 131071 1048575 4194303\n",
"1\n29\n31 16383 15 127 255 3 4095 536870911 7 63 318805 2097151 1 16777215 134217727 524287 511 8388607 67108863 1023 8191 2047 32767 33554431 268435455 65535 131071 1048575 4194303\n",
"2\n6\n5 -2 4 8 6 5\n4\n8 2 4 2\n",
"1\n29\n31 16383 15 127 255 3 4095 536870911 7 63 318805 1051398 1 16777215 134217727 524287 511 8388607 67108863 1023 8191 2047 32767 33554431 268435455 65535 131071 1048575 4194303\n",
"1\n29\n31 16383 15 127 255 3 4095 536870911 7 63 318805 1051398 1 16777215 134217727 524287 511 8388607 67108863 1023 11905 2047 32767 33554431 268435455 65535 131071 1048575 4194303\n",
"1\n29\n31 16383 15 127 255 3 4095 536870911 7 63 318805 566596 1 16777215 134217727 524287 511 8388607 67108863 1023 11905 2047 32767 33554431 268435455 65535 131071 1048575 4194303\n",
"1\n29\n31 16383 27 127 255 3 4095 536870911 7 63 318805 566596 1 16777215 134217727 524287 511 8388607 67108863 1023 11905 2047 32767 33554431 268435455 65535 131071 1048575 4194303\n",
"1\n29\n31 16383 27 127 255 3 4095 536870911 7 63 318805 566596 1 17121512 134217727 524287 511 8388607 67108863 1023 11905 2047 32767 33554431 268435455 65535 131071 1048575 4194303\n",
"2\n6\n5 -2 6 8 6 5\n4\n8 1 4 2\n",
"1\n29\n31 16383 15 127 255 3 4095 536870911 7 63 318805 2097151 1 16777215 134217727 524287 511 8388607 67108863 1023 8191 2047 32767 33554431 268435455 65535 239326 1048575 4194303\n",
"2\n6\n5 -4 4 8 6 5\n4\n8 1 4 2\n",
"1\n29\n31 16383 15 127 255 3 4095 536870911 7 63 318805 1051398 1 16777215 134217727 524287 915 8388607 67108863 1023 8191 2047 32767 33554431 268435455 65535 131071 1048575 4194303\n",
"1\n29\n31 16383 15 127 255 3 4095 536870911 7 63 318805 1051398 1 16777215 134217727 524287 511 15554909 67108863 1023 11905 2047 32767 33554431 268435455 65535 131071 1048575 4194303\n",
"1\n29\n31 16383 15 127 255 3 4095 536870911 7 63 318805 566596 1 16777215 159670400 524287 511 8388607 67108863 1023 11905 2047 32767 33554431 268435455 65535 131071 1048575 4194303\n",
"1\n29\n31 16383 27 127 255 3 4095 536870911 7 63 513980 566596 1 16777215 134217727 524287 511 8388607 67108863 1023 11905 2047 32767 33554431 268435455 65535 131071 1048575 4194303\n",
"1\n29\n31 16383 27 127 255 3 4095 447420925 7 63 318805 566596 1 17121512 134217727 524287 511 8388607 67108863 1023 11905 2047 32767 33554431 268435455 65535 131071 1048575 4194303\n",
"2\n6\n5 -2 6 8 0 5\n4\n8 1 4 2\n",
"1\n29\n31 16383 15 127 255 3 4095 536870911 7 63 318805 2097151 1 16777215 134217727 524287 511 8388607 67108863 1023 8191 2047 21746 33554431 268435455 65535 239326 1048575 4194303\n",
"2\n6\n5 -4 4 8 6 5\n4\n8 1 4 4\n",
"1\n29\n31 16383 19 127 255 3 4095 536870911 7 63 318805 1051398 1 16777215 134217727 524287 915 8388607 67108863 1023 8191 2047 32767 33554431 268435455 65535 131071 1048575 4194303\n",
"1\n29\n31 4290 15 127 255 3 4095 536870911 7 63 318805 1051398 1 16777215 134217727 524287 511 15554909 67108863 1023 11905 2047 32767 33554431 268435455 65535 131071 1048575 4194303\n",
"1\n29\n31 16383 15 127 255 3 4095 536870911 7 63 318805 566596 0 16777215 159670400 524287 511 8388607 67108863 1023 11905 2047 32767 33554431 268435455 65535 131071 1048575 4194303\n",
"1\n29\n7 16383 27 127 255 3 4095 536870911 7 63 513980 566596 1 16777215 134217727 524287 511 8388607 67108863 1023 11905 2047 32767 33554431 268435455 65535 131071 1048575 4194303\n",
"1\n29\n31 9387 27 127 255 3 4095 447420925 7 63 318805 566596 1 17121512 134217727 524287 511 8388607 67108863 1023 11905 2047 32767 33554431 268435455 65535 131071 1048575 4194303\n",
"2\n6\n5 -2 6 8 0 5\n4\n13 1 4 2\n",
"1\n29\n31 16383 15 127 255 3 4095 536870911 7 63 318805 2097151 1 16777215 134217727 524287 511 8388607 67108863 1023 9571 2047 21746 33554431 268435455 65535 239326 1048575 4194303\n",
"2\n6\n5 -4 8 8 6 5\n4\n8 1 4 4\n",
"1\n29\n31 16383 19 127 255 3 4095 536870911 7 63 318805 833436 1 16777215 134217727 524287 915 8388607 67108863 1023 8191 2047 32767 33554431 268435455 65535 131071 1048575 4194303\n",
"1\n29\n53 4290 15 127 255 3 4095 536870911 7 63 318805 1051398 1 16777215 134217727 524287 511 15554909 67108863 1023 11905 2047 32767 33554431 268435455 65535 131071 1048575 4194303\n",
"1\n29\n31 6304 15 127 255 3 4095 536870911 7 63 318805 566596 0 16777215 159670400 524287 511 8388607 67108863 1023 11905 2047 32767 33554431 268435455 65535 131071 1048575 4194303\n",
"1\n29\n7 16383 27 127 255 3 4095 536870911 7 63 513980 476451 1 16777215 134217727 524287 511 8388607 67108863 1023 11905 2047 32767 33554431 268435455 65535 131071 1048575 4194303\n",
"1\n29\n31 9387 27 127 255 3 4095 447420925 13 63 318805 566596 1 17121512 134217727 524287 511 8388607 67108863 1023 11905 2047 32767 33554431 268435455 65535 131071 1048575 4194303\n",
"2\n6\n5 -2 6 8 0 5\n4\n26 1 4 2\n",
"1\n29\n31 16383 15 127 255 3 4095 536870911 7 63 318805 2097151 1 16777215 134217727 524287 511 8388607 67108863 1023 9571 2047 21746 33554431 4225164 65535 239326 1048575 4194303\n",
"1\n29\n31 17591 19 127 255 3 4095 536870911 7 63 318805 833436 1 16777215 134217727 524287 915 8388607 67108863 1023 8191 2047 32767 33554431 268435455 65535 131071 1048575 4194303\n",
"1\n29\n53 4290 15 127 255 3 4095 255207509 7 63 318805 1051398 1 16777215 134217727 524287 511 15554909 67108863 1023 11905 2047 32767 33554431 268435455 65535 131071 1048575 4194303\n",
"1\n29\n31 6304 15 127 255 3 4095 536870911 7 63 318805 566596 0 16777215 159670400 524287 511 10299238 67108863 1023 11905 2047 32767 33554431 268435455 65535 131071 1048575 4194303\n",
"1\n29\n7 16383 27 127 255 3 4095 536870911 8 63 513980 476451 1 16777215 134217727 524287 511 8388607 67108863 1023 11905 2047 32767 33554431 268435455 65535 131071 1048575 4194303\n",
"1\n29\n31 9387 27 127 503 3 4095 447420925 13 63 318805 566596 1 17121512 134217727 524287 511 8388607 67108863 1023 11905 2047 32767 33554431 268435455 65535 131071 1048575 4194303\n",
"2\n6\n5 -2 6 8 0 7\n4\n26 1 4 2\n",
"1\n29\n31 16383 15 127 255 3 4095 536870911 7 63 318805 2097151 2 16777215 134217727 524287 511 8388607 67108863 1023 9571 2047 21746 33554431 4225164 65535 239326 1048575 4194303\n",
"1\n29\n56 17591 19 127 255 3 4095 536870911 7 63 318805 833436 1 16777215 134217727 524287 915 8388607 67108863 1023 8191 2047 32767 33554431 268435455 65535 131071 1048575 4194303\n",
"1\n29\n53 4290 15 127 255 3 4095 255207509 7 63 318805 1051398 1 16777215 134217727 524287 289 15554909 67108863 1023 11905 2047 32767 33554431 268435455 65535 131071 1048575 4194303\n",
"1\n29\n31 6304 9 127 255 3 4095 536870911 7 63 318805 566596 0 16777215 159670400 524287 511 10299238 67108863 1023 11905 2047 32767 33554431 268435455 65535 131071 1048575 4194303\n",
"1\n29\n7 16383 27 127 255 3 4095 536870911 8 63 513980 476451 1 16777215 134217727 524287 511 8388607 67108863 1023 11905 2047 32767 23246973 268435455 65535 131071 1048575 4194303\n",
"1\n29\n31 9387 27 127 503 3 4095 447420925 13 63 318805 566596 1 17121512 134217727 524287 511 8388607 67108863 1023 11905 2047 32767 33554431 268435455 7397 131071 1048575 4194303\n",
"2\n6\n5 -4 6 8 0 7\n4\n26 1 4 2\n",
"1\n29\n31 16383 15 127 255 3 4095 536870911 7 63 318805 2097151 2 16777215 134217727 524287 511 8388607 67108863 1023 9571 2047 21746 33554431 4225164 65535 239326 1048575 3165366\n",
"1\n29\n56 17591 19 127 255 3 4095 900608061 7 63 318805 833436 1 16777215 134217727 524287 915 8388607 67108863 1023 8191 2047 32767 33554431 268435455 65535 131071 1048575 4194303\n",
"1\n29\n53 6895 15 127 255 3 4095 255207509 7 63 318805 1051398 1 16777215 134217727 524287 289 15554909 67108863 1023 11905 2047 32767 33554431 268435455 65535 131071 1048575 4194303\n",
"1\n29\n31 6304 9 127 255 3 4095 536870911 7 63 318805 566596 1 16777215 159670400 524287 511 10299238 67108863 1023 11905 2047 32767 33554431 268435455 65535 131071 1048575 4194303\n",
"1\n29\n0 16383 27 127 255 3 4095 536870911 8 63 513980 476451 1 16777215 134217727 524287 511 8388607 67108863 1023 11905 2047 32767 23246973 268435455 65535 131071 1048575 4194303\n",
"1\n29\n31 9387 27 127 503 3 4095 447420925 13 63 318805 566596 1 17121512 134217727 524287 511 8388607 67108863 1252 11905 2047 32767 33554431 268435455 7397 131071 1048575 4194303\n",
"2\n6\n5 -4 6 8 0 7\n4\n26 2 4 2\n",
"1\n29\n31 16383 15 127 255 3 4095 536870911 7 63 318805 2097151 2 19255365 134217727 524287 511 8388607 67108863 1023 9571 2047 21746 33554431 4225164 65535 239326 1048575 3165366\n",
"1\n29\n56 17591 19 127 255 3 4095 900608061 7 106 318805 833436 1 16777215 134217727 524287 915 8388607 67108863 1023 8191 2047 32767 33554431 268435455 65535 131071 1048575 4194303\n",
"1\n29\n31 6304 9 127 255 3 4095 873088899 7 63 318805 566596 1 16777215 159670400 524287 511 10299238 67108863 1023 11905 2047 32767 33554431 268435455 65535 131071 1048575 4194303\n",
"1\n29\n31 1630 27 127 503 3 4095 447420925 13 63 318805 566596 1 17121512 134217727 524287 511 8388607 67108863 1252 11905 2047 32767 33554431 268435455 7397 131071 1048575 4194303\n",
"2\n6\n5 -7 6 8 0 7\n4\n26 2 4 2\n",
"1\n29\n31 16383 15 127 255 3 4095 536870911 7 63 249574 2097151 2 19255365 134217727 524287 511 8388607 67108863 1023 9571 2047 21746 33554431 4225164 65535 239326 1048575 3165366\n",
"1\n29\n56 17591 19 127 255 3 4095 900608061 7 25 318805 833436 1 16777215 134217727 524287 915 8388607 67108863 1023 8191 2047 32767 33554431 268435455 65535 131071 1048575 4194303\n",
"1\n29\n31 1630 27 127 503 3 4095 447420925 13 63 318805 566596 1 17121512 134217727 524287 511 8388607 67108863 1252 11905 2047 32767 33554431 417440475 7397 131071 1048575 4194303\n",
"2\n6\n5 -7 6 8 0 7\n4\n26 2 1 2\n",
"1\n29\n31 1630 27 127 503 3 4095 447420925 13 63 318805 566596 1 17121512 134217727 524287 511 8388607 67108863 1252 11905 2047 32767 2662295 417440475 7397 131071 1048575 4194303\n",
"2\n6\n5 -7 11 8 0 7\n4\n26 2 1 2\n",
"1\n29\n31 1630 27 127 503 3 4095 447420925 13 63 318805 566596 1 2800424 134217727 524287 511 8388607 67108863 1252 11905 2047 32767 2662295 417440475 7397 131071 1048575 4194303\n",
"2\n6\n5 -7 11 8 0 7\n4\n44 2 1 2\n",
"1\n29\n31 1630 27 127 503 3 4095 447420925 13 63 318805 566596 1 2800424 134217727 524287 511 2718397 67108863 1252 11905 2047 32767 2662295 417440475 7397 131071 1048575 4194303\n",
"2\n6\n5 -7 11 8 0 7\n4\n44 4 1 2\n",
"1\n29\n31 1630 27 127 995 3 4095 447420925 13 63 318805 566596 1 2800424 134217727 524287 511 2718397 67108863 1252 11905 2047 32767 2662295 417440475 7397 131071 1048575 4194303\n",
"1\n29\n31 1630 27 127 995 3 4095 447420925 13 63 318805 566596 1 2800424 134217727 524287 511 2718397 67108863 1252 11905 2047 32767 2662295 417440475 13062 131071 1048575 4194303\n",
"1\n29\n31 1630 27 127 995 3 4095 447420925 13 63 318805 566596 1 2800424 134217727 524287 511 2718397 67108863 1252 257 2047 32767 2662295 417440475 13062 131071 1048575 4194303\n",
"1\n29\n31 2411 27 127 995 3 4095 447420925 13 63 318805 566596 1 2800424 134217727 524287 511 2718397 67108863 1252 257 2047 32767 2662295 417440475 13062 131071 1048575 4194303\n",
"1\n29\n31 2411 27 127 995 2 4095 447420925 13 63 318805 566596 1 2800424 134217727 524287 511 2718397 67108863 1252 257 2047 32767 2662295 417440475 13062 131071 1048575 4194303\n",
"1\n29\n31 2411 27 127 995 2 4095 447420925 13 63 318805 566596 1 2800424 134217727 524287 511 2718397 67108863 1252 257 2047 32767 2662295 417440475 13062 131071 1048575 4956865\n",
"1\n29\n31 2411 27 127 995 2 4095 447420925 13 63 318805 566596 1 2800424 134217727 524287 511 2718397 67108863 1252 257 1636 32767 2662295 417440475 13062 131071 1048575 4956865\n",
"1\n29\n31 2411 27 127 995 2 4095 447420925 13 63 318805 566596 1 2800424 134217727 524287 511 2718397 67108863 1252 257 1636 32767 2662295 417440475 13062 131071 490463 4956865\n",
"1\n29\n31 2411 27 127 995 2 4095 447420925 13 63 318805 566596 2 2800424 134217727 524287 511 2718397 67108863 1252 257 1636 32767 2662295 417440475 13062 131071 490463 4956865\n",
"1\n29\n31 2411 27 127 995 2 4095 447420925 13 63 318805 566596 2 2800424 134217727 524287 511 2718397 67108863 1252 257 1636 32767 4810762 417440475 13062 131071 490463 4956865\n",
"1\n29\n31 2411 27 127 995 2 4095 447420925 13 63 318805 566596 2 2800424 134217727 524287 511 2718397 80403221 1252 257 1636 32767 4810762 417440475 13062 131071 490463 4956865\n",
"1\n29\n31 2411 27 127 995 2 4095 447420925 13 63 318805 566596 2 2800424 134217727 524287 511 2718397 80403221 1252 257 1636 32767 4810762 417440475 13062 131071 354423 4956865\n",
"1\n29\n31 2411 27 127 995 2 4095 447420925 13 63 318805 566596 2 2800424 134217727 524287 511 2718397 80403221 1692 257 1636 32767 4810762 417440475 13062 131071 354423 4956865\n",
"1\n29\n31 2411 27 12 995 2 4095 447420925 13 63 318805 566596 2 2800424 134217727 524287 511 2718397 80403221 1692 257 1636 32767 4810762 417440475 13062 131071 354423 4956865\n",
"1\n29\n31 2411 27 12 995 2 4095 447420925 13 63 318805 566596 2 2800424 134217727 524287 511 2718397 80403221 1692 257 1636 32767 4810762 417440475 13062 77906 354423 4956865\n",
"1\n29\n31 2411 27 12 995 2 4095 447420925 13 63 318805 566596 2 5421085 134217727 524287 511 2718397 80403221 1692 257 1636 32767 4810762 417440475 13062 77906 354423 4956865\n",
"1\n29\n31 2411 27 12 995 2 4095 447420925 13 63 318805 566596 2 5421085 134217727 524287 891 2718397 80403221 1692 257 1636 32767 4810762 417440475 13062 77906 354423 4956865\n",
"1\n29\n31 2411 27 12 995 2 4095 447420925 13 63 318805 566596 2 5421085 134217727 524287 444 2718397 80403221 1692 257 1636 32767 4810762 417440475 13062 77906 354423 4956865\n",
"1\n29\n31 16383 15 127 255 3 4095 536870911 7 63 262143 2097151 1 16777215 134217727 524287 511 8388607 67108863 2010 8191 2047 32767 33554431 268435455 65535 131071 1048575 4194303\n",
"2\n6\n5 -2 4 8 6 5\n4\n0 1 4 2\n",
"1\n29\n31 16383 15 127 255 3 4095 536870911 7 63 318805 2097151 1 16777215 134217727 524287 191 8388607 67108863 1023 8191 2047 32767 33554431 268435455 65535 131071 1048575 4194303\n",
"2\n6\n5 -2 4 8 8 5\n4\n8 2 4 2\n",
"1\n29\n31 16383 15 127 255 3 4095 536870911 7 63 318805 1051398 1 16777215 134217727 524287 511 8388607 67108863 1023 8191 2041 32767 33554431 268435455 65535 131071 1048575 4194303\n",
"1\n29\n31 16383 15 127 255 3 4095 536870911 7 63 318805 1051398 1 16777215 134217727 524287 511 8388607 24771206 1023 11905 2047 32767 33554431 268435455 65535 131071 1048575 4194303\n",
"1\n29\n31 16383 15 127 255 3 4095 536870911 7 63 507871 566596 1 16777215 134217727 524287 511 8388607 67108863 1023 11905 2047 32767 33554431 268435455 65535 131071 1048575 4194303\n",
"1\n29\n31 16383 27 127 255 3 4095 536870911 7 63 318805 566596 1 16777215 134217727 524287 511 8388607 67108863 1023 11905 2047 32767 33554431 268435455 65535 90317 1048575 4194303\n",
"1\n29\n31 16383 27 127 255 6 4095 536870911 7 63 318805 566596 1 17121512 134217727 524287 511 8388607 67108863 1023 11905 2047 32767 33554431 268435455 65535 131071 1048575 4194303\n",
"2\n6\n5 -2 8 8 6 5\n4\n8 1 4 2\n",
"1\n29\n31 16383 15 127 255 1 4095 536870911 7 63 318805 2097151 1 16777215 134217727 524287 511 8388607 67108863 1023 8191 2047 32767 33554431 268435455 65535 239326 1048575 4194303\n"
],
"output": [
"5 5 4 6 -2 8\n2 4 1 8\n",
"32767 65535 16383 131071 8191 262143 4095 524287 2047 1048575 1023 2097151 511 4194303 255 8388607 127 16777215 63 33554431 31 67108863 15 134217727 7 268435455 3 536870911 1\n",
"32767 16383 65535 8191 131071 4095 318805 2047 524287 1023 1048575 511 2097151 255 4194303 127 8388607 63 16777215 31 33554431 15 67108863 7 134217727 3 268435455 1 536870911 \n",
"5 5 4 6 -2 8 \n2 4 2 8 \n",
"32767 16383 65535 8191 131071 4095 318805 2047 524287 1023 1048575 511 1051398 255 4194303 127 8388607 63 16777215 31 33554431 15 67108863 7 134217727 3 268435455 1 536870911 \n",
"32767 16383 65535 11905 131071 4095 318805 2047 524287 1023 1048575 511 1051398 255 4194303 127 8388607 63 16777215 31 33554431 15 67108863 7 134217727 3 268435455 1 536870911 \n",
"32767 16383 65535 11905 131071 4095 318805 2047 524287 1023 566596 511 1048575 255 4194303 127 8388607 63 16777215 31 33554431 15 67108863 7 134217727 3 268435455 1 536870911 \n",
"32767 16383 65535 11905 131071 4095 318805 2047 524287 1023 566596 511 1048575 255 4194303 127 8388607 63 16777215 31 33554431 27 67108863 7 134217727 3 268435455 1 536870911 \n",
"32767 16383 65535 11905 131071 4095 318805 2047 524287 1023 566596 511 1048575 255 4194303 127 8388607 63 17121512 31 33554431 27 67108863 7 134217727 3 268435455 1 536870911 \n",
"5 6 5 6 -2 8 \n2 4 1 8 \n",
"32767 16383 65535 8191 239326 4095 318805 2047 524287 1023 1048575 511 2097151 255 4194303 127 8388607 63 16777215 31 33554431 15 67108863 7 134217727 3 268435455 1 536870911 \n",
"5 5 4 6 -4 8 \n2 4 1 8 \n",
"32767 16383 65535 8191 131071 4095 318805 2047 524287 1023 1048575 915 1051398 255 4194303 127 8388607 63 16777215 31 33554431 15 67108863 7 134217727 3 268435455 1 536870911 \n",
"32767 16383 65535 11905 131071 4095 318805 2047 524287 1023 1048575 511 1051398 255 4194303 127 15554909 63 16777215 31 33554431 15 67108863 7 134217727 3 268435455 1 536870911 \n",
"32767 16383 65535 11905 131071 4095 318805 2047 524287 1023 566596 511 1048575 255 4194303 127 8388607 63 16777215 31 33554431 15 67108863 7 159670400 3 268435455 1 536870911 \n",
"32767 16383 65535 11905 131071 4095 513980 2047 524287 1023 566596 511 1048575 255 4194303 127 8388607 63 16777215 31 33554431 27 67108863 7 134217727 3 268435455 1 536870911 \n",
"32767 16383 65535 11905 131071 4095 318805 2047 524287 1023 566596 511 1048575 255 4194303 127 8388607 63 17121512 31 33554431 27 67108863 7 134217727 3 268435455 1 447420925 \n",
"5 5 0 6 -2 8 \n2 4 1 8 \n",
"21746 16383 65535 8191 239326 4095 318805 2047 524287 1023 1048575 511 2097151 255 4194303 127 8388607 63 16777215 31 33554431 15 67108863 7 134217727 3 268435455 1 536870911 \n",
"5 5 4 6 -4 8 \n4 4 1 8 \n",
"32767 16383 65535 8191 131071 4095 318805 2047 524287 1023 1048575 915 1051398 255 4194303 127 8388607 63 16777215 31 33554431 19 67108863 7 134217727 3 268435455 1 536870911 \n",
"32767 11905 65535 4290 131071 4095 318805 2047 524287 1023 1048575 511 1051398 255 4194303 127 15554909 63 16777215 31 33554431 15 67108863 7 134217727 3 268435455 1 536870911 \n",
"32767 16383 65535 11905 131071 4095 318805 2047 524287 1023 566596 511 1048575 255 4194303 127 8388607 63 16777215 31 33554431 15 67108863 7 159670400 3 268435455 0 536870911 \n",
"32767 16383 65535 11905 131071 4095 513980 2047 524287 1023 566596 511 1048575 255 4194303 127 8388607 63 16777215 27 33554431 7 67108863 7 134217727 3 268435455 1 536870911 \n",
"32767 11905 65535 9387 131071 4095 318805 2047 524287 1023 566596 511 1048575 255 4194303 127 8388607 63 17121512 31 33554431 27 67108863 7 134217727 3 268435455 1 447420925 \n",
"5 5 0 6 -2 8 \n2 4 1 13 \n",
"21746 16383 65535 9571 239326 4095 318805 2047 524287 1023 1048575 511 2097151 255 4194303 127 8388607 63 16777215 31 33554431 15 67108863 7 134217727 3 268435455 1 536870911 \n",
"5 6 5 8 -4 8 \n4 4 1 8 \n",
"32767 16383 65535 8191 131071 4095 318805 2047 524287 1023 833436 915 1048575 255 4194303 127 8388607 63 16777215 31 33554431 19 67108863 7 134217727 3 268435455 1 536870911 \n",
"32767 11905 65535 4290 131071 4095 318805 2047 524287 1023 1048575 511 1051398 255 4194303 127 15554909 63 16777215 53 33554431 15 67108863 7 134217727 3 268435455 1 536870911 \n",
"32767 11905 65535 6304 131071 4095 318805 2047 524287 1023 566596 511 1048575 255 4194303 127 8388607 63 16777215 31 33554431 15 67108863 7 159670400 3 268435455 0 536870911 \n",
"32767 16383 65535 11905 131071 4095 476451 2047 513980 1023 524287 511 1048575 255 4194303 127 8388607 63 16777215 27 33554431 7 67108863 7 134217727 3 268435455 1 536870911 \n",
"32767 11905 65535 9387 131071 4095 318805 2047 524287 1023 566596 511 1048575 255 4194303 127 8388607 63 17121512 31 33554431 27 67108863 13 134217727 3 268435455 1 447420925 \n",
"5 5 0 6 -2 8 \n2 4 1 26 \n",
"21746 16383 65535 9571 239326 4095 318805 2047 524287 1023 1048575 511 2097151 255 4194303 127 4225164 63 8388607 31 16777215 15 33554431 7 67108863 3 134217727 1 536870911 \n",
"32767 17591 65535 8191 131071 4095 318805 2047 524287 1023 833436 915 1048575 255 4194303 127 8388607 63 16777215 31 33554431 19 67108863 7 134217727 3 268435455 1 536870911 \n",
"32767 11905 65535 4290 131071 4095 318805 2047 524287 1023 1048575 511 1051398 255 4194303 127 15554909 63 16777215 53 33554431 15 67108863 7 134217727 3 255207509 1 268435455 \n",
"32767 11905 65535 6304 131071 4095 318805 2047 524287 1023 566596 511 1048575 255 4194303 127 10299238 63 16777215 31 33554431 15 67108863 7 159670400 3 268435455 0 536870911 \n",
"32767 16383 65535 11905 131071 4095 476451 2047 513980 1023 524287 511 1048575 255 4194303 127 8388607 63 16777215 27 33554431 8 67108863 7 134217727 3 268435455 1 536870911 \n",
"32767 11905 65535 9387 131071 4095 318805 2047 524287 1023 566596 511 1048575 503 4194303 127 8388607 63 17121512 31 33554431 27 67108863 13 134217727 3 268435455 1 447420925 \n",
"5 6 0 7 -2 8 \n2 4 1 26 \n",
"21746 16383 65535 9571 239326 4095 318805 2047 524287 1023 1048575 511 2097151 255 4194303 127 4225164 63 8388607 31 16777215 15 33554431 7 67108863 3 134217727 2 536870911 \n",
"32767 17591 65535 8191 131071 4095 318805 2047 524287 1023 833436 915 1048575 255 4194303 127 8388607 63 16777215 56 33554431 19 67108863 7 134217727 3 268435455 1 536870911 \n",
"32767 11905 65535 4290 131071 4095 318805 2047 524287 1023 1048575 289 1051398 255 4194303 127 15554909 63 16777215 53 33554431 15 67108863 7 134217727 3 255207509 1 268435455 \n",
"32767 11905 65535 6304 131071 4095 318805 2047 524287 1023 566596 511 1048575 255 4194303 127 10299238 63 16777215 31 33554431 9 67108863 7 159670400 3 268435455 0 536870911 \n",
"32767 16383 65535 11905 131071 4095 476451 2047 513980 1023 524287 511 1048575 255 4194303 127 8388607 63 16777215 27 23246973 8 67108863 7 134217727 3 268435455 1 536870911 \n",
"11905 9387 32767 7397 131071 4095 318805 2047 524287 1023 566596 511 1048575 503 4194303 127 8388607 63 17121512 31 33554431 27 67108863 13 134217727 3 268435455 1 447420925 \n",
"5 6 0 7 -4 8 \n2 4 1 26 \n",
"21746 16383 65535 9571 239326 4095 318805 2047 524287 1023 1048575 511 2097151 255 3165366 127 4225164 63 8388607 31 16777215 15 33554431 7 67108863 3 134217727 2 536870911 \n",
"32767 17591 65535 8191 131071 4095 318805 2047 524287 1023 833436 915 1048575 255 4194303 127 8388607 63 16777215 56 33554431 19 67108863 7 134217727 3 268435455 1 900608061 \n",
"32767 11905 65535 6895 131071 4095 318805 2047 524287 1023 1048575 289 1051398 255 4194303 127 15554909 63 16777215 53 33554431 15 67108863 7 134217727 3 255207509 1 268435455 \n",
"32767 11905 65535 6304 131071 4095 318805 2047 524287 1023 566596 511 1048575 255 4194303 127 10299238 63 16777215 31 33554431 9 67108863 7 159670400 3 268435455 1 536870911 \n",
"32767 16383 65535 11905 131071 4095 476451 2047 513980 1023 524287 511 1048575 255 4194303 127 8388607 63 16777215 27 23246973 8 67108863 3 134217727 1 268435455 0 536870911 \n",
"11905 9387 32767 7397 131071 4095 318805 2047 524287 1252 566596 511 1048575 503 4194303 127 8388607 63 17121512 31 33554431 27 67108863 13 134217727 3 268435455 1 447420925 \n",
"5 6 0 7 -4 8 \n2 4 2 26 \n",
"21746 16383 65535 9571 239326 4095 318805 2047 524287 1023 1048575 511 2097151 255 3165366 127 4225164 63 8388607 31 19255365 15 33554431 7 67108863 3 134217727 2 536870911 \n",
"32767 17591 65535 8191 131071 4095 318805 2047 524287 1023 833436 915 1048575 255 4194303 127 8388607 106 16777215 56 33554431 19 67108863 7 134217727 3 268435455 1 900608061 \n",
"32767 11905 65535 6304 131071 4095 318805 2047 524287 1023 566596 511 1048575 255 4194303 127 10299238 63 16777215 31 33554431 9 67108863 7 159670400 3 268435455 1 873088899 \n",
"11905 7397 32767 4095 131071 2047 318805 1630 524287 1252 566596 511 1048575 503 4194303 127 8388607 63 17121512 31 33554431 27 67108863 13 134217727 3 268435455 1 447420925 \n",
"5 6 0 7 -7 8 \n2 4 2 26 \n",
"21746 16383 65535 9571 239326 4095 249574 2047 524287 1023 1048575 511 2097151 255 3165366 127 4225164 63 8388607 31 19255365 15 33554431 7 67108863 3 134217727 2 536870911 \n",
"32767 17591 65535 8191 131071 4095 318805 2047 524287 1023 833436 915 1048575 255 4194303 127 8388607 56 16777215 25 33554431 19 67108863 7 134217727 3 268435455 1 900608061 \n",
"11905 7397 32767 4095 131071 2047 318805 1630 524287 1252 566596 511 1048575 503 4194303 127 8388607 63 17121512 31 33554431 27 67108863 13 134217727 3 417440475 1 447420925 \n",
"5 6 0 7 -7 8 \n2 2 1 26 \n",
"11905 7397 32767 4095 131071 2047 318805 1630 524287 1252 566596 511 1048575 503 2662295 127 4194303 63 8388607 31 17121512 27 67108863 13 134217727 3 417440475 1 447420925 \n",
"5 7 0 8 -7 11 \n2 2 1 26 \n",
"11905 7397 32767 4095 131071 2047 318805 1630 524287 1252 566596 511 1048575 503 2662295 127 2800424 63 4194303 31 8388607 27 67108863 13 134217727 3 417440475 1 447420925 \n",
"5 7 0 8 -7 11 \n2 2 1 44 \n",
"11905 7397 32767 4095 131071 2047 318805 1630 524287 1252 566596 511 1048575 503 2662295 127 2718397 63 2800424 31 4194303 27 67108863 13 134217727 3 417440475 1 447420925 \n",
"5 7 0 8 -7 11 \n2 4 1 44 \n",
"11905 7397 32767 4095 131071 2047 318805 1630 524287 1252 566596 995 1048575 511 2662295 127 2718397 63 2800424 31 4194303 27 67108863 13 134217727 3 417440475 1 447420925 \n",
"13062 11905 32767 4095 131071 2047 318805 1630 524287 1252 566596 995 1048575 511 2662295 127 2718397 63 2800424 31 4194303 27 67108863 13 134217727 3 417440475 1 447420925 \n",
"13062 4095 32767 2047 131071 1630 318805 1252 524287 995 566596 511 1048575 257 2662295 127 2718397 63 2800424 31 4194303 27 67108863 13 134217727 3 417440475 1 447420925 \n",
"13062 4095 32767 2411 131071 2047 318805 1252 524287 995 566596 511 1048575 257 2662295 127 2718397 63 2800424 31 4194303 27 67108863 13 134217727 3 417440475 1 447420925 \n",
"13062 4095 32767 2411 131071 2047 318805 1252 524287 995 566596 511 1048575 257 2662295 127 2718397 63 2800424 31 4194303 27 67108863 13 134217727 2 417440475 1 447420925 \n",
"13062 4095 32767 2411 131071 2047 318805 1252 524287 995 566596 511 1048575 257 2662295 127 2718397 63 2800424 31 4956865 27 67108863 13 134217727 2 417440475 1 447420925 \n",
"13062 4095 32767 2411 131071 1636 318805 1252 524287 995 566596 511 1048575 257 2662295 127 2718397 63 2800424 31 4956865 27 67108863 13 134217727 2 417440475 1 447420925 \n",
"13062 4095 32767 2411 131071 1636 318805 1252 490463 995 524287 511 566596 257 2662295 127 2718397 63 2800424 31 4956865 27 67108863 13 134217727 2 417440475 1 447420925 \n",
"13062 4095 32767 2411 131071 1636 318805 1252 490463 995 524287 511 566596 257 2662295 127 2718397 63 2800424 31 4956865 27 67108863 13 134217727 2 417440475 2 447420925 \n",
"13062 4095 32767 2411 131071 1636 318805 1252 490463 995 524287 511 566596 257 2718397 127 2800424 63 4810762 31 4956865 27 67108863 13 134217727 2 417440475 2 447420925 \n",
"13062 4095 32767 2411 131071 1636 318805 1252 490463 995 524287 511 566596 257 2718397 127 2800424 63 4810762 31 4956865 27 80403221 13 134217727 2 417440475 2 447420925 \n",
"13062 4095 32767 2411 131071 1636 318805 1252 354423 995 524287 511 566596 257 2718397 127 2800424 63 4810762 31 4956865 27 80403221 13 134217727 2 417440475 2 447420925 \n",
"13062 4095 32767 2411 131071 1692 318805 1636 354423 995 524287 511 566596 257 2718397 127 2800424 63 4810762 31 4956865 27 80403221 13 134217727 2 417440475 2 447420925 \n",
"13062 4095 32767 2411 131071 1692 318805 1636 354423 995 524287 511 566596 257 2718397 63 2800424 31 4810762 27 4956865 13 80403221 12 134217727 2 417440475 2 447420925 \n",
"13062 4095 32767 2411 77906 1692 318805 1636 354423 995 524287 511 566596 257 2718397 63 2800424 31 4810762 27 4956865 13 80403221 12 134217727 2 417440475 2 447420925 \n",
"13062 4095 32767 2411 77906 1692 318805 1636 354423 995 524287 511 566596 257 2718397 63 4810762 31 4956865 27 5421085 13 80403221 12 134217727 2 417440475 2 447420925 \n",
"13062 4095 32767 2411 77906 1692 318805 1636 354423 995 524287 891 566596 257 2718397 63 4810762 31 4956865 27 5421085 13 80403221 12 134217727 2 417440475 2 447420925 \n",
"13062 4095 32767 2411 77906 1692 318805 1636 354423 995 524287 444 566596 257 2718397 63 4810762 31 4956865 27 5421085 13 80403221 12 134217727 2 417440475 2 447420925 \n",
"32767 16383 65535 8191 131071 4095 262143 2047 524287 2010 1048575 511 2097151 255 4194303 127 8388607 63 16777215 31 33554431 15 67108863 7 134217727 3 268435455 1 536870911 \n",
"5 5 4 6 -2 8 \n1 2 0 4 \n",
"32767 16383 65535 8191 131071 4095 318805 2047 524287 1023 1048575 255 2097151 191 4194303 127 8388607 63 16777215 31 33554431 15 67108863 7 134217727 3 268435455 1 536870911 \n",
"5 5 4 8 -2 8 \n2 4 2 8 \n",
"32767 16383 65535 8191 131071 4095 318805 2041 524287 1023 1048575 511 1051398 255 4194303 127 8388607 63 16777215 31 33554431 15 67108863 7 134217727 3 268435455 1 536870911 \n",
"32767 16383 65535 11905 131071 4095 318805 2047 524287 1023 1048575 511 1051398 255 4194303 127 8388607 63 16777215 31 24771206 15 33554431 7 134217727 3 268435455 1 536870911 \n",
"32767 16383 65535 11905 131071 4095 507871 2047 524287 1023 566596 511 1048575 255 4194303 127 8388607 63 16777215 31 33554431 15 67108863 7 134217727 3 268435455 1 536870911 \n",
"32767 16383 65535 11905 90317 4095 318805 2047 524287 1023 566596 511 1048575 255 4194303 127 8388607 63 16777215 31 33554431 27 67108863 7 134217727 3 268435455 1 536870911 \n",
"32767 16383 65535 11905 131071 4095 318805 2047 524287 1023 566596 511 1048575 255 4194303 127 8388607 63 17121512 31 33554431 27 67108863 7 134217727 6 268435455 1 536870911 \n",
"5 6 5 8 -2 8 \n2 4 1 8 \n",
"32767 16383 65535 8191 239326 4095 318805 2047 524287 1023 1048575 511 2097151 255 4194303 127 8388607 63 16777215 31 33554431 15 67108863 7 134217727 1 268435455 1 536870911 \n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You have array of n numbers a_{1}, a_{2}, …, a_{n}.
Rearrange these numbers to satisfy |a_{1} - a_{2}| ≤ |a_{2} - a_{3}| ≤ … ≤ |a_{n-1} - a_{n}|, where |x| denotes absolute value of x. It's always possible to find such rearrangement.
Note that all numbers in a are not necessarily different. In other words, some numbers of a may be same.
You have to answer independent t test cases.
Input
The first line contains a single integer t (1 ≤ t ≤ 10^{4}) — the number of test cases.
The first line of each test case contains single integer n (3 ≤ n ≤ 10^{5}) — the length of array a. It is guaranteed that the sum of values of n over all test cases in the input does not exceed 10^{5}.
The second line of each test case contains n integers a_{1}, a_{2}, …, a_{n} (-10^{9} ≤ a_{i} ≤ 10^{9}).
Output
For each test case, print the rearranged version of array a which satisfies given condition. If there are multiple valid rearrangements, print any of them.
Example
Input
2
6
5 -2 4 8 6 5
4
8 1 4 2
Output
5 5 4 6 8 -2
1 2 4 8
Note
In the first test case, after given rearrangement, |a_{1} - a_{2}| = 0 ≤ |a_{2} - a_{3}| = 1 ≤ |a_{3} - a_{4}| = 2 ≤ |a_{4} - a_{5}| = 2 ≤ |a_{5} - a_{6}| = 10. There are other possible answers like "5 4 5 6 -2 8".
In the second test case, after given rearrangement, |a_{1} - a_{2}| = 1 ≤ |a_{2} - a_{3}| = 2 ≤ |a_{3} - a_{4}| = 4. There are other possible answers like "2 4 8 1".
### Input:
2
6
5 -2 4 8 6 5
4
8 1 4 2
### Output:
5 5 4 6 -2 8
2 4 1 8
### Input:
1
29
31 16383 15 127 255 3 4095 536870911 7 63 262143 2097151 1 16777215 134217727 524287 511 8388607 67108863 1023 8191 2047 32767 33554431 268435455 65535 131071 1048575 4194303
### Output:
32767 65535 16383 131071 8191 262143 4095 524287 2047 1048575 1023 2097151 511 4194303 255 8388607 127 16777215 63 33554431 31 67108863 15 134217727 7 268435455 3 536870911 1
### Code:
for _ in range(int(input())):
n = int(input())
ls = sorted(list(map(int, input().split())))
mid = n // 2
if n % 2 == 0:
mid -= 1
i = mid - 1
turn = True
j = mid + 1
ar = []
ar.append(ls[mid])
while i >= 0 or j < n:
if turn and j < n:
ar.append(ls[j])
j += 1
elif not turn and i >= 0:
ar.append(ls[i])
i -= 1
turn = not turn
print(*ar)
|
1360_F. Spy-string_10807
|
You are given n strings a_1, a_2, …, a_n: all of them have the same length m. The strings consist of lowercase English letters.
Find any string s of length m such that each of the given n strings differs from s in at most one position. Formally, for each given string a_i, there is no more than one position j such that a_i[j] ≠ s[j].
Note that the desired string s may be equal to one of the given strings a_i, or it may differ from all the given strings.
For example, if you have the strings abac and zbab, then the answer to the problem might be the string abab, which differs from the first only by the last character, and from the second only by the first.
Input
The first line contains an integer t (1 ≤ t ≤ 100) — the number of test cases. Then t test cases follow.
Each test case starts with a line containing two positive integers n (1 ≤ n ≤ 10) and m (1 ≤ m ≤ 10) — the number of strings and their length.
Then follow n strings a_i, one per line. Each of them has length m and consists of lowercase English letters.
Output
Print t answers to the test cases. Each answer (if it exists) is a string of length m consisting of lowercase English letters. If there are several answers, print any of them. If the answer does not exist, print "-1" ("minus one", without quotes).
Example
Input
5
2 4
abac
zbab
2 4
aaaa
bbbb
3 3
baa
aaa
aab
2 2
ab
bb
3 1
a
b
c
Output
abab
-1
aaa
ab
z
Note
The first test case was explained in the statement.
In the second test case, the answer does not exist.
|
# cook your dish here
#code
import math
import collections
from sys import stdin,stdout,setrecursionlimit
from bisect import bisect_left as bsl
from bisect import bisect_right as bsr
import heapq as hq
setrecursionlimit(2**20)
def strcmp(s1,s2,m):
cnt = 0
for i in range(m):
if(s1[i]!=s2[i]):
cnt+=1
return cnt
t = int(stdin.readline())
for _ in range(t):
#n = int(stdin.readline())
n, m = list(map(int, stdin.readline().rstrip().split()))
a = []
for i in range(n):
a.append(stdin.readline().split()[0])
if(m==1):
print(a[0])
continue
else:
ans = -1
if(n==2):
l = []
for i in range(m):
if(a[0][i]!=a[1][i]):
l.append(i)
if(len(l)>=3):
ans = -1
else:
if(len(l)==1 or len(l)==0):
ans=a[0]
else:
ans = ''
for i in range(m):
if(i==l[0]):
ans+=a[1][i]
else:
ans+=a[0][i]
print(ans)
continue
else:
d = [[0]*n for i in range(n)]
for i in range(n):
for j in range(i+1,n):
d[i][j] = strcmp(a[i],a[j],m)
d[j][i] = d[i][j]
pos = -1
for i in range(n):
mx = -1
for j in range(n):
mx = max(mx,d[i][j])
if(mx<=1):
pos = i
break
if(mx==2):
pos = -1
for j in range(n):
if(d[i][j]==2):
pos = j
break
l = []
for k in range(m):
if(a[i][k]!=a[pos][k]):
l.append(k)
ans = ''
for k in range(m):
if(k==l[0]):
ans+=a[pos][k]
else:
ans+=a[i][k]
mx = -1
for k in range(n):
mx = max(mx,strcmp(ans,a[k],m))
if(mx<=1):
a[pos] = ans
break
else:
pos = -1
if(pos==-1):
print(pos)
else:
print(a[pos])
|
{
"input": [
"5\n2 4\nabac\nzbab\n2 4\naaaa\nbbbb\n3 3\nbaa\naaa\naab\n2 2\nab\nbb\n3 1\na\nb\nc\n",
"5\n2 4\nabac\nzbab\n2 4\naaaa\nbbbb\n3 3\nbaa\naaa\naab\n2 2\nab\nbb\n3 1\na\nb\nc\n",
"5\n2 4\nabac\nbabz\n2 4\naaaa\nbbbb\n3 3\nbaa\naaa\naab\n2 2\nab\nbb\n3 1\na\nb\nc\n",
"5\n2 4\nabac\nbabz\n2 4\naaaa\nbbbb\n3 3\nbaa\naaa\naab\n2 2\nba\nbb\n3 1\na\nb\nc\n",
"5\n2 4\nabac\nbabz\n2 4\naaaa\nbbbb\n3 3\nbba\naaa\naab\n2 2\nba\nbb\n2 1\na\nb\nc\n",
"5\n2 4\nabac\nzbab\n2 4\naaaa\nbbbb\n3 3\nbaa\naaa\naab\n2 2\nba\nbb\n2 1\na\nb\nc\n",
"5\n2 4\nabac\nbabz\n2 4\naaaa\nbbbb\n3 3\nbba\naaa\naab\n2 2\nab\nbb\n2 1\na\nb\nc\n",
"5\n2 4\nabac\nbabz\n2 4\naaaa\nbbbb\n3 3\nbba\naaa\nabb\n2 2\nba\nbb\n2 1\na\nb\nc\n",
"5\n2 4\nabac\nbabz\n2 4\naaaa\nbbca\n3 3\nbab\naaa\naab\n2 2\naa\nbb\n2 1\na\nb\nc\n",
"5\n2 4\nabac\nbabz\n2 4\naaaa\nbbbb\n3 3\nbba\naaa\naab\n2 2\nb`\nbb\n2 1\na\nb\nc\n",
"5\n2 4\nabac\nbabz\n2 4\naaaa\nbbca\n3 3\nbba\naaa\nbab\n2 2\naa\nbb\n2 1\na\nb\nc\n",
"5\n2 4\nabac\nzbab\n2 4\naa`a\nbbbb\n3 3\nbaa\naaa\naab\n2 2\nab\nbb\n3 1\na\nb\nc\n",
"5\n2 4\nabac\nbabz\n2 4\naaa`\nbbbb\n3 3\nbaa\naaa\naab\n2 2\nab\nbb\n3 1\na\nb\nc\n",
"5\n2 4\nabac\nbabz\n2 4\naaaa\nbbbb\n3 3\nbaa\naaa\naab\n2 2\nba\nbb\n2 1\na\nb\nc\n",
"5\n2 4\nabac\nbabz\n2 4\naaaa\nbbbb\n3 3\naba\naaa\naab\n2 2\nba\nbb\n3 1\na\nb\nc\n",
"5\n2 4\nabbc\nzbab\n2 4\naaaa\nbbbb\n3 3\nbaa\naaa\naab\n2 2\nba\nbb\n3 1\na\nb\nc\n",
"5\n2 4\nabbc\nbabz\n2 4\naaaa\nbbbb\n3 3\nbaa\naaa\naab\n2 2\nba\nbb\n2 1\na\nb\nc\n",
"5\n2 4\nabac\nbabz\n2 4\naaaa\nabbb\n3 3\nbba\naaa\naab\n2 2\nab\nbb\n2 1\na\nb\nc\n",
"5\n2 4\nabac\nbabz\n2 4\naaaa\nacbb\n3 3\nbba\naaa\naab\n2 2\nab\nbb\n2 1\na\nb\nc\n",
"5\n2 4\nabac\nbaby\n2 4\naaaa\nbbbb\n3 3\nbaa\naaa\naab\n2 2\nba\nbb\n2 1\na\nb\nc\n",
"5\n2 4\nabac\nbabz\n2 4\naaaa\nbbbb\n3 3\nbba\naaa\naab\n2 2\nba\nbb\n2 1\na\na\nc\n",
"5\n2 4\nabac\naabz\n2 4\naaaa\nbbbb\n3 3\nbba\naaa\naab\n2 2\nab\nbb\n2 1\na\nb\nc\n",
"5\n2 4\nabac\nbabz\n2 4\naaaa\nbbbb\n3 3\nbba\naab\nabb\n2 2\nba\nbb\n2 1\na\nb\nc\n",
"5\n2 4\nabac\naabz\n2 4\nabaa\nbbbb\n3 3\nbba\naaa\naab\n2 2\nab\nbb\n2 1\na\nb\nc\n",
"5\n2 4\nabac\nbabz\n2 4\naaa`\nbbbb\n3 3\nbaa\naaa\naab\n2 2\nab\nbb\n3 1\na\nb\nd\n",
"5\n2 4\nabac\nbabz\n2 4\naaaa\nbbbb\n3 3\nbba\naaa\na`b\n2 2\nab\nbb\n2 1\na\nb\nc\n",
"5\n2 4\nabac\nbabz\n2 4\naaaa\nbbbb\n3 3\nbba\naaa\nabb\n2 2\nba\nbb\n2 1\na\nc\nc\n",
"5\n2 4\nabac\nbabz\n2 4\na`aa\nbbbb\n3 3\nbba\naaa\nabb\n2 2\nba\nbb\n2 1\na\nb\nc\n",
"5\n2 4\nabac\nbabz\n2 4\naaaa\nbbbb\n3 3\nbba\naaa\nabb\n2 2\nba\nbb\n2 1\na\na\nc\n",
"5\n2 4\nabac\nbabz\n2 4\naaaa\nbbbb\n3 3\nbba\naaa\nbbb\n2 2\nba\nbb\n2 1\na\nc\nc\n",
"5\n2 3\nabac\nbabz\n2 4\naaaa\nbbbb\n3 3\nbba\naaa\nbbb\n2 2\nba\nbb\n2 1\na\nc\nc\n",
"5\n2 4\nabac\nbabz\n2 4\naaaa\nacbb\n3 3\nbba\naaa\naab\n2 2\naa\nbb\n2 1\na\nb\nc\n",
"5\n2 4\nabac\nbabz\n2 4\naaaa\nbbbb\n3 3\nbba\naa`\naab\n2 2\nba\nbb\n2 1\na\na\nc\n",
"5\n2 4\nabac\nbabz\n2 4\naaaa\nbbca\n3 3\nbba\naaa\naab\n2 2\naa\nbb\n2 1\na\nb\nc\n",
"5\n2 4\nabac\nbaby\n2 4\naaaa\nbbbb\n3 3\nbaa\naaa\naab\n2 2\nba\nbb\n3 1\na\nb\nc\n",
"5\n2 4\nabbc\nbabz\n2 4\naaaa\nbbbb\n3 3\nbaa\naaa\naab\n2 2\nba\nbb\n2 1\na\na\nc\n",
"5\n2 4\nabac\nbabz\n2 4\naaaa\nacbb\n3 3\nbaa\naaa\naab\n2 2\naa\nbb\n2 1\na\nb\nc\n",
"5\n2 4\nabac\nbaby\n2 4\naaaa\nbbbb\n3 3\nbaa\naaa\naac\n2 2\nba\nbb\n3 1\na\nb\nc\n",
"5\n2 4\nabac\nbabz\n2 4\naaaa\nacbb\n3 3\nbba\naaa\naab\n2 2\nab\nbb\n3 1\na\nb\nc\n",
"5\n2 4\nabac\nbabz\n2 4\naaaa\nbbba\n3 3\nbba\naaa\naab\n2 2\nab\nbb\n2 1\na\nb\nc\n",
"5\n2 4\nabac\nbabz\n2 4\naaba\nbbbb\n3 3\nbba\naaa\nabb\n2 2\nba\nbb\n2 1\na\na\nc\n",
"5\n2 4\nabac\nbabz\n2 4\naaba\nbbbb\n3 3\nbba\naaa\naab\n2 2\nba\nbb\n2 1\na\na\nc\n",
"5\n2 4\nabac\nbabz\n2 4\naaaa\nacbb\n3 3\nbaa\naaa\naab\n2 2\naa\nbb\n2 1\na\nb\nd\n",
"5\n2 4\nabac\nbaby\n2 4\naaaa\nbbbb\n3 3\nbaa\naaa\naad\n2 2\nba\nbb\n3 1\na\nb\nc\n",
"5\n2 4\nabab\nbabz\n2 4\naaaa\nbbbb\n3 3\nbba\naaa\naab\n2 2\nba\nbb\n2 1\na\nb\nc\n",
"5\n2 4\nabac\nbabz\n2 4\naaaa\nacbb\n3 3\nbba\naaa\naab\n2 2\nab\nbb\n2 1\na\nb\nb\n",
"5\n2 4\nabac\naabz\n2 4\naaaa\nacbb\n3 3\nbaa\naaa\naab\n2 2\naa\nbb\n2 1\na\nb\nc\n"
],
"output": [
"zbac\n-1\naaa\nab\na\n",
"zbac\n-1\naaa\nab\na\n",
"-1\n-1\naaa\nab\na\n",
"-1\n-1\naaa\nba\na\n",
"-1\n-1\n-1\nba\na\n",
"zbac\n-1\naaa\nba\na\n",
"-1\n-1\n-1\nab\na\n",
"-1\n-1\naba\nba\na\n",
"-1\n-1\naab\nba\na\n",
"-1\n-1\n-1\nb`\na\n",
"-1\n-1\nbaa\nba\na\n",
"zbac\n-1\naaa\nab\na\n",
"-1\n-1\naaa\nab\na\n",
"-1\n-1\naaa\nba\na\n",
"-1\n-1\naaa\nba\na\n",
"-1\n-1\naaa\nba\na\n",
"-1\n-1\naaa\nba\na\n",
"-1\n-1\n-1\nab\na\n",
"-1\n-1\n-1\nab\na\n",
"-1\n-1\naaa\nba\na\n",
"-1\n-1\n-1\nba\na\n",
"-1\n-1\n-1\nab\na\n",
"-1\n-1\n-1\nba\na\n",
"-1\n-1\n-1\nab\na\n",
"-1\n-1\naaa\nab\na\n",
"-1\n-1\n-1\nab\na\n",
"-1\n-1\naba\nba\na\n",
"-1\n-1\naba\nba\na\n",
"-1\n-1\naba\nba\na\n",
"-1\n-1\n-1\nba\na\n",
"-1\n-1\n-1\nba\na\n",
"-1\n-1\n-1\nba\na\n",
"-1\n-1\n-1\nba\na\n",
"-1\n-1\n-1\nba\na\n",
"-1\n-1\naaa\nba\na\n",
"-1\n-1\naaa\nba\na\n",
"-1\n-1\naaa\nba\na\n",
"-1\n-1\naaa\nba\na\n",
"-1\n-1\n-1\nab\na\n",
"-1\n-1\n-1\nab\na\n",
"-1\n-1\naba\nba\na\n",
"-1\n-1\n-1\nba\na\n",
"-1\n-1\naaa\nba\na\n",
"-1\n-1\naaa\nba\na\n",
"-1\n-1\n-1\nba\na\n",
"-1\n-1\n-1\nab\na\n",
"-1\n-1\naaa\nba\na\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You are given n strings a_1, a_2, …, a_n: all of them have the same length m. The strings consist of lowercase English letters.
Find any string s of length m such that each of the given n strings differs from s in at most one position. Formally, for each given string a_i, there is no more than one position j such that a_i[j] ≠ s[j].
Note that the desired string s may be equal to one of the given strings a_i, or it may differ from all the given strings.
For example, if you have the strings abac and zbab, then the answer to the problem might be the string abab, which differs from the first only by the last character, and from the second only by the first.
Input
The first line contains an integer t (1 ≤ t ≤ 100) — the number of test cases. Then t test cases follow.
Each test case starts with a line containing two positive integers n (1 ≤ n ≤ 10) and m (1 ≤ m ≤ 10) — the number of strings and their length.
Then follow n strings a_i, one per line. Each of them has length m and consists of lowercase English letters.
Output
Print t answers to the test cases. Each answer (if it exists) is a string of length m consisting of lowercase English letters. If there are several answers, print any of them. If the answer does not exist, print "-1" ("minus one", without quotes).
Example
Input
5
2 4
abac
zbab
2 4
aaaa
bbbb
3 3
baa
aaa
aab
2 2
ab
bb
3 1
a
b
c
Output
abab
-1
aaa
ab
z
Note
The first test case was explained in the statement.
In the second test case, the answer does not exist.
### Input:
5
2 4
abac
zbab
2 4
aaaa
bbbb
3 3
baa
aaa
aab
2 2
ab
bb
3 1
a
b
c
### Output:
zbac
-1
aaa
ab
a
### Input:
5
2 4
abac
zbab
2 4
aaaa
bbbb
3 3
baa
aaa
aab
2 2
ab
bb
3 1
a
b
c
### Output:
zbac
-1
aaa
ab
a
### Code:
# cook your dish here
#code
import math
import collections
from sys import stdin,stdout,setrecursionlimit
from bisect import bisect_left as bsl
from bisect import bisect_right as bsr
import heapq as hq
setrecursionlimit(2**20)
def strcmp(s1,s2,m):
cnt = 0
for i in range(m):
if(s1[i]!=s2[i]):
cnt+=1
return cnt
t = int(stdin.readline())
for _ in range(t):
#n = int(stdin.readline())
n, m = list(map(int, stdin.readline().rstrip().split()))
a = []
for i in range(n):
a.append(stdin.readline().split()[0])
if(m==1):
print(a[0])
continue
else:
ans = -1
if(n==2):
l = []
for i in range(m):
if(a[0][i]!=a[1][i]):
l.append(i)
if(len(l)>=3):
ans = -1
else:
if(len(l)==1 or len(l)==0):
ans=a[0]
else:
ans = ''
for i in range(m):
if(i==l[0]):
ans+=a[1][i]
else:
ans+=a[0][i]
print(ans)
continue
else:
d = [[0]*n for i in range(n)]
for i in range(n):
for j in range(i+1,n):
d[i][j] = strcmp(a[i],a[j],m)
d[j][i] = d[i][j]
pos = -1
for i in range(n):
mx = -1
for j in range(n):
mx = max(mx,d[i][j])
if(mx<=1):
pos = i
break
if(mx==2):
pos = -1
for j in range(n):
if(d[i][j]==2):
pos = j
break
l = []
for k in range(m):
if(a[i][k]!=a[pos][k]):
l.append(k)
ans = ''
for k in range(m):
if(k==l[0]):
ans+=a[pos][k]
else:
ans+=a[i][k]
mx = -1
for k in range(n):
mx = max(mx,strcmp(ans,a[k],m))
if(mx<=1):
a[pos] = ans
break
else:
pos = -1
if(pos==-1):
print(pos)
else:
print(a[pos])
|
1380_G. Circular Dungeon_10810
|
You are creating a level for a video game. The level consists of n rooms placed in a circle. The rooms are numbered 1 through n. Each room contains exactly one exit: completing the j-th room allows you to go the (j+1)-th room (and completing the n-th room allows you to go the 1-st room).
You are given the description of the multiset of n chests: the i-th chest has treasure value c_i.
Each chest can be of one of two types:
* regular chest — when a player enters a room with this chest, he grabs the treasure and proceeds to the next room;
* mimic chest — when a player enters a room with this chest, the chest eats him alive, and he loses.
The player starts in a random room with each room having an equal probability of being chosen. The players earnings is equal to the total value of treasure chests he'd collected before he lost.
You are allowed to choose the order the chests go into the rooms. For each k from 1 to n place the chests into the rooms in such a way that:
* each room contains exactly one chest;
* exactly k chests are mimics;
* the expected value of players earnings is minimum possible.
Please note that for each k the placement is chosen independently.
It can be shown that it is in the form of P/Q where P and Q are non-negative integers and Q ≠ 0. Report the values of P ⋅ Q^{-1} \pmod {998244353}.
Input
The first contains a single integer n (2 ≤ n ≤ 3 ⋅ 10^5) — the number of rooms and the number of chests.
The second line contains n integers c_1, c_2, ..., c_n (1 ≤ c_i ≤ 10^6) — the treasure values of each chest.
Output
Print n integers — the k -th value should be equal to the minimum possible expected value of players earnings if the chests are placed into the rooms in some order and exactly k of the chests are mimics.
It can be shown that it is in the form of P/Q where P and Q are non-negative integers and Q ≠ 0. Report the values of P ⋅ Q^{-1} \pmod {998244353}.
Examples
Input
2
1 2
Output
499122177 0
Input
8
10 4 3 6 5 10 7 5
Output
499122193 249561095 249561092 873463811 499122178 124780545 623902721 0
Note
In the first example the exact values of minimum expected values are: \frac 1 2, \frac 0 2.
In the second example the exact values of minimum expected values are: \frac{132} 8, \frac{54} 8, \frac{30} 8, \frac{17} 8, \frac{12} 8, \frac 7 8, \frac 3 8, \frac 0 8.
|
import sys
sys.setrecursionlimit(10 ** 5)
int1 = lambda x: int(x) - 1
p2D = lambda x: print(*x, sep="\n")
def II(): return int(sys.stdin.readline())
def MI(): return map(int, sys.stdin.readline().split())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def SI(): return sys.stdin.readline()[:-1]
def solve():
cs = [aa[0]]
for a in aa[1:]: cs.append((cs[-1] + a) % md)
# print(cs)
inv = pow(n, md - 2, md)
ans = []
for k in range(1, n):
cur = 0
for i in range(1, n):
if n - 1 - k * i < 0: break
cur = (cur + cs[n - 1 - k * i]) % md
cur = cur * inv % md
ans.append(cur)
ans.append(0)
print(*ans)
md=998244353
n=II()
aa=LI()
aa.sort()
solve()
|
{
"input": [
"2\n1 2\n",
"8\n10 4 3 6 5 10 7 5\n",
"50\n499 780 837 984 481 526 944 482 862 136 265 605 5 631 974 967 574 293 969 467 573 845 102 224 17 873 648 120 694 996 244 313 404 129 899 583 541 314 525 496 443 857 297 78 575 2 430 137 387 319\n",
"10\n20 1 15 17 11 2 15 3 16 3\n",
"50\n499 780 837 984 481 526 944 482 862 136 265 605 5 631 974 967 574 293 969 467 573 845 102 224 17 873 648 120 694 996 244 574 404 129 899 583 541 314 525 496 443 857 297 78 575 2 430 137 387 319\n",
"10\n20 1 15 17 11 2 15 3 16 4\n",
"2\n0 2\n",
"8\n10 5 3 6 5 10 7 5\n",
"50\n499 780 837 984 799 526 944 482 862 136 265 605 5 631 974 967 574 293 969 467 573 845 102 224 17 873 648 120 694 996 244 574 404 129 899 583 541 314 525 496 443 857 297 78 575 2 430 137 387 319\n",
"10\n20 1 15 17 7 2 15 3 16 4\n",
"8\n10 5 6 6 5 10 7 5\n",
"50\n499 780 837 984 799 526 944 482 862 136 265 605 5 631 974 967 574 293 969 467 573 845 102 224 17 873 648 120 694 996 244 574 404 129 899 583 541 314 525 496 443 857 297 78 575 2 430 137 387 491\n",
"10\n20 1 15 17 7 2 15 3 5 4\n",
"50\n499 780 837 984 799 526 944 482 862 136 265 605 5 631 974 967 574 293 969 467 573 845 102 224 17 873 648 120 694 996 244 574 404 129 899 583 541 314 525 496 443 857 297 78 575 2 430 137 387 911\n",
"10\n20 1 15 17 7 2 15 3 2 4\n",
"50\n499 780 1621 984 799 526 944 482 862 136 265 605 5 631 974 967 574 293 969 467 573 845 102 224 17 873 648 120 694 996 244 574 404 129 899 583 541 314 525 496 443 857 297 78 575 2 430 137 387 911\n",
"10\n20 1 15 17 1 2 15 3 2 4\n",
"8\n16 5 6 9 5 10 7 5\n",
"50\n499 780 1621 984 72 526 944 482 862 136 265 605 5 631 974 967 574 293 969 467 573 845 102 224 17 873 648 120 694 996 244 574 404 129 899 583 541 314 525 496 443 857 297 78 575 2 430 137 387 911\n",
"10\n20 1 15 17 2 2 15 3 2 4\n",
"8\n16 5 6 10 5 10 7 5\n",
"50\n499 780 1621 63 72 526 944 482 862 136 265 605 5 631 974 967 574 293 969 467 573 845 102 224 17 873 648 120 694 996 244 574 404 129 899 583 541 314 525 496 443 857 297 78 575 2 430 137 387 911\n",
"10\n20 1 15 17 4 2 15 3 2 4\n",
"8\n16 5 6 18 5 10 7 5\n",
"50\n499 780 1621 63 72 526 944 482 862 136 265 605 5 631 974 967 574 293 969 467 573 845 102 224 17 873 648 120 694 996 244 574 404 129 899 583 632 314 525 496 443 857 297 78 575 2 430 137 387 911\n",
"10\n20 1 15 17 4 3 15 3 2 4\n",
"8\n16 5 6 12 5 10 7 5\n",
"50\n499 780 1621 63 72 526 944 482 862 136 265 605 5 631 974 967 574 187 969 467 573 845 102 224 17 873 648 120 694 996 244 574 404 129 899 583 632 314 525 496 443 857 297 78 575 2 430 137 387 911\n",
"8\n16 5 6 12 6 10 7 5\n",
"50\n499 780 1621 63 72 526 944 482 862 136 265 605 5 631 974 967 713 187 969 467 573 845 102 224 17 873 648 120 694 996 244 574 404 129 899 583 632 314 525 496 443 857 297 78 575 2 430 137 387 911\n",
"10\n27 1 15 24 4 3 15 3 2 4\n",
"8\n16 5 6 12 2 10 7 5\n",
"50\n499 780 1621 63 72 526 944 482 862 136 265 605 5 631 974 967 713 187 969 467 573 845 102 224 17 873 648 120 694 1722 244 574 404 129 899 583 632 314 525 496 443 857 297 78 575 2 430 137 387 911\n",
"10\n27 1 15 24 4 1 15 3 2 4\n",
"8\n16 5 11 12 2 10 7 5\n",
"50\n499 780 1621 63 72 526 944 482 862 136 265 605 5 631 974 967 713 187 969 467 573 845 102 224 17 873 648 120 239 1722 244 574 404 129 899 583 632 314 525 496 443 857 297 78 575 2 430 137 387 911\n",
"10\n27 1 15 24 0 1 15 3 2 4\n",
"8\n16 5 11 12 2 14 7 5\n",
"50\n499 780 1621 63 72 526 944 482 862 136 265 605 5 616 974 967 713 187 969 467 573 845 102 224 17 873 648 120 239 1722 244 574 404 129 899 583 632 314 525 496 443 857 297 78 575 2 430 137 387 911\n",
"10\n27 1 15 24 0 1 15 3 2 1\n",
"8\n16 5 11 12 2 14 10 5\n",
"50\n499 780 1621 63 72 526 944 482 862 136 265 605 5 616 974 967 713 187 969 467 573 845 71 224 17 873 648 120 239 1722 244 574 404 129 899 583 632 314 525 496 443 857 297 78 575 2 430 137 387 911\n",
"10\n27 2 15 24 0 1 15 3 2 1\n",
"8\n16 7 11 12 2 14 10 5\n",
"50\n499 780 1621 63 72 526 944 482 862 136 265 605 5 616 974 967 713 187 969 467 573 845 71 224 17 873 648 120 239 1722 438 574 404 129 899 583 632 314 525 496 443 857 297 78 575 2 430 137 387 911\n",
"10\n27 2 9 24 0 1 15 3 2 1\n",
"50\n499 1400 1621 63 72 526 944 482 862 136 265 605 5 616 974 967 713 187 969 467 573 845 71 224 17 873 648 120 239 1722 438 574 404 129 899 583 632 314 525 496 443 857 297 78 575 2 430 137 387 911\n",
"10\n27 2 9 47 0 1 15 3 2 1\n",
"8\n24 7 11 22 2 14 10 5\n",
"50\n499 1400 1621 63 72 526 944 482 862 136 265 605 5 616 974 967 713 187 969 467 573 845 71 224 17 873 648 120 239 1722 438 574 404 129 899 583 632 314 525 496 443 857 241 78 575 2 430 137 387 911\n",
"10\n27 0 9 47 0 1 15 3 2 1\n",
"8\n24 7 11 22 2 14 10 8\n",
"50\n499 1400 1621 123 72 526 944 482 862 136 265 605 5 616 974 967 713 187 969 467 573 845 71 224 17 873 648 120 239 1722 438 574 404 129 899 583 632 314 525 496 443 857 241 78 575 2 430 137 387 911\n",
"10\n27 0 6 47 0 1 15 3 2 1\n",
"8\n24 7 11 22 2 14 10 0\n",
"50\n499 1400 1621 123 72 526 944 482 862 136 265 605 5 616 974 967 713 187 969 467 573 845 71 224 17 316 648 120 239 1722 438 574 404 129 899 583 632 314 525 496 443 857 241 78 575 2 430 137 387 911\n",
"10\n27 0 6 47 0 1 15 6 2 1\n",
"8\n24 7 11 22 2 13 10 0\n",
"50\n499 1400 1621 123 72 526 944 482 862 136 265 605 5 616 974 967 713 187 969 467 573 845 71 224 17 316 648 120 239 1722 438 574 404 129 899 583 639 314 525 496 443 857 241 78 575 2 430 137 387 911\n",
"10\n27 0 6 47 0 1 15 6 1 1\n",
"8\n24 7 11 22 2 13 0 0\n",
"50\n499 1400 1621 33 72 526 944 482 862 136 265 605 5 616 974 967 713 187 969 467 573 845 71 224 17 316 648 120 239 1722 438 574 404 129 899 583 639 314 525 496 443 857 241 78 575 2 430 137 387 911\n",
"10\n27 0 3 47 0 1 15 6 1 1\n",
"2\n0 3\n",
"8\n18 5 6 6 5 10 7 5\n",
"8\n16 5 6 6 5 10 7 5\n",
"10\n27 1 15 17 4 3 15 3 2 4\n",
"8\n24 7 11 12 2 14 10 5\n"
],
"output": [
"499122177 0 ",
"499122193 249561095 249561092 873463811 499122178 124780545 623902721 0 ",
"559025033 419266602 618914066 938351557 598948057 39930938 778631560 339403895 758666411 758666317 798596015 139754679 718736351 798595854 419262961 499122476 618911772 19965136 119789548 339403284 898420103 938349861 259543686 59894803 99824567 738700943 618911611 159719199 938349785 559016922 758665784 119789390 698771107 159719150 918384852 339403121 319438228 938349721 39929798 19 159719111 738700833 978279475 838525263 638876390 319438195 838525257 618911499 319438193 0 ",
"898419945 898419929 6 399297745 2 698771048 798595483 898419918 299473306 0 ",
"479165633 898423964 878457646 99826336 858491616 539053137 439228499 838526088 818561086 79860170 379333398 319438672 758666134 938350072 479157630 818560676 838525535 279508673 379333085 598946821 499122367 419262802 838525415 978279612 858490279 519087189 159719212 39929880 578981821 359368054 978279544 179684053 539052012 119789376 578981772 339403121 319438228 938349721 39929798 19 159719111 738700833 978279475 838525263 638876390 319438195 838525257 618911499 319438193 0 \n",
"698771075 798595494 598946618 698771051 299473308 1 798595483 898419918 299473306 0 \n",
"0 0 \n",
"748683282 873463816 4 748683267 374341634 1 623902721 0 \n",
"638884838 419266727 918387454 479159215 259545023 319439395 938350688 419263470 918385530 339403710 978280018 898420404 978279898 179684368 698771391 818560679 678806441 598946868 419262861 978279677 878455223 139754385 439227675 678806307 898420054 399297867 59894777 698771153 578981821 359368054 978279544 179684053 539052012 119789376 578981772 339403121 319438228 938349721 39929798 19 159719111 738700833 978279475 838525263 638876390 319438195 838525257 618911499 319438193 0 \n",
"698771073 399297752 399297747 499122180 99824437 1 798595483 898419918 299473306 0 \n",
"499122196 873463817 374341637 374341635 124780546 748683266 374341633 0 \n",
"539060513 519091217 379335539 379334806 539053462 79860767 19965897 239579499 479158025 59895301 119789883 938350185 19965326 219614149 898420268 598946927 79859834 119789582 938349928 499122391 399297937 658841452 958314742 199649021 419262768 918384934 578981844 219613867 159719196 39929864 818560450 439227587 638876449 55 578981772 339403121 319438228 938349721 39929798 19 159719111 738700833 978279475 838525263 638876390 319438195 838525257 618911499 319438193 0 \n",
"499122198 99824444 399297746 499122179 499122178 1 798595483 898419918 299473306 0 \n",
"778639288 718740151 279511144 419264609 818561903 878456268 119790348 978280332 858490889 59895310 539052520 299473807 738701267 259543929 878455385 219614076 479157578 359368229 658841511 938349908 179684181 439227696 79859713 199649022 519087204 359368097 858490263 519087173 159719196 39929864 818560450 439227587 638876449 55 578981772 339403121 319438228 938349721 39929798 19 159719111 738700833 978279475 838525263 638876390 319438195 838525257 618911499 319438193 0 \n",
"99824455 698771055 898419922 598946614 598946613 399297742 499122177 898419918 299473306 0 \n",
"199657584 179688210 359370698 738702806 119790859 778631835 958315606 898420785 618912245 559017487 738701391 578982226 738701267 259543929 878455385 219614076 479157578 359368229 658841511 938349908 179684181 439227696 79859713 199649022 519087204 359368097 858490263 519087173 159719196 39929864 818560450 439227587 638876449 55 578981772 339403121 319438228 938349721 39929798 19 159719111 738700833 978279475 838525263 638876390 319438195 838525257 618911499 319438193 0 \n",
"798595499 199648877 499122180 499122178 698771048 798595483 199648871 598946612 299473306 0 \n",
"623902741 499122185 249561093 374341635 124780546 748683266 374341633 0 \n",
"539060247 419266649 219616355 978281352 798596942 379334031 738701795 778631417 898420625 738701435 798596020 718736407 419263047 898420291 858490477 778630895 638876657 79859795 19965111 638876589 618911685 439227685 459192557 658841415 878455162 379332975 39929885 678806261 559016929 339403162 958314652 159719161 519087120 99824484 858490186 838525293 459192433 559016863 519087084 678806176 259543545 499122187 359367975 159719102 838525260 359367969 838525257 618911499 319438193 0 \n",
"199648888 399297748 99824439 99824437 1 99824436 499122177 898419918 299473306 0 \n",
"374341653 374341641 249561093 374341635 124780546 748683266 374341633 0 \n",
"7856 778634401 698773503 439229298 559018218 858491254 798596402 658842049 618912166 499122755 578982229 219614201 179684376 339403431 59894975 838525538 259543787 79859780 638876596 539052142 798595657 99824594 39929919 79859681 958314701 618911611 259543634 139754302 918384888 539052025 738700887 99824493 678806210 439227559 419262666 39929806 139754236 99824457 259543549 838525271 79859560 938349701 738700828 419262633 938349695 419262630 838525257 618911499 319438193 0 \n",
"499122195 898419925 4 698771049 598946613 399297742 499122177 898419918 299473306 0 \n",
"623902742 374341641 249561093 374341635 124780546 748683266 374341633 0 \n",
"379340744 219617580 499124643 798597273 519088450 698772162 698771971 119790102 399298411 339403661 758666215 279508864 239579039 399298094 119789638 239578928 499122433 798595715 79859759 319438385 578981900 219613917 39929919 79859681 958314701 618911611 259543634 139754302 918384888 539052025 738700887 99824493 678806210 439227559 419262666 39929806 139754236 99824457 259543549 838525271 79859560 938349701 738700828 419262633 938349695 419262630 838525257 618911499 319438193 0 \n",
"598946631 798595490 598946616 2 898419919 698771048 798595483 898419918 299473306 0 \n",
"124780565 374341641 249561093 374341635 124780546 748683266 374341633 0 \n",
"259551344 3784 459194844 638878158 798596854 419263731 898420831 279509190 39930436 459192977 878455531 878455470 319438583 479157638 199649182 319438472 578981977 359368196 698771255 359368157 618911672 259543689 79859691 119789453 120 658841383 299473406 179684074 958314660 578981797 778630659 139754265 718735982 479157331 459192438 559016868 519087089 678806181 259543549 838525271 79859560 938349701 738700828 419262633 938349695 419262630 838525257 618911499 319438193 0 \n",
"499122198 124780553 124780549 249561091 2 748683266 374341633 0 \n",
"878462886 39933579 718738389 798597264 778631974 359369076 838526175 299474081 239579310 858490721 618912002 618911941 59895054 678806511 39930087 598946892 199649124 818560599 638876594 19965077 618911672 259543689 79859691 119789453 120 658841383 299473406 179684074 958314660 578981797 778630659 139754265 718735982 479157331 459192438 559016868 519087089 678806181 259543549 838525271 79859560 938349701 738700828 419262633 938349695 419262630 838525257 618911499 319438193 0 \n",
"698771067 798595490 598946616 2 898419919 698771048 798595483 898419918 299473306 0 \n",
"748683283 499122184 4 748683267 499122178 124780545 748683265 0 \n",
"379340722 39933579 718738389 798597264 778631974 359369076 838526175 299474081 239579310 858490721 618912002 618911941 59895054 678806511 39930087 598946892 199649124 818560599 638876594 19965077 618911672 259543689 79859691 119789453 120 658841383 299473406 179684074 958314660 578981797 778630659 139754265 718735982 479157331 459192438 559016868 519087089 678806181 259543549 838525271 79859560 938349701 738700828 419262633 938349695 419262630 838525257 618911499 319438193 0 \n",
"199648889 698771054 399297745 99824437 299473307 99824436 199648871 598946612 299473306 0 \n",
"873463829 748683273 499122181 623902723 499122178 124780545 748683265 0 \n",
"459200036 618915188 918387185 539053677 658842609 79860622 499123065 179684733 698771691 738701379 379333340 259543959 139754588 898420255 39930075 539052220 199649115 958314801 598946813 259543715 519087230 818560520 658841410 359368092 399297856 39929879 918384900 698771133 319438270 519087132 878455091 459192455 219613804 199648911 299473341 259543562 519087089 678806181 259543549 838525271 79859560 938349701 738700828 419262633 938349695 419262630 838525257 618911499 319438193 0 \n",
"99824451 99824441 3 598946613 99824436 199648871 598946612 299473306 0 0 \n",
"21 499122185 374341637 623902723 499122178 124780545 748683265 0 \n",
"59902290 419266315 419265007 938351417 958315914 279509492 698771935 379333603 798596126 838525814 479157775 359368394 239579023 337 139754510 638876655 199649115 958314801 598946813 259543715 519087230 818560520 658841410 359368092 399297856 39929879 918384900 698771133 319438270 519087132 878455091 459192455 219613804 199648911 299473341 259543562 519087089 678806181 259543549 838525271 79859560 938349701 738700828 419262633 938349695 419262630 838525257 618911499 319438193 0 \n",
"598946626 5 798595485 698771048 499122177 898419918 598946612 299473306 0 0 \n",
"499122199 748683274 5 249561091 499122178 124780545 748683265 0 \n",
"7602 139757883 319440563 718737653 618912829 59895730 938350576 79860294 299473947 555 479157773 978279891 858490520 618911834 559017137 718736202 279508662 39929995 678806360 339403262 598946777 738700971 199649007 898420042 938349806 578981829 459192497 239578730 858490220 59894729 419262688 52 758665754 738700861 838525291 798595512 59894686 219613778 798595499 379332868 618911510 479157298 279508425 798595487 279508422 419262630 838525257 618911499 319438193 0 \n",
"399297756 898419923 399297744 1 798595483 199648871 598946612 299473306 0 0 \n",
"249561112 249561098 748683270 3 249561090 124780545 748683265 0 \n",
"938357419 818564105 638878796 379334603 439228869 978280554 958315479 578982485 419263281 838525823 758666201 59895094 938350076 698771390 359368274 139754484 299473554 79859773 718736138 379333040 638876555 778630749 239578785 938349820 978279584 618911607 499122275 279508508 898419998 818560441 19964950 379332909 958314626 718735975 698771082 798595512 59894686 219613778 798595499 379332868 618911510 479157298 279508425 798595487 279508422 419262630 838525257 618911499 319438193 0 \n",
"13 99824440 598946614 1 798595483 199648871 598946612 299473306 0 0 \n",
"7778 559020598 199651291 559018594 978280825 119790415 419263531 119790085 798596137 958315147 578982219 958315013 938350076 698771390 359368274 139754484 299473554 79859773 718736138 379333040 638876555 778630749 239578785 938349820 978279584 618911607 499122275 279508508 898419998 818560441 19964950 379332909 958314626 718735975 698771082 798595512 59894686 219613778 798595499 379332868 618911510 479157298 279508425 798595487 279508422 419262630 838525257 618911499 319438193 0 \n",
"898419931 99824440 598946614 1 798595483 199648871 598946612 299473306 0 0 \n",
"748683290 10 748683270 3 249561090 124780545 748683265 0 \n",
"519094803 239582386 638878794 878456778 379334206 319439280 738701719 279509177 918385456 79860113 698771538 39930206 19965269 778630936 439227820 219614030 379333100 119789546 758665911 419262813 678806328 818560522 279508558 978279593 19965004 658841380 539052048 319438281 938349771 858490214 59894723 419262682 46 758665748 858490178 798595512 59894686 219613778 798595499 379332868 618911510 479157298 279508425 798595487 279508422 419262630 838525257 618911499 319438193 0 \n",
"698771059 4 399297743 99824436 199648871 598946612 299473306 0 0 0 \n",
"623902748 11 124780550 623902724 873463811 873463810 748683265 0 \n",
"459200194 19968654 978281891 778632355 119790684 519088159 339403985 279509183 259544188 479157859 399298236 838525692 818560755 578982069 578982032 419262903 578981973 319438419 958314784 618911686 878455201 319438347 159719237 578981853 618911617 259543640 139754308 918384894 539052031 459192474 658841336 19964942 598946659 359368008 459192438 399297772 658841299 818560391 399297759 978279481 219613770 79859558 898419925 698771052 219613761 698771049 838525257 618911499 319438193 0 \n",
"11 99824439 499122178 99824436 199648871 598946612 299473306 0 0 0 \n",
"748683286 873463817 4 623902723 873463810 748683265 0 0 \n",
"958322152 559020498 898422273 658842981 259544854 519088126 159719976 19965629 758666345 598947163 738701301 918385226 239579019 638876721 778630894 559017105 838525499 99824656 19965087 339403262 259543697 718736084 219613894 798595607 818560484 698771152 479157385 99824522 19964965 219613827 578981786 159719150 598946659 359368008 459192438 399297772 658841299 818560391 399297759 978279481 219613770 79859558 898419925 698771052 219613761 698771049 838525257 618911499 319438193 0 \n",
"598946624 898419922 399297743 1 199648871 598946612 299473306 0 0 0 \n",
"21 8 4 623902723 873463810 748683265 0 0 \n",
"638883961 898423579 379335210 519088772 499123499 758666771 399298621 638877128 379333491 219614309 359368447 539052372 858490518 259543867 778630894 559017105 838525499 99824656 19965087 339403262 259543697 718736084 219613894 798595607 818560484 698771152 479157385 99824522 19964965 219613827 578981786 159719150 598946659 359368008 459192438 399297772 658841299 818560391 399297759 978279481 219613770 79859558 898419925 698771052 219613761 698771049 838525257 618911499 319438193 0 \n",
"99824447 299473310 99824437 698771048 898419918 598946612 299473306 0 0 0 \n",
"124780559 748683270 499122179 873463810 748683265 0 0 0 \n",
"898427413 718739556 39932104 818562059 559018145 958315629 869 638877119 39930403 618912043 459192876 339403496 658841642 59894991 239578939 758665972 39930013 299473523 219613954 539052129 459192564 618911646 738700955 399297864 419262741 299473409 79859642 698771132 618911575 818560437 179684043 758665760 199648916 958314618 59894695 29 259543556 419262648 16 578981738 818560380 678806168 479157295 4 479157292 618911500 838525257 618911499 319438193 0 \n",
"499122187 499122180 199648872 798595483 898419918 598946612 299473306 0 0 0 \n",
"0 0 \n",
"499122196 873463817 374341637 374341635 124780546 748683266 374341633 0 \n",
"499122196 873463817 374341637 374341635 124780546 748683266 374341633 0 \n",
"598946631 798595490 598946616 2 898419919 698771048 798595483 898419918 299473306 0 \n",
"249561112 249561098 748683270 3 249561090 124780545 748683265 0 \n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
You are creating a level for a video game. The level consists of n rooms placed in a circle. The rooms are numbered 1 through n. Each room contains exactly one exit: completing the j-th room allows you to go the (j+1)-th room (and completing the n-th room allows you to go the 1-st room).
You are given the description of the multiset of n chests: the i-th chest has treasure value c_i.
Each chest can be of one of two types:
* regular chest — when a player enters a room with this chest, he grabs the treasure and proceeds to the next room;
* mimic chest — when a player enters a room with this chest, the chest eats him alive, and he loses.
The player starts in a random room with each room having an equal probability of being chosen. The players earnings is equal to the total value of treasure chests he'd collected before he lost.
You are allowed to choose the order the chests go into the rooms. For each k from 1 to n place the chests into the rooms in such a way that:
* each room contains exactly one chest;
* exactly k chests are mimics;
* the expected value of players earnings is minimum possible.
Please note that for each k the placement is chosen independently.
It can be shown that it is in the form of P/Q where P and Q are non-negative integers and Q ≠ 0. Report the values of P ⋅ Q^{-1} \pmod {998244353}.
Input
The first contains a single integer n (2 ≤ n ≤ 3 ⋅ 10^5) — the number of rooms and the number of chests.
The second line contains n integers c_1, c_2, ..., c_n (1 ≤ c_i ≤ 10^6) — the treasure values of each chest.
Output
Print n integers — the k -th value should be equal to the minimum possible expected value of players earnings if the chests are placed into the rooms in some order and exactly k of the chests are mimics.
It can be shown that it is in the form of P/Q where P and Q are non-negative integers and Q ≠ 0. Report the values of P ⋅ Q^{-1} \pmod {998244353}.
Examples
Input
2
1 2
Output
499122177 0
Input
8
10 4 3 6 5 10 7 5
Output
499122193 249561095 249561092 873463811 499122178 124780545 623902721 0
Note
In the first example the exact values of minimum expected values are: \frac 1 2, \frac 0 2.
In the second example the exact values of minimum expected values are: \frac{132} 8, \frac{54} 8, \frac{30} 8, \frac{17} 8, \frac{12} 8, \frac 7 8, \frac 3 8, \frac 0 8.
### Input:
2
1 2
### Output:
499122177 0
### Input:
8
10 4 3 6 5 10 7 5
### Output:
499122193 249561095 249561092 873463811 499122178 124780545 623902721 0
### Code:
import sys
sys.setrecursionlimit(10 ** 5)
int1 = lambda x: int(x) - 1
p2D = lambda x: print(*x, sep="\n")
def II(): return int(sys.stdin.readline())
def MI(): return map(int, sys.stdin.readline().split())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def SI(): return sys.stdin.readline()[:-1]
def solve():
cs = [aa[0]]
for a in aa[1:]: cs.append((cs[-1] + a) % md)
# print(cs)
inv = pow(n, md - 2, md)
ans = []
for k in range(1, n):
cur = 0
for i in range(1, n):
if n - 1 - k * i < 0: break
cur = (cur + cs[n - 1 - k * i]) % md
cur = cur * inv % md
ans.append(cur)
ans.append(0)
print(*ans)
md=998244353
n=II()
aa=LI()
aa.sort()
solve()
|
1424_G. Years_10815
|
During one of the space missions, humans have found an evidence of previous life at one of the planets. They were lucky enough to find a book with birth and death years of each individual that had been living at this planet. What's interesting is that these years are in the range (1, 10^9)! Therefore, the planet was named Longlifer.
In order to learn more about Longlifer's previous population, scientists need to determine the year with maximum number of individuals that were alive, as well as the number of alive individuals in that year. Your task is to help scientists solve this problem!
Input
The first line contains an integer n (1 ≤ n ≤ 10^5) — the number of people.
Each of the following n lines contain two integers b and d (1 ≤ b < d ≤ 10^9) representing birth and death year (respectively) of each individual.
Output
Print two integer numbers separated by blank character, y — the year with a maximum number of people alive and k — the number of people alive in year y.
In the case of multiple possible solutions, print the solution with minimum year.
Examples
Input
3
1 5
2 4
5 6
Output
2 2
Input
4
3 4
4 5
4 6
8 10
Output
4 2
Note
You can assume that an individual living from b to d has been born at the beginning of b and died at the beginning of d, and therefore living for d - b years.
|
dct = {}
for i in range(int(input())):
a,b = map(int,input().split())
dct[a] = dct.get(a,0)+1
dct[b] = dct.get(b,0)-1
cnt = curr = y = 0
for i in sorted(dct.keys()):
curr += dct[i]
if curr > cnt :
cnt = curr
y = i
print(y,cnt)
|
{
"input": [
"3\n1 5\n2 4\n5 6\n",
"4\n3 4\n4 5\n4 6\n8 10\n",
"1\n1 2\n",
"1\n1 1000000000\n",
"1\n125 126\n",
"3\n1 2\n2 4\n2 4\n",
"1\n1 3\n",
"1\n0 1000000000\n",
"3\n1 2\n2 4\n0 4\n",
"3\n0 2\n2 4\n0 4\n",
"4\n3 4\n4 8\n4 6\n8 10\n",
"4\n3 8\n4 8\n4 9\n8 10\n",
"3\n2 2\n2 4\n1 3\n",
"1\n2 1101000100\n",
"4\n3 9\n4 8\n6 9\n8 10\n",
"3\n0 2\n1 3\n1 3\n",
"4\n3 13\n5 8\n8 9\n8 10\n",
"1\n123 126\n",
"1\n0 1001000000\n",
"1\n0 1001000100\n",
"3\n0 2\n2 2\n0 4\n",
"3\n0 2\n2 2\n0 6\n",
"1\n0 3\n",
"3\n1 2\n2 4\n1 4\n",
"1\n1 1001000000\n",
"1\n1 1001000100\n",
"3\n0 2\n2 4\n0 6\n",
"4\n3 4\n4 8\n4 9\n8 10\n",
"1\n0 1\n",
"3\n1 2\n2 4\n1 3\n",
"1\n1 1101000000\n",
"1\n1 1001001100\n",
"1\n0 2\n",
"1\n1 1101000100\n",
"1\n0 1001001100\n",
"4\n3 9\n4 8\n4 9\n8 10\n",
"1\n0 6\n",
"3\n2 2\n2 3\n1 3\n",
"1\n0 1001001101\n",
"1\n0 12\n",
"3\n0 2\n2 3\n1 3\n",
"1\n1 1111000100\n",
"1\n0 1101001101\n",
"4\n3 9\n5 8\n6 9\n8 10\n",
"1\n1 1111100100\n",
"1\n1 1001001101\n",
"4\n3 13\n5 8\n6 9\n8 10\n",
"3\n1 2\n1 3\n1 3\n",
"1\n0 1111100100\n",
"1\n0 1000001100\n",
"3\n1 2\n1 3\n0 3\n",
"1\n0 1111100101\n",
"1\n0 1000001000\n",
"3\n0 2\n1 3\n0 3\n",
"1\n0 1111101100\n",
"1\n0 1000001010\n",
"1\n0 1111110100\n",
"1\n1 1000001010\n",
"1\n1 1010001010\n",
"1\n1 1000001000\n",
"1\n1 0001000000\n",
"1\n1 0101000000\n",
"1\n1 0101100000\n",
"1\n2 0101000000\n",
"1\n1 0101000100\n",
"1\n1 0101100100\n",
"1\n0 0101000100\n",
"1\n0 0100000100\n",
"1\n0 0100000110\n",
"1\n1 0100000110\n",
"1\n1 0100000010\n",
"1\n1 0000000010\n",
"1\n1 0100010010\n",
"1\n1 0000010010\n",
"1\n0 0000010010\n",
"1\n0 0010010010\n",
"1\n1 1000000001\n",
"1\n1 6\n",
"3\n1 2\n1 4\n0 4\n",
"1\n0 1001010000\n",
"3\n0 2\n2 4\n0 2\n",
"1\n0 1001000101\n",
"3\n0 2\n2 2\n1 4\n",
"3\n0 1\n2 2\n0 6\n",
"4\n3 4\n4 7\n4 6\n8 10\n",
"1\n2 3\n",
"3\n2 2\n2 4\n1 4\n"
],
"output": [
"2 2\n",
"4 2\n",
"1 1\n",
"1 1\n",
"125 1\n",
"2 2\n",
"1 1\n",
"0 1\n",
"1 2\n",
"0 2\n",
"4 2\n",
"4 3\n",
"2 2\n",
"2 1\n",
"6 3\n",
"1 3\n",
"8 3\n",
"123 1\n",
"0 1\n",
"0 1\n",
"0 2\n",
"0 2\n",
"0 1\n",
"1 2\n",
"1 1\n",
"1 1\n",
"0 2\n",
"4 2\n",
"0 1\n",
"1 2\n",
"1 1\n",
"1 1\n",
"0 1\n",
"1 1\n",
"0 1\n",
"4 3\n",
"0 1\n",
"2 2\n",
"0 1\n",
"0 1\n",
"1 2\n",
"1 1\n",
"0 1\n",
"6 3\n",
"1 1\n",
"1 1\n",
"6 3\n",
"1 3\n",
"0 1\n",
"0 1\n",
"1 3\n",
"0 1\n",
"0 1\n",
"1 3\n",
"0 1\n",
"0 1\n",
"0 1\n",
"1 1\n",
"1 1\n",
"1 1\n",
"1 1\n",
"1 1\n",
"1 1\n",
"2 1\n",
"1 1\n",
"1 1\n",
"0 1\n",
"0 1\n",
"0 1\n",
"1 1\n",
"1 1\n",
"1 1\n",
"1 1\n",
"1 1\n",
"0 1\n",
"0 1\n",
"1 1\n",
"1 1\n",
"1 3\n",
"0 1\n",
"0 2\n",
"0 1\n",
"1 2\n",
"0 2\n",
"4 2\n",
"2 1\n",
"2 2\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
During one of the space missions, humans have found an evidence of previous life at one of the planets. They were lucky enough to find a book with birth and death years of each individual that had been living at this planet. What's interesting is that these years are in the range (1, 10^9)! Therefore, the planet was named Longlifer.
In order to learn more about Longlifer's previous population, scientists need to determine the year with maximum number of individuals that were alive, as well as the number of alive individuals in that year. Your task is to help scientists solve this problem!
Input
The first line contains an integer n (1 ≤ n ≤ 10^5) — the number of people.
Each of the following n lines contain two integers b and d (1 ≤ b < d ≤ 10^9) representing birth and death year (respectively) of each individual.
Output
Print two integer numbers separated by blank character, y — the year with a maximum number of people alive and k — the number of people alive in year y.
In the case of multiple possible solutions, print the solution with minimum year.
Examples
Input
3
1 5
2 4
5 6
Output
2 2
Input
4
3 4
4 5
4 6
8 10
Output
4 2
Note
You can assume that an individual living from b to d has been born at the beginning of b and died at the beginning of d, and therefore living for d - b years.
### Input:
3
1 5
2 4
5 6
### Output:
2 2
### Input:
4
3 4
4 5
4 6
8 10
### Output:
4 2
### Code:
dct = {}
for i in range(int(input())):
a,b = map(int,input().split())
dct[a] = dct.get(a,0)+1
dct[b] = dct.get(b,0)-1
cnt = curr = y = 0
for i in sorted(dct.keys()):
curr += dct[i]
if curr > cnt :
cnt = curr
y = i
print(y,cnt)
|
1445_C. Division_10819
|
Oleg's favorite subjects are History and Math, and his favorite branch of mathematics is division.
To improve his division skills, Oleg came up with t pairs of integers p_i and q_i and for each pair decided to find the greatest integer x_i, such that:
* p_i is divisible by x_i;
* x_i is not divisible by q_i.
Oleg is really good at division and managed to find all the answers quickly, how about you?
Input
The first line contains an integer t (1 ≤ t ≤ 50) — the number of pairs.
Each of the following t lines contains two integers p_i and q_i (1 ≤ p_i ≤ 10^{18}; 2 ≤ q_i ≤ 10^{9}) — the i-th pair of integers.
Output
Print t integers: the i-th integer is the largest x_i such that p_i is divisible by x_i, but x_i is not divisible by q_i.
One can show that there is always at least one value of x_i satisfying the divisibility conditions for the given constraints.
Example
Input
3
10 4
12 6
179 822
Output
10
4
179
Note
For the first pair, where p_1 = 10 and q_1 = 4, the answer is x_1 = 10, since it is the greatest divisor of 10 and 10 is not divisible by 4.
For the second pair, where p_2 = 12 and q_2 = 6, note that
* 12 is not a valid x_2, since 12 is divisible by q_2 = 6;
* 6 is not valid x_2 as well: 6 is also divisible by q_2 = 6.
The next available divisor of p_2 = 12 is 4, which is the answer, since 4 is not divisible by 6.
|
"""
#If FastIO not needed, used this and don't forget to strip
#import sys, math
#input = sys.stdin.readline
"""
import os
import sys
from io import BytesIO, IOBase
import heapq as h
from bisect import bisect_left, bisect_right
from types import GeneratorType
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
import os
self.os = os
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = self.os.read(self._fd, max(self.os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = self.os.read(self._fd, max(self.os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
self.os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
from collections import defaultdict as dd, deque as dq
import math, string
def getInts():
return [int(s) for s in input().split()]
def getInt():
return int(input())
def getStrs():
return [s for s in input().split()]
def getStr():
return input()
def listStr():
return list(input())
MOD = 10**9+7
"""
Start with P
P has factors pi**qi
X = P, is X % Q == 0, doesn't work
Need the largest factor of P s.t. factor % Q = 0
30
10
1 2 3 5 6 10 15 30 so 15 is the answer
If P//Q is the smallest factor of P, the answer is the next smallest factor
Otherwise, the answer is either the next factor, or a smaller factor which doesn't divide P//Q
We need to remove a combination of factors from P until it doesn't divide Q any more
50 = 2*2*5
100 = 2*2*5*5
10 = 2*5
30 = 2*3*5
Answer = 5*5
"""
from functools import reduce
def factors(n):
return set(reduce(list.__add__,
([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0)))
def solve():
P, Q = getInts()
if P < Q:
return P
if P % Q > 0:
return P
facs = sorted(list(factors(Q)))
best = 0
for fac in facs:
if fac == 1:
continue
power = 1
while P % fac**power == 0:
#print(P,fac,power,flush=True)
tmp = P//(fac**power)
if tmp % Q > 0:
best = max(best,tmp)
power += 1
return best
for _ in range(getInt()):
print(solve())
|
{
"input": [
"3\n10 4\n12 6\n179 822\n",
"1\n42034266112 80174\n",
"10\n246857872446986130 713202678\n857754240051582063 933416507\n873935277189052612 530795521\n557307185726829409 746530097\n173788420792057536 769449696\n101626841876448103 132345797\n598448092106640578 746411314\n733629261048200000 361714100\n981271355542147402 38\n559754147245184151 431517529\n",
"10\n228282288 228282288\n1000000000000000000 1000000000\n1244094302301841 35271721\n998005893107997601 999002449\n999999874000003969 999999937\n956980859148255595 5\n1 323\n1 1000000000\n424001357601318819 537974673\n100000000 1000000000\n",
"1\n60169954380 80174\n",
"10\n246857872446986130 713202678\n857754240051582063 933416507\n873935277189052612 530795521\n557307185726829409 746530097\n173788420792057536 769449696\n82363793032335887 132345797\n598448092106640578 746411314\n733629261048200000 361714100\n981271355542147402 38\n559754147245184151 431517529\n",
"10\n228282288 191428673\n1000000000000000000 1000000000\n1244094302301841 35271721\n998005893107997601 999002449\n999999874000003969 999999937\n956980859148255595 5\n1 323\n1 1000000000\n424001357601318819 537974673\n100000000 1000000000\n",
"3\n10 4\n12 4\n179 822\n",
"10\n246857872446986130 884113456\n857754240051582063 933416507\n873935277189052612 530795521\n557307185726829409 746530097\n173788420792057536 769449696\n82363793032335887 132345797\n598448092106640578 746411314\n733629261048200000 361714100\n981271355542147402 38\n559754147245184151 431517529\n",
"10\n228282288 191428673\n1000000000000000000 1000000000\n1244094302301841 35271721\n998005893107997601 999002449\n367730850598317303 999999937\n956980859148255595 5\n1 323\n1 1000000000\n424001357601318819 537974673\n100000000 1000000000\n",
"10\n335584723051996295 884113456\n857754240051582063 933416507\n873935277189052612 530795521\n557307185726829409 746530097\n173788420792057536 769449696\n82363793032335887 132345797\n598448092106640578 746411314\n733629261048200000 361714100\n981271355542147402 38\n559754147245184151 431517529\n",
"10\n228282288 191428673\n1000000000000000000 1000000000\n1244094302301841 35271721\n998005893107997601 999002449\n367730850598317303 999999937\n956980859148255595 5\n1 323\n1 1000000000\n291064467892143351 537974673\n100000000 1000000000\n",
"3\n10 7\n4 4\n179 822\n",
"10\n335584723051996295 884113456\n857754240051582063 933416507\n873935277189052612 530795521\n557307185726829409 746530097\n173788420792057536 769449696\n82363793032335887 132345797\n598448092106640578 686913140\n733629261048200000 361714100\n981271355542147402 38\n559754147245184151 431517529\n",
"10\n228282288 191428673\n1000000000000000000 1000000000\n1244094302301841 35271721\n998005893107997601 999002449\n428368972161239813 999999937\n956980859148255595 5\n1 323\n1 1000000000\n291064467892143351 537974673\n100000000 1000000000\n",
"1\n14686764191 144795\n",
"10\n228282288 191428673\n1000000000000000000 1000000000\n1244094302301841 35271721\n998005893107997601 999002449\n428368972161239813 999999937\n956980859148255595 5\n1 323\n1 1000000000\n291064467892143351 537974673\n110000000 1000000000\n",
"1\n6319474934 144795\n",
"10\n335584723051996295 884113456\n857754240051582063 1527900094\n873935277189052612 530795521\n557307185726829409 746530097\n173788420792057536 769449696\n82363793032335887 14057644\n598448092106640578 686913140\n733629261048200000 361714100\n981271355542147402 38\n559754147245184151 431517529\n",
"10\n228282288 191428673\n1000000000000000000 1000000000\n624705174700002 35271721\n998005893107997601 999002449\n428368972161239813 999999937\n956980859148255595 5\n1 323\n1 1000000000\n291064467892143351 537974673\n110000000 1000000000\n",
"1\n5576019098 144795\n",
"10\n335584723051996295 884113456\n857754240051582063 1527900094\n873935277189052612 1016316366\n557307185726829409 746530097\n173788420792057536 769449696\n82363793032335887 14057644\n598448092106640578 686913140\n733629261048200000 361714100\n981271355542147402 38\n559754147245184151 431517529\n",
"10\n228282288 191428673\n1000000000000000000 1000000000\n624705174700002 35271721\n1771336840338025823 999002449\n428368972161239813 999999937\n956980859148255595 5\n1 323\n1 1000000000\n291064467892143351 537974673\n110000000 1000000000\n",
"10\n335584723051996295 884113456\n857754240051582063 1527900094\n873935277189052612 1016316366\n557307185726829409 746530097\n173788420792057536 769449696\n82363793032335887 14057644\n598448092106640578 686913140\n733629261048200000 548887058\n981271355542147402 38\n559754147245184151 431517529\n",
"1\n5697359804 235336\n",
"10\n629312442766399206 884113456\n857754240051582063 1527900094\n873935277189052612 1016316366\n557307185726829409 746530097\n173788420792057536 769449696\n82363793032335887 14057644\n598448092106640578 686913140\n733629261048200000 548887058\n981271355542147402 38\n559754147245184151 431517529\n",
"1\n7508985026 235336\n",
"1\n7832627406 235336\n",
"10\n629312442766399206 884113456\n857754240051582063 302790021\n873935277189052612 1016316366\n557307185726829409 746530097\n173788420792057536 769449696\n82363793032335887 14057644\n598448092106640578 686913140\n733629261048200000 548887058\n1286713648467123503 38\n559754147245184151 431517529\n",
"1\n10742348479 235336\n",
"10\n228282288 194474005\n1000000000001000000 1000000000\n624705174700002 33933044\n1771336840338025823 999002449\n428368972161239813 999999937\n956980859148255595 5\n1 323\n1 1000000000\n291064467892143351 502150106\n110000000 1000000000\n",
"1\n5752978525 235336\n",
"10\n228282288 194474005\n1000000000001000000 1000000000\n796096413598469 33933044\n1771336840338025823 999002449\n428368972161239813 1049913570\n956980859148255595 5\n1 323\n1 1000000000\n291064467892143351 502150106\n110000000 1000000000\n",
"1\n6973179412 280409\n",
"1\n10802323266 39847\n",
"10\n228282288 354300157\n1000000000001000000 1000000000\n796096413598469 33933044\n117617623045706281 999002449\n428368972161239813 1049913570\n956980859148255595 5\n1 30\n1 1000000000\n291064467892143351 502150106\n110000000 1010000000\n",
"10\n629312442766399206 533816173\n857754240051582063 302790021\n873935277189052612 1316592437\n557307185726829409 746530097\n286803888063493394 769449696\n82363793032335887 24611833\n598448092106640578 686913140\n733629261048200000 604297264\n1286713648467123503 38\n559754147245184151 431517529\n",
"10\n629312442766399206 533816173\n857754240051582063 302790021\n873935277189052612 1316592437\n557307185726829409 746530097\n286803888063493394 769449696\n82363793032335887 24611833\n598448092106640578 686913140\n733629261048200000 604297264\n1286713648467123503 38\n720344145802748717 431517529\n",
"10\n228282288 354300157\n1000000000001000000 1000000000\n796096413598469 33933044\n117617623045706281 999002449\n103839921659619004 1304050814\n956980859148255595 5\n1 30\n1 1000000000\n291064467892143351 502150106\n110000000 1010000000\n",
"1\n17510594487 681\n",
"10\n629312442766399206 533816173\n857754240051582063 302790021\n873935277189052612 1316592437\n557307185726829409 746530097\n286803888063493394 769449696\n163487930194272002 24611833\n598448092106640578 686913140\n733629261048200000 604297264\n1286713648467123503 38\n720344145802748717 431517529\n",
"10\n228282288 354300157\n1000000000001100000 1000000000\n796096413598469 33933044\n117617623045706281 999002449\n103839921659619004 1304050814\n956980859148255595 5\n1 30\n1 1000000000\n291064467892143351 502150106\n110000000 1010000000\n",
"10\n629312442766399206 533816173\n891914827865404228 302790021\n873935277189052612 1316592437\n557307185726829409 746530097\n286803888063493394 769449696\n163487930194272002 24611833\n598448092106640578 686913140\n733629261048200000 604297264\n1286713648467123503 38\n720344145802748717 431517529\n",
"10\n228282288 354300157\n1000000000001100000 1000000000\n426445146207421 33933044\n117617623045706281 999002449\n103839921659619004 1304050814\n956980859148255595 5\n1 30\n1 1000000000\n291064467892143351 502150106\n110000000 1010000000\n",
"1\n8248061909 833\n",
"10\n622457341638479796 533816173\n891914827865404228 302790021\n873935277189052612 1316592437\n557307185726829409 746530097\n286803888063493394 769449696\n163487930194272002 24611833\n598448092106640578 686913140\n733629261048200000 604297264\n1286713648467123503 38\n720344145802748717 431517529\n",
"10\n228282288 354300157\n1000000000001100000 1000000000\n426445146207421 33933044\n193472003780811255 999002449\n103839921659619004 1304050814\n956980859148255595 5\n1 30\n1 1000000000\n291064467892143351 502150106\n110000000 1010000000\n",
"10\n228282288 354300157\n1000000000001100000 1000000000\n721244911895861 33933044\n193472003780811255 999002449\n103839921659619004 1304050814\n956980859148255595 5\n1 30\n1 1000000000\n291064467892143351 502150106\n110000000 1010000000\n",
"1\n12831814671 1175\n",
"10\n228282288 354300157\n1000000000001100000 1000000000\n721244911895861 33933044\n193472003780811255 87934725\n103839921659619004 1304050814\n956980859148255595 5\n1 30\n1 1000000000\n138332107573769400 502150106\n110000000 1010000000\n",
"1\n9204856756 192\n",
"1\n8421415367 192\n",
"10\n622457341638479796 338608092\n891914827865404228 279127582\n873935277189052612 1316592437\n557307185726829409 746530097\n286803888063493394 769449696\n28943295091599321 24611833\n598448092106640578 352238501\n733629261048200000 672172589\n1286713648467123503 46\n720344145802748717 536120027\n",
"10\n622457341638479796 338608092\n891914827865404228 279127582\n873935277189052612 1316592437\n859803368805468629 746530097\n286803888063493394 769449696\n28943295091599321 24611833\n598448092106640578 352238501\n733629261048200000 672172589\n1286713648467123503 46\n720344145802748717 536120027\n",
"10\n622457341638479796 338608092\n891914827865404228 279127582\n1567895284521734914 1071397817\n859803368805468629 746530097\n286803888063493394 769449696\n28943295091599321 24611833\n598448092106640578 352238501\n733629261048200000 672172589\n1286713648467123503 46\n720344145802748717 536120027\n",
"1\n60169954380 148658\n",
"3\n10 7\n12 4\n179 822\n",
"1\n60169954380 146587\n",
"1\n60169954380 144795\n",
"10\n335584723051996295 884113456\n857754240051582063 933416507\n873935277189052612 530795521\n557307185726829409 746530097\n173788420792057536 769449696\n82363793032335887 14057644\n598448092106640578 686913140\n733629261048200000 361714100\n981271355542147402 38\n559754147245184151 431517529\n",
"1\n5576019098 235336\n",
"10\n228282288 107502835\n1000000000000000000 1000000000\n624705174700002 35271721\n1771336840338025823 999002449\n428368972161239813 999999937\n956980859148255595 5\n1 323\n1 1000000000\n291064467892143351 537974673\n110000000 1000000000\n",
"10\n228282288 194474005\n1000000000000000000 1000000000\n624705174700002 35271721\n1771336840338025823 999002449\n428368972161239813 999999937\n956980859148255595 5\n1 323\n1 1000000000\n291064467892143351 537974673\n110000000 1000000000\n",
"10\n629312442766399206 884113456\n857754240051582063 302790021\n873935277189052612 1016316366\n557307185726829409 746530097\n173788420792057536 769449696\n82363793032335887 14057644\n598448092106640578 686913140\n733629261048200000 548887058\n981271355542147402 38\n559754147245184151 431517529\n",
"10\n228282288 194474005\n1000000000000000000 1000000000\n624705174700002 33933044\n1771336840338025823 999002449\n428368972161239813 999999937\n956980859148255595 5\n1 323\n1 1000000000\n291064467892143351 537974673\n110000000 1000000000\n",
"10\n228282288 194474005\n1000000000000000000 1000000000\n624705174700002 33933044\n1771336840338025823 999002449\n428368972161239813 999999937\n956980859148255595 5\n1 323\n1 1000000000\n291064467892143351 502150106\n110000000 1000000000\n",
"10\n629312442766399206 884113456\n857754240051582063 302790021\n873935277189052612 1548633593\n557307185726829409 746530097\n173788420792057536 769449696\n82363793032335887 14057644\n598448092106640578 686913140\n733629261048200000 548887058\n1286713648467123503 38\n559754147245184151 431517529\n",
"10\n629312442766399206 884113456\n857754240051582063 302790021\n873935277189052612 1548633593\n557307185726829409 746530097\n173788420792057536 769449696\n82363793032335887 24611833\n598448092106640578 686913140\n733629261048200000 548887058\n1286713648467123503 38\n559754147245184151 431517529\n",
"10\n228282288 194474005\n1000000000001000000 1000000000\n624705174700002 33933044\n1771336840338025823 999002449\n428368972161239813 1049913570\n956980859148255595 5\n1 323\n1 1000000000\n291064467892143351 502150106\n110000000 1000000000\n",
"1\n5752978525 178787\n",
"10\n629312442766399206 884113456\n857754240051582063 302790021\n873935277189052612 1548633593\n557307185726829409 746530097\n173788420792057536 769449696\n82363793032335887 24611833\n598448092106640578 686913140\n733629261048200000 604297264\n1286713648467123503 38\n559754147245184151 431517529\n",
"1\n5752978525 280409\n",
"10\n629312442766399206 884113456\n857754240051582063 302790021\n873935277189052612 1126454300\n557307185726829409 746530097\n173788420792057536 769449696\n82363793032335887 24611833\n598448092106640578 686913140\n733629261048200000 604297264\n1286713648467123503 38\n559754147245184151 431517529\n",
"10\n228282288 194474005\n1000000000001000000 1000000000\n796096413598469 33933044\n1771336840338025823 999002449\n428368972161239813 1049913570\n956980859148255595 5\n1 30\n1 1000000000\n291064467892143351 502150106\n110000000 1000000000\n",
"10\n629312442766399206 884113456\n857754240051582063 302790021\n873935277189052612 1316592437\n557307185726829409 746530097\n173788420792057536 769449696\n82363793032335887 24611833\n598448092106640578 686913140\n733629261048200000 604297264\n1286713648467123503 38\n559754147245184151 431517529\n",
"10\n228282288 194474005\n1000000000001000000 1000000000\n796096413598469 33933044\n1771336840338025823 999002449\n428368972161239813 1049913570\n956980859148255595 5\n1 30\n1 1000000000\n291064467892143351 502150106\n110000000 1010000000\n",
"1\n6973179412 39847\n",
"10\n629312442766399206 343546698\n857754240051582063 302790021\n873935277189052612 1316592437\n557307185726829409 746530097\n173788420792057536 769449696\n82363793032335887 24611833\n598448092106640578 686913140\n733629261048200000 604297264\n1286713648467123503 38\n559754147245184151 431517529\n",
"10\n228282288 354300157\n1000000000001000000 1000000000\n796096413598469 33933044\n1771336840338025823 999002449\n428368972161239813 1049913570\n956980859148255595 5\n1 30\n1 1000000000\n291064467892143351 502150106\n110000000 1010000000\n",
"10\n629312442766399206 533816173\n857754240051582063 302790021\n873935277189052612 1316592437\n557307185726829409 746530097\n173788420792057536 769449696\n82363793032335887 24611833\n598448092106640578 686913140\n733629261048200000 604297264\n1286713648467123503 38\n559754147245184151 431517529\n",
"1\n10802323266 3680\n",
"10\n228282288 354300157\n1000000000001000000 1000000000\n796096413598469 33933044\n117617623045706281 999002449\n428368972161239813 1304050814\n956980859148255595 5\n1 30\n1 1000000000\n291064467892143351 502150106\n110000000 1010000000\n",
"1\n10802323266 681\n",
"1\n17510594487 833\n",
"1\n8248061909 602\n",
"10\n622457341638479796 533816173\n891914827865404228 302790021\n873935277189052612 1316592437\n557307185726829409 746530097\n286803888063493394 769449696\n163487930194272002 24611833\n598448092106640578 686913140\n733629261048200000 604297264\n1286713648467123503 38\n720344145802748717 536120027\n",
"1\n8248061909 1175\n",
"10\n622457341638479796 533816173\n891914827865404228 302790021\n873935277189052612 1316592437\n557307185726829409 746530097\n286803888063493394 769449696\n163487930194272002 24611833\n598448092106640578 352238501\n733629261048200000 604297264\n1286713648467123503 38\n720344145802748717 536120027\n",
"10\n228282288 354300157\n1000000000001100000 1000000000\n721244911895861 33933044\n193472003780811255 87934725\n103839921659619004 1304050814\n956980859148255595 5\n1 30\n1 1000000000\n291064467892143351 502150106\n110000000 1010000000\n",
"10\n622457341638479796 533816173\n891914827865404228 279127582\n873935277189052612 1316592437\n557307185726829409 746530097\n286803888063493394 769449696\n163487930194272002 24611833\n598448092106640578 352238501\n733629261048200000 604297264\n1286713648467123503 38\n720344145802748717 536120027\n",
"1\n12831814671 240\n",
"10\n622457341638479796 533816173\n891914827865404228 279127582\n873935277189052612 1316592437\n557307185726829409 746530097\n286803888063493394 769449696\n163487930194272002 24611833\n598448092106640578 352238501\n733629261048200000 604297264\n1286713648467123503 46\n720344145802748717 536120027\n",
"1\n12831814671 192\n",
"10\n622457341638479796 338608092\n891914827865404228 279127582\n873935277189052612 1316592437\n557307185726829409 746530097\n286803888063493394 769449696\n163487930194272002 24611833\n598448092106640578 352238501\n733629261048200000 604297264\n1286713648467123503 46\n720344145802748717 536120027\n",
"10\n622457341638479796 338608092\n891914827865404228 279127582\n873935277189052612 1316592437\n557307185726829409 746530097\n286803888063493394 769449696\n163487930194272002 24611833\n598448092106640578 352238501\n733629261048200000 672172589\n1286713648467123503 46\n720344145802748717 536120027\n",
"1\n8421415367 150\n",
"1\n8421415367 143\n",
"10\n622457341638479796 338608092\n891914827865404228 279127582\n873935277189052612 1071397817\n859803368805468629 746530097\n286803888063493394 769449696\n28943295091599321 24611833\n598448092106640578 352238501\n733629261048200000 672172589\n1286713648467123503 46\n720344145802748717 536120027\n",
"1\n8421415367 177\n",
"1\n8421415367 47\n",
"10\n622457341638479796 338608092\n891914827865404228 279127582\n1567895284521734914 1071397817\n859803368805468629 746530097\n286803888063493394 769449696\n28943295091599321 24611833\n598448092106640578 352238501\n733629261048200000 672172589\n1286713648467123503 46\n720344145802748717 846112776\n",
"1\n8421415367 83\n",
"10\n622457341638479796 338608092\n891914827865404228 279127582\n1567895284521734914 1097731973\n859803368805468629 746530097\n286803888063493394 769449696\n28943295091599321 24611833\n598448092106640578 352238501\n733629261048200000 672172589\n1286713648467123503 46\n720344145802748717 846112776\n"
],
"output": [
"10\n4\n179\n",
"1048576\n",
"123428936223493065\n918940509\n37932865019708\n1\n57929473597352512\n767888699\n299224046053320289\n31896924393400000\n490635677771073701\n26946235365387\n",
"114141144\n976562500000000\n5939\n31607\n1\n191396171829651119\n1\n1\n424001357601318819\n100000000\n",
"60169954380\n",
"123428936223493065\n918940509\n37932865019708\n1\n57929473597352512\n82363793032335887\n299224046053320289\n31896924393400000\n490635677771073701\n26946235365387\n",
"228282288\n976562500000000\n5939\n31607\n1\n191396171829651119\n1\n1\n424001357601318819\n100000000\n",
"10\n6\n179\n",
"246857872446986130\n918940509\n37932865019708\n1\n57929473597352512\n82363793032335887\n299224046053320289\n31896924393400000\n490635677771073701\n26946235365387\n",
"228282288\n976562500000000\n5939\n31607\n367730850598317303\n191396171829651119\n1\n1\n424001357601318819\n100000000\n",
"335584723051996295\n918940509\n37932865019708\n1\n57929473597352512\n82363793032335887\n299224046053320289\n31896924393400000\n490635677771073701\n26946235365387\n",
"228282288\n976562500000000\n5939\n31607\n367730850598317303\n191396171829651119\n1\n1\n291064467892143351\n100000000\n",
"10\n2\n179\n",
"335584723051996295\n918940509\n37932865019708\n1\n57929473597352512\n82363793032335887\n598448092106640578\n31896924393400000\n490635677771073701\n26946235365387\n",
"228282288\n976562500000000\n5939\n31607\n428368972161239813\n191396171829651119\n1\n1\n291064467892143351\n100000000\n",
"14686764191\n",
"228282288\n976562500000000\n5939\n31607\n428368972161239813\n191396171829651119\n1\n1\n291064467892143351\n110000000\n",
"6319474934\n",
"335584723051996295\n857754240051582063\n37932865019708\n1\n57929473597352512\n82363793032335887\n598448092106640578\n31896924393400000\n490635677771073701\n26946235365387\n",
"228282288\n976562500000000\n624705174700002\n31607\n428368972161239813\n191396171829651119\n1\n1\n291064467892143351\n110000000\n",
"5576019098\n",
"335584723051996295\n857754240051582063\n873935277189052612\n1\n57929473597352512\n82363793032335887\n598448092106640578\n31896924393400000\n490635677771073701\n26946235365387\n",
"228282288\n976562500000000\n624705174700002\n1771336840338025823\n428368972161239813\n191396171829651119\n1\n1\n291064467892143351\n110000000\n",
"335584723051996295\n857754240051582063\n873935277189052612\n1\n57929473597352512\n82363793032335887\n598448092106640578\n733629261048200000\n490635677771073701\n26946235365387\n",
"5697359804\n",
"629312442766399206\n857754240051582063\n873935277189052612\n1\n57929473597352512\n82363793032335887\n598448092106640578\n733629261048200000\n490635677771073701\n26946235365387\n",
"7508985026\n",
"7832627406\n",
"629312442766399206\n857754240051582063\n873935277189052612\n1\n57929473597352512\n82363793032335887\n598448092106640578\n733629261048200000\n1286713648467123503\n26946235365387\n",
"10742348479\n",
"228282288\n1000000000001000000\n624705174700002\n1771336840338025823\n428368972161239813\n191396171829651119\n1\n1\n291064467892143351\n110000000\n",
"5752978525\n",
"228282288\n1000000000001000000\n796096413598469\n1771336840338025823\n428368972161239813\n191396171829651119\n1\n1\n291064467892143351\n110000000\n",
"6973179412\n",
"10802323266\n",
"228282288\n1000000000001000000\n796096413598469\n117617623045706281\n428368972161239813\n191396171829651119\n1\n1\n291064467892143351\n110000000\n",
"629312442766399206\n857754240051582063\n873935277189052612\n1\n286803888063493394\n82363793032335887\n598448092106640578\n733629261048200000\n1286713648467123503\n26946235365387\n",
"629312442766399206\n857754240051582063\n873935277189052612\n1\n286803888063493394\n82363793032335887\n598448092106640578\n733629261048200000\n1286713648467123503\n720344145802748717\n",
"228282288\n1000000000001000000\n796096413598469\n117617623045706281\n103839921659619004\n191396171829651119\n1\n1\n291064467892143351\n110000000\n",
"17510594487\n",
"629312442766399206\n857754240051582063\n873935277189052612\n1\n286803888063493394\n163487930194272002\n598448092106640578\n733629261048200000\n1286713648467123503\n720344145802748717\n",
"228282288\n1000000000001100000\n796096413598469\n117617623045706281\n103839921659619004\n191396171829651119\n1\n1\n291064467892143351\n110000000\n",
"629312442766399206\n891914827865404228\n873935277189052612\n1\n286803888063493394\n163487930194272002\n598448092106640578\n733629261048200000\n1286713648467123503\n720344145802748717\n",
"228282288\n1000000000001100000\n426445146207421\n117617623045706281\n103839921659619004\n191396171829651119\n1\n1\n291064467892143351\n110000000\n",
"8248061909\n",
"622457341638479796\n891914827865404228\n873935277189052612\n1\n286803888063493394\n163487930194272002\n598448092106640578\n733629261048200000\n1286713648467123503\n720344145802748717\n",
"228282288\n1000000000001100000\n426445146207421\n193472003780811255\n103839921659619004\n191396171829651119\n1\n1\n291064467892143351\n110000000\n",
"228282288\n1000000000001100000\n721244911895861\n193472003780811255\n103839921659619004\n191396171829651119\n1\n1\n291064467892143351\n110000000\n",
"12831814671\n",
"228282288\n1000000000001100000\n721244911895861\n193472003780811255\n103839921659619004\n191396171829651119\n1\n1\n138332107573769400\n110000000\n",
"9204856756\n",
"8421415367\n",
"622457341638479796\n891914827865404228\n873935277189052612\n1\n286803888063493394\n28943295091599321\n598448092106640578\n733629261048200000\n1286713648467123503\n720344145802748717\n",
"622457341638479796\n891914827865404228\n873935277189052612\n859803368805468629\n286803888063493394\n28943295091599321\n598448092106640578\n733629261048200000\n1286713648467123503\n720344145802748717\n",
"622457341638479796\n891914827865404228\n1567895284521734914\n859803368805468629\n286803888063493394\n28943295091599321\n598448092106640578\n733629261048200000\n1286713648467123503\n720344145802748717\n",
"60169954380\n",
"10\n6\n179\n",
"60169954380\n",
"60169954380\n",
"335584723051996295\n918940509\n37932865019708\n1\n57929473597352512\n82363793032335887\n598448092106640578\n31896924393400000\n490635677771073701\n26946235365387\n",
"5576019098\n",
"228282288\n976562500000000\n624705174700002\n1771336840338025823\n428368972161239813\n191396171829651119\n1\n1\n291064467892143351\n110000000\n",
"228282288\n976562500000000\n624705174700002\n1771336840338025823\n428368972161239813\n191396171829651119\n1\n1\n291064467892143351\n110000000\n",
"629312442766399206\n857754240051582063\n873935277189052612\n1\n57929473597352512\n82363793032335887\n598448092106640578\n733629261048200000\n490635677771073701\n26946235365387\n",
"228282288\n976562500000000\n624705174700002\n1771336840338025823\n428368972161239813\n191396171829651119\n1\n1\n291064467892143351\n110000000\n",
"228282288\n976562500000000\n624705174700002\n1771336840338025823\n428368972161239813\n191396171829651119\n1\n1\n291064467892143351\n110000000\n",
"629312442766399206\n857754240051582063\n873935277189052612\n1\n57929473597352512\n82363793032335887\n598448092106640578\n733629261048200000\n1286713648467123503\n26946235365387\n",
"629312442766399206\n857754240051582063\n873935277189052612\n1\n57929473597352512\n82363793032335887\n598448092106640578\n733629261048200000\n1286713648467123503\n26946235365387\n",
"228282288\n1000000000001000000\n624705174700002\n1771336840338025823\n428368972161239813\n191396171829651119\n1\n1\n291064467892143351\n110000000\n",
"5752978525\n",
"629312442766399206\n857754240051582063\n873935277189052612\n1\n57929473597352512\n82363793032335887\n598448092106640578\n733629261048200000\n1286713648467123503\n26946235365387\n",
"5752978525\n",
"629312442766399206\n857754240051582063\n873935277189052612\n1\n57929473597352512\n82363793032335887\n598448092106640578\n733629261048200000\n1286713648467123503\n26946235365387\n",
"228282288\n1000000000001000000\n796096413598469\n1771336840338025823\n428368972161239813\n191396171829651119\n1\n1\n291064467892143351\n110000000\n",
"629312442766399206\n857754240051582063\n873935277189052612\n1\n57929473597352512\n82363793032335887\n598448092106640578\n733629261048200000\n1286713648467123503\n26946235365387\n",
"228282288\n1000000000001000000\n796096413598469\n1771336840338025823\n428368972161239813\n191396171829651119\n1\n1\n291064467892143351\n110000000\n",
"6973179412\n",
"629312442766399206\n857754240051582063\n873935277189052612\n1\n57929473597352512\n82363793032335887\n598448092106640578\n733629261048200000\n1286713648467123503\n26946235365387\n",
"228282288\n1000000000001000000\n796096413598469\n1771336840338025823\n428368972161239813\n191396171829651119\n1\n1\n291064467892143351\n110000000\n",
"629312442766399206\n857754240051582063\n873935277189052612\n1\n57929473597352512\n82363793032335887\n598448092106640578\n733629261048200000\n1286713648467123503\n26946235365387\n",
"10802323266\n",
"228282288\n1000000000001000000\n796096413598469\n117617623045706281\n428368972161239813\n191396171829651119\n1\n1\n291064467892143351\n110000000\n",
"10802323266\n",
"17510594487\n",
"8248061909\n",
"622457341638479796\n891914827865404228\n873935277189052612\n1\n286803888063493394\n163487930194272002\n598448092106640578\n733629261048200000\n1286713648467123503\n720344145802748717\n",
"8248061909\n",
"622457341638479796\n891914827865404228\n873935277189052612\n1\n286803888063493394\n163487930194272002\n598448092106640578\n733629261048200000\n1286713648467123503\n720344145802748717\n",
"228282288\n1000000000001100000\n721244911895861\n193472003780811255\n103839921659619004\n191396171829651119\n1\n1\n291064467892143351\n110000000\n",
"622457341638479796\n891914827865404228\n873935277189052612\n1\n286803888063493394\n163487930194272002\n598448092106640578\n733629261048200000\n1286713648467123503\n720344145802748717\n",
"12831814671\n",
"622457341638479796\n891914827865404228\n873935277189052612\n1\n286803888063493394\n163487930194272002\n598448092106640578\n733629261048200000\n1286713648467123503\n720344145802748717\n",
"12831814671\n",
"622457341638479796\n891914827865404228\n873935277189052612\n1\n286803888063493394\n163487930194272002\n598448092106640578\n733629261048200000\n1286713648467123503\n720344145802748717\n",
"622457341638479796\n891914827865404228\n873935277189052612\n1\n286803888063493394\n163487930194272002\n598448092106640578\n733629261048200000\n1286713648467123503\n720344145802748717\n",
"8421415367\n",
"8421415367\n",
"622457341638479796\n891914827865404228\n873935277189052612\n859803368805468629\n286803888063493394\n28943295091599321\n598448092106640578\n733629261048200000\n1286713648467123503\n720344145802748717\n",
"8421415367\n",
"8421415367\n",
"622457341638479796\n891914827865404228\n1567895284521734914\n859803368805468629\n286803888063493394\n28943295091599321\n598448092106640578\n733629261048200000\n1286713648467123503\n720344145802748717\n",
"8421415367\n",
"622457341638479796\n891914827865404228\n1567895284521734914\n859803368805468629\n286803888063493394\n28943295091599321\n598448092106640578\n733629261048200000\n1286713648467123503\n720344145802748717\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Oleg's favorite subjects are History and Math, and his favorite branch of mathematics is division.
To improve his division skills, Oleg came up with t pairs of integers p_i and q_i and for each pair decided to find the greatest integer x_i, such that:
* p_i is divisible by x_i;
* x_i is not divisible by q_i.
Oleg is really good at division and managed to find all the answers quickly, how about you?
Input
The first line contains an integer t (1 ≤ t ≤ 50) — the number of pairs.
Each of the following t lines contains two integers p_i and q_i (1 ≤ p_i ≤ 10^{18}; 2 ≤ q_i ≤ 10^{9}) — the i-th pair of integers.
Output
Print t integers: the i-th integer is the largest x_i such that p_i is divisible by x_i, but x_i is not divisible by q_i.
One can show that there is always at least one value of x_i satisfying the divisibility conditions for the given constraints.
Example
Input
3
10 4
12 6
179 822
Output
10
4
179
Note
For the first pair, where p_1 = 10 and q_1 = 4, the answer is x_1 = 10, since it is the greatest divisor of 10 and 10 is not divisible by 4.
For the second pair, where p_2 = 12 and q_2 = 6, note that
* 12 is not a valid x_2, since 12 is divisible by q_2 = 6;
* 6 is not valid x_2 as well: 6 is also divisible by q_2 = 6.
The next available divisor of p_2 = 12 is 4, which is the answer, since 4 is not divisible by 6.
### Input:
3
10 4
12 6
179 822
### Output:
10
4
179
### Input:
1
42034266112 80174
### Output:
1048576
### Code:
"""
#If FastIO not needed, used this and don't forget to strip
#import sys, math
#input = sys.stdin.readline
"""
import os
import sys
from io import BytesIO, IOBase
import heapq as h
from bisect import bisect_left, bisect_right
from types import GeneratorType
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
import os
self.os = os
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = self.os.read(self._fd, max(self.os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = self.os.read(self._fd, max(self.os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n") + (not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
self.os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s: self.buffer.write(s.encode("ascii"))
self.read = lambda: self.buffer.read().decode("ascii")
self.readline = lambda: self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda: sys.stdin.readline().rstrip("\r\n")
from collections import defaultdict as dd, deque as dq
import math, string
def getInts():
return [int(s) for s in input().split()]
def getInt():
return int(input())
def getStrs():
return [s for s in input().split()]
def getStr():
return input()
def listStr():
return list(input())
MOD = 10**9+7
"""
Start with P
P has factors pi**qi
X = P, is X % Q == 0, doesn't work
Need the largest factor of P s.t. factor % Q = 0
30
10
1 2 3 5 6 10 15 30 so 15 is the answer
If P//Q is the smallest factor of P, the answer is the next smallest factor
Otherwise, the answer is either the next factor, or a smaller factor which doesn't divide P//Q
We need to remove a combination of factors from P until it doesn't divide Q any more
50 = 2*2*5
100 = 2*2*5*5
10 = 2*5
30 = 2*3*5
Answer = 5*5
"""
from functools import reduce
def factors(n):
return set(reduce(list.__add__,
([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0)))
def solve():
P, Q = getInts()
if P < Q:
return P
if P % Q > 0:
return P
facs = sorted(list(factors(Q)))
best = 0
for fac in facs:
if fac == 1:
continue
power = 1
while P % fac**power == 0:
#print(P,fac,power,flush=True)
tmp = P//(fac**power)
if tmp % Q > 0:
best = max(best,tmp)
power += 1
return best
for _ in range(getInt()):
print(solve())
|
146_C. Lucky Conversion_10823
|
Petya loves lucky numbers very much. Everybody knows that lucky numbers are positive integers whose decimal record contains only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.
Petya has two strings a and b of the same length n. The strings consist only of lucky digits. Petya can perform operations of two types:
* replace any one digit from string a by its opposite (i.e., replace 4 by 7 and 7 by 4);
* swap any pair of digits in string a.
Petya is interested in the minimum number of operations that are needed to make string a equal to string b. Help him with the task.
Input
The first and the second line contains strings a and b, correspondingly. Strings a and b have equal lengths and contain only lucky digits. The strings are not empty, their length does not exceed 105.
Output
Print on the single line the single number — the minimum number of operations needed to convert string a into string b.
Examples
Input
47
74
Output
1
Input
774
744
Output
1
Input
777
444
Output
3
Note
In the first sample it is enough simply to swap the first and the second digit.
In the second sample we should replace the second digit with its opposite.
In the third number we should replace all three digits with their opposites.
|
a=input()
b=input()
da={'4':0,'7':0}
db={'4':0,'7':0}
for i in a:
da[i]+=1
for i in b:
db[i]+=1
dif=0
for i in range(len(a)):
if(a[i]!=b[i]):
dif+=1
ans=0
if(da==db):
ans=dif//2
else:
x=abs(da['4']-db['4'])
ans+=x
dif-=x
ans+=(dif//2)
print(ans)
|
{
"input": [
"47\n74\n",
"774\n744\n",
"777\n444\n",
"44447777447744444777777747477444777444447744444\n47444747774774744474747744447744477747777777447\n",
"74747474\n77777777\n",
"77747\n47474\n",
"474777477774444\n774747777774477\n",
"47744447444\n74477447744\n",
"4447744774744774744747744774474474444447477477444747477444\n7477477444744774744744774774744474744447744774744477744477\n",
"4747447477\n4747444744\n",
"4744744447774474447474774\n4477774777444444444777447\n",
"44747744777777444\n47774747747744777\n",
"47747477747744447774774444444777444747474747777774\n44777444774477447777444774477777477774444477447777\n",
"77447447444777777744744747744747774747477774777774447447777474477477774774777\n74777777444744447447474474477747747444444447447774444444747777444747474777447\n",
"44447774444474477747774774477777474774744744477444447777477477744747477774744444744777777777747777477447744774744444747477744744\n77777474477477747774777777474474477444474777477747747777477747747744474474747774747747444777474444744744444477477777747744747477\n",
"774774747744474477447477777447477747477474777477744744747444774474477477747474477447774444774744777\n744477444747477447477777774477447444447747477747477747774477474447474477477474444777444444447474747\n",
"47744474447747744777777447\n44744747477474777744777477\n",
"7\n4\n",
"444\n444\n",
"447444777744\n777747744477\n",
"47777777777\n77777777774\n",
"7777777777\n7777777774\n",
"7\n7\n",
"4\n7\n",
"444444444444\n777777777777\n",
"47\n77\n",
"4\n4\n",
"444\n777\n",
"47\n47\n"
],
"output": [
"1\n",
"1\n",
"3\n",
"13\n",
"4\n",
"3\n",
"4\n",
"4\n",
"14\n",
"3\n",
"8\n",
"6\n",
"14\n",
"28\n",
"37\n",
"27\n",
"7\n",
"1\n",
"0\n",
"6\n",
"1\n",
"1\n",
"0\n",
"1\n",
"12\n",
"1\n",
"0\n",
"3\n",
"0\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
Petya loves lucky numbers very much. Everybody knows that lucky numbers are positive integers whose decimal record contains only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.
Petya has two strings a and b of the same length n. The strings consist only of lucky digits. Petya can perform operations of two types:
* replace any one digit from string a by its opposite (i.e., replace 4 by 7 and 7 by 4);
* swap any pair of digits in string a.
Petya is interested in the minimum number of operations that are needed to make string a equal to string b. Help him with the task.
Input
The first and the second line contains strings a and b, correspondingly. Strings a and b have equal lengths and contain only lucky digits. The strings are not empty, their length does not exceed 105.
Output
Print on the single line the single number — the minimum number of operations needed to convert string a into string b.
Examples
Input
47
74
Output
1
Input
774
744
Output
1
Input
777
444
Output
3
Note
In the first sample it is enough simply to swap the first and the second digit.
In the second sample we should replace the second digit with its opposite.
In the third number we should replace all three digits with their opposites.
### Input:
47
74
### Output:
1
### Input:
774
744
### Output:
1
### Code:
a=input()
b=input()
da={'4':0,'7':0}
db={'4':0,'7':0}
for i in a:
da[i]+=1
for i in b:
db[i]+=1
dif=0
for i in range(len(a)):
if(a[i]!=b[i]):
dif+=1
ans=0
if(da==db):
ans=dif//2
else:
x=abs(da['4']-db['4'])
ans+=x
dif-=x
ans+=(dif//2)
print(ans)
|
1519_B. The Cake Is a Lie_10828
|
There is a n × m grid. You are standing at cell (1, 1) and your goal is to finish at cell (n, m).
You can move to the neighboring cells to the right or down. In other words, suppose you are standing at cell (x, y). You can:
* move right to the cell (x, y + 1) — it costs x burles;
* move down to the cell (x + 1, y) — it costs y burles.
Can you reach cell (n, m) spending exactly k burles?
Input
The first line contains the single integer t (1 ≤ t ≤ 100) — the number of test cases.
The first and only line of each test case contains three integers n, m, and k (1 ≤ n, m ≤ 100; 0 ≤ k ≤ 10^4) — the sizes of grid and the exact amount of money you need to spend.
Output
For each test case, if you can reach cell (n, m) spending exactly k burles, print YES. Otherwise, print NO.
You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES are all recognized as positive answer).
Example
Input
6
1 1 0
2 2 2
2 2 3
2 2 4
1 4 3
100 100 10000
Output
YES
NO
YES
NO
YES
NO
Note
In the first test case, you are already in the final cell, so you spend 0 burles.
In the second, third and fourth test cases, there are two paths from (1, 1) to (2, 2): (1, 1) → (1, 2) → (2, 2) or (1, 1) → (2, 1) → (2, 2). Both costs 1 + 2 = 3 burles, so it's the only amount of money you can spend.
In the fifth test case, there is the only way from (1, 1) to (1, 4) and it costs 1 + 1 + 1 = 3 burles.
|
t = int(input())
while t > 0:
n, m, k = map(int, input().split())
if k == n * m - 1:
print('Yes')
else:
print('No')
t -= 1
|
{
"input": [
"6\n1 1 0\n2 2 2\n2 2 3\n2 2 4\n1 4 3\n100 100 10000\n",
"9\n1 1 0\n2 2 2\n2 2 3\n2 2 4\n1 4 3\n100 100 10000\n3 3 7\n3 3 9\n2 4 8\n",
"9\n1 1 0\n2 2 2\n2 2 3\n2 2 4\n1 4 3\n100 100 11000\n3 3 7\n3 3 9\n2 4 8\n",
"9\n1 1 0\n2 2 4\n2 2 3\n2 2 -1\n1 1 3\n100 100 11000\n3 3 7\n3 1 9\n2 3 8\n",
"9\n1 2 0\n2 2 0\n2 2 3\n2 2 -2\n1 1 1\n100 100 11000\n2 3 7\n3 1 9\n1 6 8\n",
"9\n1 2 0\n2 4 0\n4 2 3\n2 2 -2\n1 1 1\n100 100 11000\n2 3 7\n3 1 1\n1 6 8\n",
"6\n1 1 0\n2 2 4\n2 2 3\n2 2 4\n1 4 3\n100 100 10000\n",
"9\n1 1 0\n2 2 4\n2 2 1\n2 2 4\n1 4 3\n100 100 11000\n3 3 7\n3 3 9\n2 3 8\n",
"9\n1 1 1\n2 2 4\n2 2 3\n2 2 0\n1 4 3\n100 100 11000\n3 3 7\n3 1 9\n2 3 8\n",
"9\n1 1 0\n2 2 4\n2 2 3\n2 2 -2\n1 1 1\n100 100 11000\n2 3 7\n3 1 9\n2 6 11\n",
"6\n1 1 0\n2 2 4\n2 2 3\n2 2 4\n1 4 2\n100 100 10000\n",
"9\n1 1 0\n2 2 4\n2 1 3\n2 2 0\n1 8 3\n100 100 11000\n3 3 7\n3 3 15\n2 3 8\n",
"9\n1 1 1\n2 1 4\n2 2 3\n2 2 -2\n1 1 1\n100 100 11000\n2 2 7\n3 1 9\n2 6 11\n",
"9\n1 2 0\n2 4 0\n4 2 3\n2 2 -2\n2 1 1\n100 100 11100\n2 3 12\n1 1 1\n1 3 8\n",
"9\n1 1 0\n2 2 4\n2 2 3\n2 2 -1\n1 1 1\n100 100 11000\n2 4 7\n3 1 9\n2 6 8\n",
"6\n1 1 0\n2 2 4\n3 2 3\n2 2 4\n1 4 3\n100 100 10000\n",
"6\n1 1 0\n2 2 4\n2 2 2\n2 2 4\n1 4 2\n100 100 10000\n",
"9\n1 1 1\n2 1 4\n2 4 3\n2 2 -2\n1 1 1\n100 100 11000\n2 2 7\n3 1 9\n2 6 11\n",
"6\n1 1 1\n2 2 4\n2 2 2\n2 2 4\n1 4 2\n100 100 10000\n",
"9\n1 1 0\n2 2 4\n2 2 3\n2 2 -1\n2 1 1\n100 100 10000\n2 4 7\n3 1 9\n2 6 8\n",
"9\n1 1 1\n2 2 3\n1 2 3\n2 2 -1\n1 4 6\n100 100 11000\n3 3 7\n3 1 9\n2 3 8\n",
"9\n1 1 0\n2 2 2\n2 2 3\n2 2 4\n1 4 3\n100 100 11000\n3 3 7\n3 3 9\n2 3 8\n",
"9\n1 1 0\n2 2 4\n2 2 3\n2 2 4\n1 4 3\n100 100 11000\n3 3 7\n3 3 9\n2 3 8\n",
"9\n1 1 0\n2 2 4\n2 2 3\n2 2 0\n1 4 3\n100 100 11000\n3 3 7\n3 3 9\n2 3 8\n",
"9\n1 1 0\n2 2 4\n2 2 3\n2 2 0\n1 4 3\n100 100 11000\n3 3 7\n3 1 9\n2 3 8\n",
"9\n1 1 0\n2 2 4\n2 2 3\n2 2 -1\n1 4 3\n100 100 11000\n3 3 7\n3 1 9\n2 3 8\n",
"9\n1 1 0\n2 2 4\n2 2 3\n2 2 -1\n1 1 1\n100 100 11000\n3 3 7\n3 1 9\n2 3 8\n",
"9\n1 1 0\n2 2 4\n2 2 3\n2 2 -1\n1 1 1\n100 100 11000\n2 3 7\n3 1 9\n2 3 8\n",
"9\n1 1 0\n2 2 4\n2 2 3\n2 2 -1\n1 1 1\n100 100 11000\n2 3 7\n3 1 9\n2 6 8\n",
"9\n1 1 0\n2 2 4\n2 2 3\n2 2 -2\n1 1 1\n100 100 11000\n2 3 7\n3 1 9\n2 6 8\n",
"9\n1 1 0\n2 2 0\n2 2 3\n2 2 -2\n1 1 1\n100 100 11000\n2 3 7\n3 1 9\n2 6 8\n",
"9\n1 1 0\n2 2 0\n2 2 3\n2 2 -2\n1 1 1\n100 100 11000\n2 3 7\n3 1 9\n1 6 8\n",
"9\n1 2 0\n2 4 0\n2 2 3\n2 2 -2\n1 1 1\n100 100 11000\n2 3 7\n3 1 9\n1 6 8\n",
"9\n1 2 0\n2 4 0\n2 2 3\n2 2 -2\n1 1 1\n100 100 11000\n2 3 7\n3 1 1\n1 6 8\n",
"9\n1 2 0\n2 4 0\n4 2 3\n2 2 -2\n1 1 1\n100 100 11000\n2 3 7\n3 1 1\n1 3 8\n",
"9\n1 2 0\n2 4 0\n4 2 3\n2 2 -2\n1 1 1\n100 100 11000\n2 3 7\n3 1 1\n2 3 8\n",
"9\n1 1 0\n1 2 2\n2 2 3\n2 2 4\n1 4 3\n100 100 11000\n3 3 7\n3 3 9\n2 4 8\n",
"9\n1 1 0\n2 2 4\n2 2 3\n2 2 0\n1 4 3\n100 100 11000\n3 3 7\n3 3 15\n2 3 8\n",
"9\n1 1 0\n2 2 4\n2 2 3\n2 2 -1\n1 4 3\n100 100 11000\n5 3 7\n3 1 9\n2 3 8\n",
"9\n1 1 0\n2 2 4\n2 2 3\n2 2 -1\n1 1 1\n100 100 11000\n5 3 7\n3 1 9\n2 3 8\n",
"9\n1 1 0\n2 2 4\n2 2 3\n2 2 -1\n1 1 1\n100 100 11000\n2 3 7\n5 1 9\n2 3 8\n",
"9\n1 1 0\n2 2 4\n2 2 3\n2 2 -1\n1 1 1\n100 100 11000\n2 3 7\n3 1 9\n2 2 8\n",
"9\n1 1 0\n2 2 0\n2 2 3\n2 2 -2\n1 1 1\n100 100 11010\n2 3 7\n3 1 9\n2 6 8\n",
"9\n1 1 0\n2 2 0\n2 2 3\n2 2 -2\n1 1 1\n100 100 11000\n2 3 7\n3 1 9\n1 4 8\n",
"9\n1 2 0\n2 2 0\n2 2 3\n2 2 -2\n1 1 1\n100 100 01000\n2 3 7\n3 1 9\n1 6 8\n",
"9\n1 2 0\n2 4 0\n2 2 3\n2 2 -2\n1 1 1\n100 100 11000\n2 3 7\n3 2 1\n1 6 8\n",
"9\n1 2 0\n2 4 0\n4 2 3\n2 2 -2\n1 1 1\n100 100 11000\n2 3 12\n3 1 1\n1 3 8\n",
"9\n1 1 0\n2 2 2\n2 2 3\n2 2 4\n1 4 3\n100 100 11000\n3 3 7\n3 3 12\n2 4 8\n",
"9\n1 1 0\n2 2 4\n2 2 0\n2 2 4\n1 4 3\n100 100 11000\n3 3 7\n3 3 9\n2 3 8\n",
"9\n1 1 0\n2 2 4\n2 2 3\n2 2 0\n1 8 3\n100 100 11000\n3 3 7\n3 3 15\n2 3 8\n",
"9\n1 1 1\n2 2 4\n2 2 3\n2 2 0\n1 4 3\n100 100 11000\n3 3 7\n3 1 13\n2 3 8\n",
"9\n1 1 0\n2 2 4\n2 2 3\n2 2 -1\n2 1 1\n100 100 11000\n5 3 7\n3 1 9\n2 3 8\n",
"9\n1 1 0\n2 1 4\n2 2 3\n2 2 -2\n1 1 1\n100 100 11000\n2 3 7\n3 1 9\n2 6 11\n",
"9\n1 1 0\n2 2 0\n2 2 3\n2 2 -2\n1 2 1\n100 100 11010\n2 3 7\n3 1 9\n2 6 8\n",
"9\n1 1 0\n2 2 0\n2 2 3\n2 4 -2\n1 1 1\n100 100 11000\n2 3 7\n3 1 9\n1 4 8\n",
"9\n1 2 0\n2 4 0\n2 2 3\n3 2 -2\n1 1 1\n100 100 11000\n2 3 7\n3 2 1\n1 6 8\n",
"9\n1 2 0\n2 4 0\n4 2 3\n2 2 -2\n1 1 1\n100 100 11100\n2 3 12\n3 1 1\n1 3 8\n",
"9\n1 1 0\n2 2 2\n2 2 3\n2 2 4\n1 1 3\n100 100 11000\n3 3 7\n3 3 12\n2 4 8\n",
"9\n1 1 0\n2 2 4\n2 2 0\n2 2 4\n1 4 3\n100 100 11000\n3 3 7\n3 3 9\n2 3 6\n",
"9\n1 1 0\n2 1 4\n2 2 3\n2 2 -2\n1 1 1\n100 100 11000\n2 2 7\n3 1 9\n2 6 11\n",
"9\n1 1 0\n3 2 0\n2 2 3\n2 4 -2\n1 1 1\n100 100 11000\n2 3 7\n3 1 9\n1 4 8\n",
"9\n1 2 0\n2 4 0\n4 2 3\n2 2 -2\n1 1 1\n100 100 01100\n2 3 12\n3 1 1\n1 3 8\n",
"9\n1 1 0\n2 2 2\n2 1 3\n2 2 4\n1 1 3\n100 100 11000\n3 3 7\n3 3 12\n2 4 8\n",
"9\n1 1 0\n2 2 4\n2 1 3\n2 2 0\n1 8 0\n100 100 11000\n3 3 7\n3 3 15\n2 3 8\n",
"9\n1 2 0\n2 4 0\n4 2 3\n2 2 -2\n1 1 1\n100 100 11100\n2 3 12\n1 1 1\n1 3 8\n",
"9\n1 1 0\n2 2 2\n2 1 3\n2 2 4\n1 1 3\n100 100 11000\n3 6 7\n3 3 12\n2 4 8\n",
"9\n1 1 0\n2 2 4\n2 1 3\n2 1 0\n1 8 0\n100 100 11000\n3 3 7\n3 3 15\n2 3 8\n",
"9\n1 1 0\n2 2 2\n2 1 3\n2 2 4\n1 1 2\n100 100 11000\n3 6 7\n3 3 12\n2 4 8\n",
"9\n2 1 0\n2 2 2\n2 1 3\n2 2 4\n1 1 2\n100 100 11000\n3 6 7\n3 3 12\n2 4 8\n",
"9\n2 1 0\n2 2 0\n2 1 3\n2 2 4\n1 1 2\n100 100 11000\n3 6 7\n3 3 12\n2 4 8\n",
"9\n2 1 0\n2 2 0\n2 1 3\n2 2 4\n1 1 2\n100 100 11000\n3 6 7\n3 3 23\n2 4 8\n",
"9\n2 1 0\n2 2 0\n4 1 3\n2 2 4\n1 1 2\n100 100 11000\n3 6 7\n3 3 23\n2 4 8\n",
"9\n2 1 0\n2 2 0\n4 1 3\n2 2 4\n1 1 2\n100 100 11000\n3 6 1\n3 3 23\n2 4 8\n",
"9\n1 1 0\n2 2 2\n2 2 3\n2 2 4\n1 4 6\n100 100 10000\n3 3 7\n3 3 9\n2 4 8\n",
"9\n1 1 0\n2 2 2\n2 1 3\n2 2 4\n1 4 3\n100 100 11000\n3 3 7\n3 3 9\n2 4 8\n",
"9\n1 1 0\n2 2 2\n2 2 3\n2 2 4\n1 4 3\n100 100 11000\n3 3 7\n3 3 9\n2 3 16\n",
"9\n1 1 0\n2 4 4\n2 2 3\n2 2 4\n1 4 3\n100 100 11000\n3 3 7\n3 3 9\n2 3 8\n",
"9\n1 1 1\n2 2 4\n2 2 3\n2 2 0\n1 4 3\n100 100 11000\n3 3 7\n3 3 9\n2 3 8\n",
"9\n1 1 0\n2 2 4\n2 2 0\n2 2 -1\n1 4 3\n100 100 11000\n3 3 7\n3 1 9\n2 3 8\n",
"9\n1 1 0\n2 2 4\n2 2 6\n2 2 -1\n1 1 3\n100 100 11000\n3 3 7\n3 1 9\n2 3 8\n",
"9\n1 1 0\n2 2 4\n2 1 3\n2 2 -1\n1 1 1\n100 100 11000\n2 3 7\n3 1 9\n2 3 8\n",
"9\n1 1 1\n2 2 0\n2 2 3\n2 2 -2\n1 1 1\n100 100 11000\n2 3 7\n3 1 9\n2 6 8\n",
"9\n1 1 0\n2 2 0\n2 2 3\n2 2 -2\n1 1 1\n100 100 11100\n2 3 7\n3 1 9\n1 6 8\n",
"9\n1 2 0\n2 2 0\n3 2 3\n2 2 -2\n1 1 1\n100 100 11000\n2 3 7\n3 1 9\n1 6 8\n",
"9\n1 2 0\n2 4 0\n2 2 3\n2 2 -2\n1 1 2\n100 100 11000\n2 3 7\n3 1 9\n1 6 8\n",
"9\n1 2 0\n2 4 0\n2 2 3\n2 2 -2\n1 1 1\n100 100 11000\n2 3 7\n3 1 0\n1 6 8\n",
"9\n1 2 0\n2 4 0\n4 2 3\n2 4 -2\n1 1 1\n100 100 11000\n2 3 7\n3 1 1\n1 3 8\n",
"9\n1 2 0\n2 4 0\n4 2 3\n2 2 -2\n1 1 1\n100 100 11000\n2 3 12\n3 1 1\n2 3 8\n",
"9\n1 1 0\n1 2 2\n2 2 3\n2 2 4\n1 4 3\n100 100 11000\n3 3 13\n3 3 9\n2 4 8\n",
"9\n1 1 0\n2 2 4\n2 2 1\n3 2 4\n1 4 3\n100 100 11000\n3 3 7\n3 3 9\n2 3 8\n",
"9\n1 1 1\n2 2 2\n2 2 3\n2 2 0\n1 4 3\n100 100 11000\n3 3 7\n3 1 9\n2 3 8\n",
"9\n1 1 0\n2 2 4\n2 2 3\n2 2 -1\n1 4 3\n100 100 11000\n5 3 7\n3 1 17\n2 3 8\n",
"9\n1 1 0\n2 2 4\n2 2 3\n2 2 -1\n1 1 1\n100 100 11000\n10 3 7\n3 1 9\n2 3 8\n",
"9\n1 1 0\n2 2 4\n2 2 3\n2 2 -1\n1 1 1\n100 100 11000\n2 3 7\n3 1 9\n4 2 8\n",
"9\n1 1 0\n2 2 0\n4 2 3\n2 2 -2\n1 1 1\n100 100 11010\n2 3 7\n3 1 9\n2 6 8\n",
"9\n1 2 0\n2 2 -1\n2 2 3\n2 2 -2\n1 1 1\n100 100 01000\n2 3 7\n3 1 9\n1 6 8\n",
"9\n1 2 0\n2 4 0\n2 2 3\n2 1 -2\n1 1 1\n100 100 11000\n2 3 7\n3 2 1\n1 6 8\n",
"9\n1 2 0\n2 4 0\n4 2 3\n2 2 -3\n1 1 1\n100 100 11000\n2 3 12\n3 1 1\n2 3 8\n",
"9\n1 1 0\n2 2 2\n2 2 3\n2 2 4\n1 4 3\n100 100 11000\n3 3 7\n3 3 6\n2 4 8\n",
"9\n1 1 0\n2 2 4\n2 2 3\n2 2 -1\n2 1 1\n100 100 11000\n5 3 7\n3 1 11\n2 3 8\n",
"9\n1 2 0\n2 1 4\n2 2 3\n2 2 -2\n1 1 1\n100 100 11000\n2 3 7\n3 1 9\n2 6 11\n",
"9\n1 1 0\n2 2 0\n2 2 3\n2 2 -2\n1 2 0\n100 100 11010\n2 3 7\n3 1 9\n2 6 8\n",
"9\n1 1 0\n2 2 0\n2 2 3\n2 4 -2\n1 1 1\n100 100 11000\n2 3 7\n3 1 9\n1 4 1\n",
"9\n1 2 1\n2 4 0\n2 2 3\n3 2 -2\n1 1 1\n100 100 11000\n2 3 7\n3 2 1\n1 6 8\n",
"9\n1 2 0\n2 4 0\n4 2 3\n2 2 -2\n1 1 1\n100 100 11101\n2 3 12\n3 1 1\n1 3 8\n",
"9\n1 1 0\n2 2 2\n2 2 3\n2 2 4\n2 1 3\n100 100 11000\n3 3 7\n3 3 12\n2 4 8\n",
"9\n1 1 0\n2 2 4\n2 1 3\n2 2 0\n1 8 3\n100 100 11000\n3 3 7\n3 3 15\n4 3 8\n",
"9\n1 1 0\n3 2 0\n2 2 2\n2 4 -2\n1 1 1\n100 100 11000\n2 3 7\n3 1 9\n1 4 8\n",
"9\n1 2 0\n2 4 0\n4 2 3\n2 2 -2\n2 1 1\n100 100 01100\n2 3 12\n3 1 1\n1 3 8\n",
"9\n1 1 0\n2 2 2\n2 1 3\n2 2 4\n1 1 2\n100 100 11000\n3 3 7\n3 3 12\n2 4 8\n",
"9\n1 2 0\n2 4 0\n4 2 3\n2 2 -2\n1 1 1\n100 100 11100\n2 3 18\n1 1 1\n1 3 8\n",
"9\n1 1 0\n2 2 2\n2 1 3\n2 2 4\n1 1 3\n100 100 11000\n3 6 7\n6 3 12\n2 4 8\n",
"9\n1 2 0\n2 4 0\n2 2 3\n2 2 -2\n2 1 1\n100 100 11100\n2 3 12\n1 1 1\n1 3 8\n",
"9\n1 1 0\n2 2 2\n2 1 3\n2 2 4\n1 1 2\n100 100 11000\n3 6 3\n3 3 12\n2 4 8\n",
"9\n2 1 0\n2 2 0\n2 1 3\n2 2 4\n1 1 2\n100 100 11000\n3 8 7\n3 3 23\n2 4 8\n",
"9\n2 1 0\n2 2 0\n4 1 0\n2 2 4\n1 1 2\n100 100 11000\n3 6 7\n3 3 23\n2 4 8\n",
"9\n2 1 0\n1 2 0\n4 1 3\n2 2 4\n1 1 2\n100 100 11000\n3 6 1\n3 3 23\n2 4 8\n",
"9\n1 1 0\n2 2 2\n1 2 3\n2 2 4\n1 4 6\n100 100 10000\n3 3 7\n3 3 9\n2 4 8\n",
"9\n1 1 0\n2 2 2\n2 1 3\n2 2 4\n1 4 3\n100 100 11000\n3 3 7\n3 3 15\n2 4 8\n",
"9\n1 1 1\n2 2 4\n2 3 3\n2 2 0\n1 4 3\n100 100 11000\n3 3 7\n3 3 9\n2 3 8\n",
"9\n1 1 0\n2 2 4\n2 2 0\n2 2 -2\n1 4 3\n100 100 11000\n3 3 7\n3 1 9\n2 3 8\n",
"9\n1 1 0\n2 2 4\n2 2 6\n2 2 -1\n1 1 3\n100 100 11000\n3 3 7\n3 1 9\n2 2 8\n",
"9\n1 1 0\n2 2 4\n2 1 3\n2 2 -1\n1 1 1\n100 100 11000\n2 3 7\n3 1 1\n2 3 8\n",
"9\n1 1 0\n2 2 4\n2 2 3\n2 2 -1\n1 1 1\n100 100 10000\n2 4 7\n3 1 9\n2 6 8\n",
"9\n1 1 1\n2 2 0\n2 2 3\n1 2 -2\n1 1 1\n100 100 11000\n2 3 7\n3 1 9\n2 6 8\n",
"9\n1 2 0\n2 2 1\n3 2 3\n2 2 -2\n1 1 1\n100 100 11000\n2 3 7\n3 1 9\n1 6 8\n",
"9\n1 2 0\n2 4 0\n2 2 3\n2 2 -2\n1 1 2\n100 100 11000\n1 3 7\n3 1 9\n1 6 8\n",
"9\n1 2 0\n2 4 0\n4 2 3\n2 4 -2\n1 1 1\n100 100 11000\n2 2 7\n3 1 1\n1 3 8\n",
"9\n1 2 0\n2 4 0\n4 2 3\n2 4 -2\n1 1 1\n100 100 11000\n2 3 12\n3 1 1\n2 3 8\n",
"6\n1 1 0\n2 2 4\n3 1 3\n2 2 4\n1 4 3\n100 100 10000\n",
"9\n1 1 0\n1 2 2\n2 3 3\n2 2 4\n1 4 3\n100 100 11000\n3 3 13\n3 3 9\n2 4 8\n",
"9\n1 1 0\n2 2 4\n2 2 1\n5 2 4\n1 4 3\n100 100 11000\n3 3 7\n3 3 9\n2 3 8\n",
"9\n1 1 1\n2 2 2\n1 2 3\n2 2 0\n1 4 3\n100 100 11000\n3 3 7\n3 1 9\n2 3 8\n",
"9\n1 1 0\n4 2 4\n2 2 3\n2 2 -1\n1 4 3\n100 100 11000\n5 3 7\n3 1 17\n2 3 8\n",
"9\n1 1 0\n2 2 4\n2 2 3\n2 2 -1\n1 1 1\n100 100 11000\n10 3 4\n3 1 9\n2 3 8\n",
"9\n1 1 0\n2 2 7\n2 2 3\n2 2 -1\n1 1 1\n100 100 11000\n2 3 7\n3 1 9\n4 2 8\n",
"9\n1 1 0\n2 3 0\n4 2 3\n2 2 -2\n1 1 1\n100 100 11010\n2 3 7\n3 1 9\n2 6 8\n",
"9\n1 2 0\n2 4 0\n2 2 3\n2 1 -2\n1 1 1\n100 100 11000\n2 3 7\n3 3 1\n1 6 8\n",
"9\n1 2 0\n2 4 0\n4 2 3\n2 3 -3\n1 1 1\n100 100 11000\n2 3 12\n3 1 1\n2 3 8\n",
"9\n1 1 0\n2 2 4\n4 2 3\n2 2 -1\n2 1 1\n100 100 11000\n5 3 7\n3 1 11\n2 3 8\n",
"9\n1 2 0\n2 1 4\n3 2 3\n2 2 -2\n1 1 1\n100 100 11000\n2 3 7\n3 1 9\n2 6 11\n",
"9\n1 1 0\n2 2 -1\n2 2 3\n2 2 -2\n1 2 0\n100 100 11010\n2 3 7\n3 1 9\n2 6 8\n",
"9\n1 2 0\n2 4 0\n4 2 3\n2 2 -2\n1 1 1\n100 100 11101\n1 3 12\n3 1 1\n1 3 8\n",
"9\n1 1 0\n2 2 2\n2 2 6\n2 2 4\n2 1 3\n100 100 11000\n3 3 7\n3 3 12\n2 4 8\n",
"9\n2 2 0\n2 4 0\n4 2 3\n2 2 -2\n2 1 1\n100 100 01100\n2 3 12\n3 1 1\n1 3 8\n",
"9\n1 1 0\n2 2 2\n2 1 3\n2 2 4\n1 1 2\n100 100 11000\n3 3 7\n3 3 12\n1 4 8\n",
"9\n1 1 1\n2 1 4\n3 4 3\n2 2 -2\n1 1 1\n100 100 11000\n2 2 7\n3 1 9\n2 6 11\n",
"9\n1 2 0\n2 4 0\n2 2 3\n2 2 0\n2 1 1\n100 100 11100\n2 3 12\n1 1 1\n1 3 8\n",
"9\n1 1 0\n2 2 2\n2 1 3\n2 2 4\n1 1 2\n100 100 11000\n4 6 3\n3 3 12\n2 4 8\n",
"9\n2 1 0\n2 2 0\n4 1 0\n2 2 4\n1 1 2\n100 100 11000\n3 3 7\n3 3 23\n2 4 8\n",
"9\n2 1 0\n1 2 0\n4 1 3\n2 2 4\n1 1 2\n100 100 11000\n3 6 1\n4 3 23\n2 4 8\n",
"9\n1 1 0\n2 2 2\n1 2 3\n2 2 4\n1 4 6\n100 100 10000\n3 3 13\n3 3 9\n2 4 8\n",
"9\n1 1 0\n2 2 2\n2 1 3\n2 2 4\n1 4 3\n100 100 11000\n3 3 7\n3 3 15\n2 8 8\n",
"9\n1 1 1\n2 2 4\n2 3 3\n2 2 -1\n1 4 3\n100 100 11000\n3 3 7\n3 3 9\n2 3 8\n",
"9\n1 1 0\n2 2 4\n2 3 0\n2 2 -2\n1 4 3\n100 100 11000\n3 3 7\n3 1 9\n2 3 8\n",
"9\n1 1 0\n2 2 4\n2 2 6\n2 2 0\n1 1 3\n100 100 11000\n3 3 7\n3 1 9\n2 2 8\n",
"9\n1 1 1\n1 2 0\n2 2 3\n1 2 -2\n1 1 1\n100 100 11000\n2 3 7\n3 1 9\n2 6 8\n",
"9\n1 2 0\n2 4 0\n4 2 3\n2 4 -2\n1 1 1\n100 100 11000\n2 2 5\n3 1 1\n1 3 8\n",
"9\n1 2 0\n2 4 1\n4 2 3\n2 4 -2\n1 1 1\n100 100 11000\n2 3 12\n3 1 1\n2 3 8\n",
"6\n1 1 0\n2 2 4\n3 1 3\n2 2 4\n1 7 3\n100 100 10000\n",
"9\n1 1 1\n2 2 2\n1 2 3\n2 2 -1\n1 4 3\n100 100 11000\n3 3 7\n3 1 9\n2 3 8\n",
"9\n1 1 0\n4 2 4\n2 2 3\n2 2 -1\n1 4 3\n100 100 11000\n5 3 7\n3 1 7\n2 3 8\n",
"9\n1 1 0\n2 2 4\n2 2 3\n2 2 -1\n1 1 1\n100 100 11000\n10 3 4\n3 1 9\n2 3 4\n",
"9\n1 1 0\n2 2 7\n2 2 3\n2 2 -1\n1 1 1\n100 100 11000\n2 3 7\n3 1 9\n4 4 8\n",
"9\n1 1 0\n2 3 0\n4 2 3\n2 2 -2\n1 1 1\n100 100 11010\n2 3 7\n3 1 9\n2 6 12\n",
"9\n1 2 -1\n2 4 0\n2 2 3\n2 1 -2\n1 1 1\n100 100 11000\n2 3 7\n3 3 1\n1 6 8\n",
"9\n1 2 0\n2 4 0\n4 2 3\n2 3 -3\n1 1 1\n100 100 11000\n2 3 12\n3 2 1\n2 3 8\n",
"9\n1 2 0\n2 1 4\n3 2 3\n2 2 -2\n1 1 1\n100 100 11000\n2 3 7\n3 1 9\n4 6 11\n",
"9\n1 1 0\n2 2 -1\n4 2 3\n2 2 -2\n1 2 0\n100 100 11010\n2 3 7\n3 1 9\n2 6 8\n",
"9\n1 2 0\n2 4 0\n4 2 3\n2 2 -1\n1 1 1\n100 100 11101\n1 3 12\n3 1 1\n1 3 8\n",
"9\n1 1 0\n2 2 2\n2 2 10\n2 2 4\n2 1 3\n100 100 11000\n3 3 7\n3 3 12\n2 4 8\n",
"9\n2 2 0\n2 4 0\n4 2 3\n2 2 -2\n2 1 1\n100 100 11100\n2 3 12\n3 1 1\n1 3 8\n",
"9\n1 1 0\n2 2 2\n2 1 3\n2 2 4\n1 1 2\n100 100 11000\n3 3 7\n3 3 22\n1 4 8\n",
"9\n1 2 0\n2 6 0\n2 2 3\n2 2 0\n2 1 1\n100 100 11100\n2 3 12\n1 1 1\n1 3 8\n",
"9\n4 1 0\n2 2 0\n4 1 0\n2 2 4\n1 1 2\n100 100 11000\n3 3 7\n3 3 23\n2 4 8\n",
"9\n2 1 0\n1 2 0\n6 1 3\n2 2 4\n1 1 2\n100 100 11000\n3 6 1\n4 3 23\n2 4 8\n",
"9\n1 1 0\n2 2 2\n1 2 3\n2 2 4\n1 4 6\n100 100 10001\n3 3 13\n3 3 9\n2 4 8\n",
"9\n1 1 0\n2 2 2\n2 1 3\n2 2 4\n1 4 3\n100 100 11000\n3 3 7\n3 3 15\n4 8 8\n",
"9\n1 1 1\n2 2 4\n2 3 3\n2 2 -1\n1 4 3\n100 100 11000\n3 3 3\n3 3 9\n2 3 8\n",
"9\n1 1 0\n2 2 6\n2 3 0\n2 2 -2\n1 4 3\n100 100 11000\n3 3 7\n3 1 9\n2 3 8\n",
"9\n1 1 0\n2 2 4\n2 2 6\n2 2 0\n2 1 3\n100 100 11000\n3 3 7\n3 1 9\n2 2 8\n",
"9\n1 1 0\n2 2 4\n2 2 3\n2 2 -1\n2 1 1\n100 100 10000\n2 4 7\n3 1 9\n3 6 8\n",
"9\n1 1 1\n1 2 0\n2 2 3\n1 2 -4\n1 1 1\n100 100 11000\n2 3 7\n3 1 9\n2 6 8\n",
"9\n1 2 -1\n2 4 0\n4 2 3\n2 4 -2\n1 1 1\n100 100 11000\n2 2 5\n3 1 1\n1 3 8\n",
"9\n1 2 0\n2 4 1\n4 2 3\n2 4 -2\n1 1 1\n100 100 11000\n2 2 12\n3 1 1\n2 3 8\n",
"9\n1 1 1\n2 2 2\n1 2 3\n2 2 -1\n1 4 6\n100 100 11000\n3 3 7\n3 1 9\n2 3 8\n",
"9\n1 1 0\n5 2 4\n2 2 3\n2 2 -1\n1 4 3\n100 100 11000\n5 3 7\n3 1 7\n2 3 8\n",
"9\n1 1 0\n2 2 4\n2 2 1\n2 2 -1\n1 1 1\n100 100 11000\n10 3 4\n3 1 9\n2 3 4\n",
"9\n1 1 0\n2 2 7\n2 2 3\n2 2 -1\n1 1 1\n100 100 11000\n2 6 7\n3 1 9\n4 4 8\n",
"9\n1 1 0\n2 3 0\n4 4 3\n2 2 -2\n1 1 1\n100 100 11010\n2 3 7\n3 1 9\n2 6 12\n",
"9\n1 2 -1\n2 4 0\n2 2 3\n2 1 -2\n1 1 1\n100 100 11000\n2 3 13\n3 3 1\n1 6 8\n",
"9\n1 2 0\n2 4 0\n1 2 3\n2 3 -3\n1 1 1\n100 100 11000\n2 3 12\n3 2 1\n2 3 8\n",
"9\n1 2 0\n2 1 4\n3 2 3\n2 2 -2\n1 1 1\n100 100 11000\n2 3 7\n1 1 9\n4 6 11\n",
"9\n1 1 0\n2 2 -1\n4 2 3\n2 2 -2\n1 2 -1\n100 100 11010\n2 3 7\n3 1 9\n2 6 8\n",
"9\n1 1 0\n2 2 2\n2 2 10\n2 2 4\n2 1 3\n100 100 01000\n3 3 7\n3 3 12\n2 4 8\n",
"9\n1 1 -1\n2 2 2\n2 1 3\n2 2 4\n1 1 2\n100 100 11000\n3 3 7\n3 3 22\n1 4 8\n",
"9\n1 2 1\n2 6 0\n2 2 3\n2 2 0\n2 1 1\n100 100 11100\n2 3 12\n1 1 1\n1 3 8\n",
"9\n4 1 0\n2 2 -1\n4 1 0\n2 2 4\n1 1 2\n100 100 11000\n3 3 7\n3 3 23\n2 4 8\n",
"9\n2 1 0\n1 2 0\n6 1 3\n2 3 4\n1 1 2\n100 100 11000\n3 6 1\n4 3 23\n2 4 8\n",
"9\n1 1 1\n2 2 4\n2 3 3\n2 2 -1\n1 4 3\n100 100 11000\n3 3 3\n3 1 9\n2 3 8\n",
"9\n1 1 0\n2 2 4\n2 2 6\n2 2 0\n2 1 3\n100 100 11001\n3 3 7\n3 1 9\n2 2 8\n",
"9\n1 1 0\n2 2 4\n2 2 3\n2 4 -1\n2 1 1\n100 100 10000\n2 4 7\n3 1 9\n3 6 8\n"
],
"output": [
"\nYES\nNO\nYES\nNO\nYES\nNO\n",
"YES\nNO\nYES\nNO\nYES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nYES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nYES\nNO\n",
"YES\nNO\nNO\nNO\nYES\nNO\nNO\nNO\nNO\n",
"NO\nNO\nYES\nNO\nYES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nYES\n",
"YES\nNO\nYES\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nYES\n",
"NO\nNO\nNO\nNO\nYES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\nNO\nYES\nNO\nNO\n",
"YES\nNO\nNO\nNO\nYES\nNO\n",
"YES\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nYES\n",
"NO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nYES\nNO\nYES\nNO\nNO\n",
"NO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nYES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nYES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nYES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nYES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nYES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nYES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nYES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nYES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nYES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nYES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nYES\nNO\nYES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nYES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nYES\n",
"YES\nNO\nYES\nNO\nYES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nYES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nYES\n",
"YES\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nYES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nYES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nYES\nNO\nNO\nNO\nNO\n",
"NO\nNO\nYES\nNO\nYES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nYES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nYES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nYES\nNO\nNO\nNO\nNO\n",
"NO\nNO\nYES\nNO\nYES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nYES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nYES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nYES\nNO\nNO\nNO\nNO\n",
"NO\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nYES\n",
"YES\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nYES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nYES\nNO\nYES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nYES\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nYES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nYES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\nNO\nYES\nNO\nNO\n",
"NO\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nYES\nNO\n",
"YES\nNO\nNO\nNO\nYES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nYES\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nYES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nYES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nYES\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nYES\n",
"YES\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nYES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nYES\n",
"NO\nNO\nYES\nNO\nYES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nYES\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nYES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nYES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nYES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nYES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nYES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nYES\nNO\nYES\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nYES\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nYES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nYES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nYES\nNO\nYES\nNO\nNO\n",
"NO\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nYES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nYES\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nYES\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"NO\nNO\nNO\nNO\nYES\nNO\nNO\nNO\nNO\n",
"YES\nNO\nNO\nNO\nNO\nNO\nNO\nNO\nNO\n",
"YES\nNO\nYES\nNO\nYES\nNO\nYES\nNO\nNO\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
There is a n × m grid. You are standing at cell (1, 1) and your goal is to finish at cell (n, m).
You can move to the neighboring cells to the right or down. In other words, suppose you are standing at cell (x, y). You can:
* move right to the cell (x, y + 1) — it costs x burles;
* move down to the cell (x + 1, y) — it costs y burles.
Can you reach cell (n, m) spending exactly k burles?
Input
The first line contains the single integer t (1 ≤ t ≤ 100) — the number of test cases.
The first and only line of each test case contains three integers n, m, and k (1 ≤ n, m ≤ 100; 0 ≤ k ≤ 10^4) — the sizes of grid and the exact amount of money you need to spend.
Output
For each test case, if you can reach cell (n, m) spending exactly k burles, print YES. Otherwise, print NO.
You may print every letter in any case you want (so, for example, the strings yEs, yes, Yes and YES are all recognized as positive answer).
Example
Input
6
1 1 0
2 2 2
2 2 3
2 2 4
1 4 3
100 100 10000
Output
YES
NO
YES
NO
YES
NO
Note
In the first test case, you are already in the final cell, so you spend 0 burles.
In the second, third and fourth test cases, there are two paths from (1, 1) to (2, 2): (1, 1) → (1, 2) → (2, 2) or (1, 1) → (2, 1) → (2, 2). Both costs 1 + 2 = 3 burles, so it's the only amount of money you can spend.
In the fifth test case, there is the only way from (1, 1) to (1, 4) and it costs 1 + 1 + 1 = 3 burles.
### Input:
6
1 1 0
2 2 2
2 2 3
2 2 4
1 4 3
100 100 10000
### Output:
YES
NO
YES
NO
YES
NO
### Input:
9
1 1 0
2 2 2
2 2 3
2 2 4
1 4 3
100 100 10000
3 3 7
3 3 9
2 4 8
### Output:
YES
NO
YES
NO
YES
NO
NO
NO
NO
### Code:
t = int(input())
while t > 0:
n, m, k = map(int, input().split())
if k == n * m - 1:
print('Yes')
else:
print('No')
t -= 1
|
1546_B. AquaMoon and Stolen String_10832
|
AquaMoon had n strings of length m each. n is an odd number.
When AquaMoon was gone, Cirno tried to pair these n strings together. After making (n-1)/(2) pairs, she found out that there was exactly one string without the pair!
In her rage, she disrupted each pair of strings. For each pair, she selected some positions (at least 1 and at most m) and swapped the letters in the two strings of this pair at the selected positions.
For example, if m = 6 and two strings "abcdef" and "xyzklm" are in one pair and Cirno selected positions 2, 3 and 6 she will swap 'b' with 'y', 'c' with 'z' and 'f' with 'm'. The resulting strings will be "ayzdem" and "xbcklf".
Cirno then stole away the string without pair and shuffled all remaining strings in arbitrary order.
AquaMoon found the remaining n-1 strings in complete disarray. Also, she remembers the initial n strings. She wants to know which string was stolen, but she is not good at programming. Can you help her?
Input
This problem is made as interactive. It means, that your solution will read the input, given by the interactor. But the interactor will give you the full input at the beginning and after that, you should print the answer. So you should solve the problem, like as you solve the usual, non-interactive problem because you won't have any interaction process. The only thing you should not forget is to flush the output buffer, after printing the answer. Otherwise, you can get an "Idleness limit exceeded" verdict. Refer to the [interactive problems guide](https://codeforces.com/blog/entry/45307) for the detailed information about flushing the output buffer.
The input consists of multiple test cases. The first line contains a single integer t (1 ≤ t ≤ 100) — the number of test cases.
The first line of each test case contains two integers n, m (1 ≤ n ≤ 10^5, 1 ≤ m ≤ 10^5) — the number of strings and the length of each string, respectively.
The next n lines each contain a string with length m, describing the original n strings. All string consists of lowercase Latin letters.
The next n-1 lines each contain a string with length m, describing the strings after Cirno exchanged and reordered them.
It is guaranteed that n is odd and that the sum of n ⋅ m over all test cases does not exceed 10^5.
Hack format:
The first line should contain a single integer t. After that t test cases should follow in the following format:
The first line should contain two integers n and m.
The following n lines should contain n strings of length m, describing the original strings.
The following (n-1)/(2) lines should describe the pairs. They should contain, in the following order: the index of the first string i (1 ≤ i ≤ n), the index of the second string j (1 ≤ j ≤ n, i ≠ j), the number of exchanged positions k (1 ≤ k ≤ m), and the list of k positions that are exchanged (k distinct indices from 1 to m in any order).
The final line should contain a permutation of integers from 1 to n, describing the way the strings should be reordered. The strings will be placed in the order indices placed in this permutation, the stolen string index will be ignored.
Output
For each test case print a single line with the stolen string.
Example
Input
3
3 5
aaaaa
bbbbb
ccccc
aaaaa
bbbbb
3 4
aaaa
bbbb
cccc
aabb
bbaa
5 6
abcdef
uuuuuu
kekeke
ekekek
xyzklm
xbcklf
eueueu
ayzdem
ukukuk
Output
ccccc
cccc
kekeke
Note
In the first test case, "aaaaa" and "bbbbb" exchanged all positions, and "ccccc" is the stolen string.
In the second test case, "aaaa" and "bbbb" exchanged two first positions, and "cccc" is the stolen string.
This is the first test in the hack format:
3
3 5
aaaaa
bbbbb
ccccc
1 2 5 1 2 3 4 5
2 1 3
3 4
aaaa
bbbb
cccc
1 2 2 1 2
2 1 3
5 6
abcdef
uuuuuu
kekeke
ekekek
xyzklm
1 5 3 2 3 6
2 4 3 2 4 6
5 4 1 2 3
|
import sys
input = sys.stdin.readline
def solve():
n, m = map(int, input().split())
original = [input() for _ in range(n)]
modified = [input() for _ in range(n-1)]
stolen_chars = []
for j in range(m):
chars_available = 0
for i in range(n):
chars_available += ord(original[i][j])
for i in range(n-1):
chars_available -= ord(modified[i][j])
stolen_chars.append(chr(chars_available))
return ''.join(stolen_chars)
t = int(input())
output = []
for _ in range(t):
print(solve())
sys.stdout.flush()
|
{
"input": [
"3\n3 5\naaaaa\nbbbbb\nccccc\naaaaa\nbbbbb\n3 4\naaaa\nbbbb\ncccc\naabb\nbbaa\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nxyzklm\nxbcklf\neueueu\nayzdem\nukukuk\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n1 2 5 1 2 3 4 5\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 2 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nxyzklm\n1 5 3 2 3 6\n2 4 3 2 4 6\n5 4 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 2 3 4 5\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 2 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nxyzklm\n1 5 3 2 3 6\n2 4 3 2 4 6\n5 4 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 4 1 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n0 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 1 2 -1 4\n2 5 5 2 4 1\n5 8 1 2 3\n",
"3\n3 1\naaaaa\nbbbbb\nccccc\n2 2 5 1 2 3 4 5\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nxyzklm\n1 5 3 2 3 6\n2 5 3 3 4 6\n5 4 1 2 3\n",
"3\n3 3\naaaaa\nbbbbb\nccccc\n2 2 5 1 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 3 2 6 6\n2 5 5 2 4 6\n5 4 1 4 0\n",
"3\n3 2\naaaaa\nbbbbb\nccccc\n2 2 5 1 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 1 2 0 6\n2 5 5 2 4 6\n5 6 1 4 3\n",
"3\n3 2\naaaaa\nbbbbb\nccccc\n2 2 2 1 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\ndkekek\nmyzklx\n1 5 1 2 0 6\n2 5 4 2 4 6\n5 6 1 4 3\n",
"3\n3 4\naaaaa\nbbbbb\nccccc\n2 2 5 1 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 3 2 6 6\n2 5 5 2 4 6\n5 4 1 4 0\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 2 3 4 5\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nxyzklm\n1 5 3 2 3 6\n2 4 3 2 4 6\n5 4 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 2 3 4 5\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nxyzklm\n1 5 3 2 3 6\n2 5 3 2 4 6\n5 4 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 2 3 4 5\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nxyzklm\n1 5 3 2 6 6\n2 5 3 2 4 6\n5 4 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 2 3 4 5\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 3 2 6 6\n2 5 3 2 4 6\n5 4 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 2 2 4 5\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 3 2 6 6\n2 5 3 2 4 6\n5 4 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 2 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 3 2 6 6\n2 5 3 2 4 6\n5 4 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 3 2 6 6\n2 5 3 2 4 6\n5 4 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 3 2 6 6\n2 5 3 2 4 6\n5 4 1 4 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 3 2 6 6\n2 5 5 2 4 6\n5 4 1 4 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 1 2 6 6\n2 5 5 2 4 6\n5 4 1 4 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 1 2 0 6\n2 5 5 2 4 6\n5 4 1 4 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 1 2 0 6\n2 5 5 2 4 6\n5 4 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 1 2 0 6\n2 5 5 2 4 6\n5 8 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 1 2 -1 6\n2 5 5 2 4 6\n5 8 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 1 2 -1 4\n2 5 5 2 4 6\n5 8 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 1 2 -1 4\n2 5 5 2 4 1\n5 8 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n0 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 1 2 -1 4\n2 5 5 2 4 1\n5 8 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n1 2 5 1 2 3 4 5\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 2 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nekekek\nekekek\nxyzklm\n1 5 3 2 3 6\n2 4 3 2 4 6\n5 4 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 2 3 4 5\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 2 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nxyzklm\n1 5 3 2 3 6\n2 4 3 2 4 7\n5 4 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 0 3 4 5\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nxyzklm\n1 5 3 2 3 6\n2 4 3 2 4 6\n5 4 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 2 3 4 5\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nxyzklm\n1 5 3 2 3 6\n2 5 3 3 4 6\n5 4 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 2 3 4 5\n2 1 3\n0 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nxyzklm\n1 5 3 2 6 6\n2 5 3 2 4 6\n5 4 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 2 2 4 5\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 3 2 6 6\n2 5 3 1 4 6\n5 4 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 2 2 4 7\n2 1 5\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 3 2 6 6\n2 5 3 2 4 6\n5 4 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 3 2 6 6\n2 5 3 2 4 8\n5 4 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 3 2 6 6\n2 5 0 2 4 6\n5 4 1 4 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 3 2 6 6\n2 5 5 2 4 6\n5 4 1 4 0\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 1 2 6 6\n2 5 5 2 4 6\n5 4 1 4 2\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 1 2 0 6\n2 5 5 2 4 6\n5 6 1 4 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 1 2 0 6\n0 5 5 2 4 6\n5 4 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 2 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 1 2 0 6\n2 5 5 2 4 6\n5 8 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 1 2 -1 6\n2 5 5 2 4 6\n5 8 0 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\nbccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 1 2 -1 4\n2 5 5 2 4 6\n5 8 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 1 2 -1 4\n2 5 5 3 4 1\n5 8 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n0 2 5 1 2 3 4 5\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 2 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nekekek\nekekek\nxyzklm\n1 5 3 2 3 6\n2 4 3 2 4 6\n5 4 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 2 3 4 5\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 2 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nxyzklm\n1 7 3 2 3 6\n2 4 3 2 4 7\n5 4 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 2 3 4 5\n2 1 3\n0 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nxyzklm\n1 5 3 1 6 6\n2 5 3 2 4 6\n5 4 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 2 2 4 5\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 3 2 6 6\n2 5 3 1 4 6\n5 3 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 2 2 4 7\n2 1 5\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 1\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 3 2 6 6\n2 5 3 2 4 6\n5 4 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 2 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 3 2 6 6\n2 5 3 2 4 8\n5 4 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 3 2 6 6\n2 5 0 2 4 6\n7 4 1 4 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 4\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 1 2 6 6\n2 5 5 2 4 6\n5 4 1 4 2\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 0 2 4 7\n1 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 1 2 0 6\n0 5 5 2 4 6\n5 4 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 1 1 2\n2 2 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 1 2 0 6\n2 5 5 2 4 6\n5 8 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 1 2 -1 8\n2 5 5 2 4 6\n5 8 0 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 0 2 4 7\n2 1 3\n3 8\naaaa\nbbbb\nbccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 1 2 -1 4\n2 5 5 2 4 6\n5 8 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 3\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 1 2 -1 4\n2 5 5 3 4 1\n5 8 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 4 1 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n0 0 2 1 3\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 1 2 -1 4\n2 5 5 2 4 1\n5 8 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n0 2 5 1 2 3 4 5\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 2 2 1 2\n2 1 3\n5 6\nabceef\nuuuuuu\nekekek\nekekek\nxyzklm\n1 5 3 2 3 6\n2 4 3 2 4 6\n5 4 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 2 3 4 5\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 2 4 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nxyzklm\n1 7 3 2 3 6\n2 4 3 2 4 7\n5 4 1 2 3\n",
"3\n3 1\naaaaa\nbbbbb\nccccc\n2 2 5 1 2 3 4 5\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nxyzklm\n1 5 2 2 3 6\n2 5 3 3 4 6\n5 4 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 2 3 4 5\n2 1 3\n0 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkfkeke\nekekek\nxyzklm\n1 5 3 1 6 6\n2 5 3 2 4 6\n5 4 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 2 2 4 7\n2 1 5\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 1\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n0 5 3 2 6 6\n2 5 3 2 4 6\n5 4 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 2 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 3 2 6 6\n2 5 3 2 3 8\n5 4 1 2 3\n",
"3\n3 3\naaaaa\nbbbba\nccccc\n2 2 5 1 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 3 2 6 6\n2 5 5 2 4 6\n5 4 1 4 0\n",
"3\n3 2\naaaaa\nbbbbb\nccccc\n2 2 5 1 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\ndkekek\nmyzklx\n1 5 1 2 0 6\n2 5 5 2 4 6\n5 6 1 4 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 0 2 4 7\n1 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyyklx\n1 5 1 2 0 6\n0 5 5 2 4 6\n5 4 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n0 0 1 1 2\n2 2 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 1 2 0 6\n2 5 5 2 4 6\n5 8 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 0 2 4 7\n2 1 3\n3 8\naaaa\nbbbb\nbccc\n1 -1 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 1 2 -1 4\n2 5 5 2 4 6\n5 8 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 3\n2 1 3\n5 3\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 1 2 -1 4\n2 5 5 3 4 1\n5 8 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 4 1 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n0 0 2 1 3\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 1 2 -1 4\n2 5 5 1 4 1\n5 8 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n0 2 5 1 2 3 4 5\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 2 2 1 2\n2 0 3\n5 6\nabceef\nuuuuuu\nekekek\nekekek\nxyzklm\n1 5 3 2 3 6\n2 4 3 2 4 6\n5 4 1 2 3\n",
"3\n6 1\naaaaa\nbbbbb\nccccc\n2 2 5 1 2 3 4 5\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nxyzklm\n1 5 2 2 3 6\n2 5 3 3 4 6\n5 4 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 2 3 4 5\n2 1 3\n0 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkfkeke\nekekek\nxyzklm\n1 5 3 1 6 6\n2 6 3 2 4 6\n5 4 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n3 2 5 1 2 2 4 7\n2 1 5\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 1\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n0 5 3 2 6 6\n2 5 3 2 4 6\n5 4 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 2 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 5 2 6 6\n2 5 3 2 3 8\n5 4 1 2 3\n",
"3\n3 3\naaaaa\nbbbba\nccccc\n2 2 5 1 0 3 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 3 2 6 6\n2 5 5 2 4 6\n5 4 1 4 0\n",
"3\n3 2\naaaaa\nbbbbb\nccccc\n2 2 5 1 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\ndkekek\nmyzklx\n1 5 1 2 0 6\n2 5 4 2 4 6\n5 6 1 4 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 0 2 4 7\n1 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 4\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyyklx\n1 5 1 2 0 6\n0 5 5 2 4 6\n5 4 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n0 0 1 1 2\n2 2 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 1 2 0 6\n2 5 5 2 4 6\n5 8 1 1 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 0 2 4 7\n2 1 3\n3 14\naaaa\nbbbb\nbccc\n1 -1 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 1 2 -1 4\n2 5 5 2 4 6\n5 8 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 3\n2 1 3\n5 3\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 1 2 -1 4\n2 5 5 3 4 1\n5 8 1 0 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 4 1 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n0 0 2 1 3\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 2 2 -1 4\n2 5 5 1 4 1\n5 8 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n0 2 5 1 2 3 4 5\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 2 2 1 2\n3 0 3\n5 6\nabceef\nuuuuuu\nekekek\nekekek\nxyzklm\n1 5 3 2 3 6\n2 4 3 2 4 6\n5 4 1 2 3\n",
"3\n6 1\naaaaa\nbbabb\nccccc\n2 2 5 1 2 3 4 5\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nxyzklm\n1 5 2 2 3 6\n2 5 3 3 4 6\n5 4 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 2 3 4 5\n2 1 3\n0 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkfkeke\nekekek\nxyzklm\n1 5 3 1 6 6\n2 6 3 1 4 6\n5 4 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 2 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 5 2 6 6\n2 5 3 2 3 8\n5 4 1 1 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 0 2 4 7\n1 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 4\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyyklx\n1 5 1 2 0 6\n0 5 5 2 2 6\n5 4 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n0 0 1 1 2\n2 2 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 1 2 0 6\n1 5 5 2 4 6\n5 8 1 1 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 0 2 4 7\n2 1 3\n3 14\naaaa\nbbbb\nbccc\n1 -1 2 1 2\n2 1 3\n5 11\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 1 2 -1 4\n2 5 5 2 4 6\n5 8 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 0 5 1 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 3\n2 1 3\n5 3\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 1 2 -1 4\n2 5 5 3 4 1\n5 8 1 0 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 4 1 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n0 0 2 1 3\n2 1 1\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 2 2 -1 4\n2 5 5 1 4 1\n5 8 1 2 3\n",
"3\n6 1\naaaaa\nbbabb\ncbccc\n2 2 5 1 2 3 4 5\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nxyzklm\n1 5 2 2 3 6\n2 5 3 3 4 6\n5 4 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 2 3 4 5\n2 1 3\n0 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkfkeke\nekekek\nxyzklm\n1 5 3 1 6 6\n2 6 3 1 4 6\n5 4 1 4 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 2 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 5 2 6 6\n2 5 3 2 3 8\n5 4 2 1 3\n",
"3\n3 2\naaaaa\nbbbbb\nccccc\n2 2 2 1 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n6 6\nabcdef\nuuuuuu\nkekeke\ndkekek\nmyzklx\n1 5 1 2 0 6\n2 5 4 2 4 6\n5 6 1 4 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 0 2 4 7\n1 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 4\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyyklx\n1 5 1 2 0 6\n0 5 5 2 0 6\n5 4 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 0 2 4 7\n2 2 3\n3 4\naaaa\nbbbb\ncccc\n0 0 1 1 2\n2 2 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 1 2 0 6\n1 5 5 2 4 6\n5 8 1 1 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 0 2 4 7\n2 1 3\n3 14\naaaa\nbbbb\nbccc\n1 -1 2 1 2\n2 1 3\n5 11\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 1 2 -1 4\n2 5 5 4 4 6\n5 8 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 4 1 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n0 0 2 1 3\n2 1 1\n0 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 2 2 -1 4\n2 5 5 1 4 1\n5 8 1 2 3\n",
"3\n6 1\naaaaa\nbbabb\ncbccc\n2 2 5 1 2 3 4 5\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nyyzklm\n1 5 2 2 3 6\n2 5 3 3 4 6\n5 4 1 2 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 1 2 3 4 5\n2 1 3\n0 4\naaaa\nbbbb\ncccc\n1 0 2 1 2\n0 1 3\n5 6\nabcdef\nuuuuuu\nkfkeke\nekekek\nxyzklm\n1 5 3 1 6 6\n2 6 3 1 4 6\n5 4 1 4 3\n",
"3\n3 5\naaaaa\nbbbbb\nccccc\n2 2 5 2 0 2 4 7\n2 1 3\n3 4\naaaa\nbbbb\ncccc\n1 1 2 1 2\n2 1 3\n5 6\nabcdef\nuuuuuu\nkekeke\nekekek\nmyzklx\n1 5 5 2 6 6\n2 5 3 2 3 8\n5 4 2 1 3\n"
],
"output": [
"ccccc\ncccc\nkekeke\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\nabcabcabcabc\n",
"abc\n\n\n",
"abcabcabc\n\n\n",
"abcabc\n\n\n",
"abcabc\n\nabcabc\n",
"abcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\nabcabcabcabc\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabc\n\n\n",
"abcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\nabcabcabcabc\n",
"abcabcabcabcabc\n\n\n",
"abc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabc\n\n\n",
"abcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\nabcabcabcabc\n",
"abcabcabcabcabc\n\n\n",
"abc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\nabcabcabcabc\n",
"abc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabc\n\nabcabc\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\nabcabcabcabc\n",
"abc\n\n\n",
"abcabcabcabcabc\n\n\n",
"abcabcabcabcabc\n\n\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
AquaMoon had n strings of length m each. n is an odd number.
When AquaMoon was gone, Cirno tried to pair these n strings together. After making (n-1)/(2) pairs, she found out that there was exactly one string without the pair!
In her rage, she disrupted each pair of strings. For each pair, she selected some positions (at least 1 and at most m) and swapped the letters in the two strings of this pair at the selected positions.
For example, if m = 6 and two strings "abcdef" and "xyzklm" are in one pair and Cirno selected positions 2, 3 and 6 she will swap 'b' with 'y', 'c' with 'z' and 'f' with 'm'. The resulting strings will be "ayzdem" and "xbcklf".
Cirno then stole away the string without pair and shuffled all remaining strings in arbitrary order.
AquaMoon found the remaining n-1 strings in complete disarray. Also, she remembers the initial n strings. She wants to know which string was stolen, but she is not good at programming. Can you help her?
Input
This problem is made as interactive. It means, that your solution will read the input, given by the interactor. But the interactor will give you the full input at the beginning and after that, you should print the answer. So you should solve the problem, like as you solve the usual, non-interactive problem because you won't have any interaction process. The only thing you should not forget is to flush the output buffer, after printing the answer. Otherwise, you can get an "Idleness limit exceeded" verdict. Refer to the [interactive problems guide](https://codeforces.com/blog/entry/45307) for the detailed information about flushing the output buffer.
The input consists of multiple test cases. The first line contains a single integer t (1 ≤ t ≤ 100) — the number of test cases.
The first line of each test case contains two integers n, m (1 ≤ n ≤ 10^5, 1 ≤ m ≤ 10^5) — the number of strings and the length of each string, respectively.
The next n lines each contain a string with length m, describing the original n strings. All string consists of lowercase Latin letters.
The next n-1 lines each contain a string with length m, describing the strings after Cirno exchanged and reordered them.
It is guaranteed that n is odd and that the sum of n ⋅ m over all test cases does not exceed 10^5.
Hack format:
The first line should contain a single integer t. After that t test cases should follow in the following format:
The first line should contain two integers n and m.
The following n lines should contain n strings of length m, describing the original strings.
The following (n-1)/(2) lines should describe the pairs. They should contain, in the following order: the index of the first string i (1 ≤ i ≤ n), the index of the second string j (1 ≤ j ≤ n, i ≠ j), the number of exchanged positions k (1 ≤ k ≤ m), and the list of k positions that are exchanged (k distinct indices from 1 to m in any order).
The final line should contain a permutation of integers from 1 to n, describing the way the strings should be reordered. The strings will be placed in the order indices placed in this permutation, the stolen string index will be ignored.
Output
For each test case print a single line with the stolen string.
Example
Input
3
3 5
aaaaa
bbbbb
ccccc
aaaaa
bbbbb
3 4
aaaa
bbbb
cccc
aabb
bbaa
5 6
abcdef
uuuuuu
kekeke
ekekek
xyzklm
xbcklf
eueueu
ayzdem
ukukuk
Output
ccccc
cccc
kekeke
Note
In the first test case, "aaaaa" and "bbbbb" exchanged all positions, and "ccccc" is the stolen string.
In the second test case, "aaaa" and "bbbb" exchanged two first positions, and "cccc" is the stolen string.
This is the first test in the hack format:
3
3 5
aaaaa
bbbbb
ccccc
1 2 5 1 2 3 4 5
2 1 3
3 4
aaaa
bbbb
cccc
1 2 2 1 2
2 1 3
5 6
abcdef
uuuuuu
kekeke
ekekek
xyzklm
1 5 3 2 3 6
2 4 3 2 4 6
5 4 1 2 3
### Input:
3
3 5
aaaaa
bbbbb
ccccc
aaaaa
bbbbb
3 4
aaaa
bbbb
cccc
aabb
bbaa
5 6
abcdef
uuuuuu
kekeke
ekekek
xyzklm
xbcklf
eueueu
ayzdem
ukukuk
### Output:
ccccc
cccc
kekeke
### Input:
3
3 5
aaaaa
bbbbb
ccccc
1 2 5 1 2 3 4 5
2 1 3
3 4
aaaa
bbbb
cccc
1 2 2 1 2
2 1 3
5 6
abcdef
uuuuuu
kekeke
ekekek
xyzklm
1 5 3 2 3 6
2 4 3 2 4 6
5 4 1 2 3
### Output:
abcabcabcabcabc
### Code:
import sys
input = sys.stdin.readline
def solve():
n, m = map(int, input().split())
original = [input() for _ in range(n)]
modified = [input() for _ in range(n-1)]
stolen_chars = []
for j in range(m):
chars_available = 0
for i in range(n):
chars_available += ord(original[i][j])
for i in range(n-1):
chars_available -= ord(modified[i][j])
stolen_chars.append(chr(chars_available))
return ''.join(stolen_chars)
t = int(input())
output = []
for _ in range(t):
print(solve())
sys.stdout.flush()
|
266_B. Queue at the School_10846
|
During the break the schoolchildren, boys and girls, formed a queue of n people in the canteen. Initially the children stood in the order they entered the canteen. However, after a while the boys started feeling awkward for standing in front of the girls in the queue and they started letting the girls move forward each second.
Let's describe the process more precisely. Let's say that the positions in the queue are sequentially numbered by integers from 1 to n, at that the person in the position number 1 is served first. Then, if at time x a boy stands on the i-th position and a girl stands on the (i + 1)-th position, then at time x + 1 the i-th position will have a girl and the (i + 1)-th position will have a boy. The time is given in seconds.
You've got the initial position of the children, at the initial moment of time. Determine the way the queue is going to look after t seconds.
Input
The first line contains two integers n and t (1 ≤ n, t ≤ 50), which represent the number of children in the queue and the time after which the queue will transform into the arrangement you need to find.
The next line contains string s, which represents the schoolchildren's initial arrangement. If the i-th position in the queue contains a boy, then the i-th character of string s equals "B", otherwise the i-th character equals "G".
Output
Print string a, which describes the arrangement after t seconds. If the i-th position has a boy after the needed time, then the i-th character a must equal "B", otherwise it must equal "G".
Examples
Input
5 1
BGGBG
Output
GBGGB
Input
5 2
BGGBG
Output
GGBGB
Input
4 1
GGGB
Output
GGGB
|
n, t = map(int, input().split())
a = list(input())
for i in range(t):
j = 0
while j < n:
while j < n and a[j] == 'G':
j += 1
while j < n and a[j] == 'B':
j += 1
if j < n:
a[j - 1], a[j] = 'G', 'B'
j += 1
for i in a:
print(i, end = '')
|
{
"input": [
"5 1\nBGGBG\n",
"5 2\nBGGBG\n",
"4 1\nGGGB\n",
"30 50\nBGGBBGGGGGGGGBBGGGBBGGBBBGBBGG\n",
"10 3\nBBGBBBBBBG\n",
"1 1\nG\n",
"46 3\nGGBBGGGGBBGBGBBBBBGGGBGGGBBGGGBBBGGBGGBBBGBGBB\n",
"50 6\nBGGBBBBGGBBBBBBGGBGBGBBBBGBBBBBBGBBBBBBBBBBBBBBBBB\n",
"1 50\nG\n",
"2 2\nBG\n",
"27 6\nGBGBGBGGGGGGBGGBGGBBGBBBGBB\n",
"50 8\nGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\n",
"6 3\nGGBBBG\n",
"50 4\nGBBGBBBGGGGGBBGGBBBBGGGBBBGBBBGGBGGBGBBBGGBGGBGGBG\n",
"50 30\nBGGGGGGBGGBGBGGGGBGBBGBBBGGBBBGBGBGGGGGBGBBGBGBGGG\n",
"22 7\nGBGGBGGGGGBBBGGBGBGBBB\n",
"10 10\nBGBGBGBGBG\n",
"50 13\nGGGBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\n",
"34 20\nBBBBGBGGGBGGGBGBGGBBBBGGBBGGGBGBBG\n",
"30 25\nBGGBBGBGGBGBGBBGBGGGGBGBGGBBBB\n",
"50 50\nBBGBBBBBBBBBBBBGBBBGBBBBBBBGBBBBBBGBBBGBBGBBGBBBGG\n",
"8 3\nBBGBGBGB\n",
"8 8\nGGGBGGBB\n",
"10 10\nBBBBBBBBBB\n",
"50 10\nBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBGB\n",
"1 1\nB\n",
"50 50\nGGBBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGBBGGGGGGBG\n",
"6 2\nBBGBBG\n",
"44 8\nBGBBBBBBBBBGGBBGBGBGGBBBBBGBBGBBBBBBBBBGBBGB\n",
"20 20\nBBGGBGGGGBBBGBBGGGBB\n",
"31 33\nBBGGBBGGBGBBBBGGBGBBBGBGGBBGBBB\n",
"1 50\nB\n",
"10 10\nGGGGGGGGGG\n",
"34 34\nBGGBBBBGGBBGBGGGGGGBBGGGGGBGGBGGGB\n",
"46 11\nBGGGGGBGBGGBGGGBBGBBGBBGGBBGBBGBGGGGGGGBGBGBGB\n",
"17 42\nBBGBGBGGGGGGBBGGG\n",
"2 1\nBB\n",
"2 1\nBG\n",
"50 8\nGGGGBGGBGGGBGBBBGGGGGGGGBBGBGBGBBGGBGGBGGGGGGGGBBG\n",
"50 50\nBBBBBBBBGGBBBBBBGBBBBBBBBBBBGBBBBBBBBBBBBBBGBBBBBB\n",
"50 10\nBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\n",
"26 3\nGBBGBBBBBGGGBGBGGGBGBGGBBG\n",
"30 58\nBGGBBGGGGGGGGBBGGGBBGGBBBGBBGG\n",
"46 5\nGGBBGGGGBBGBGBBBBBGGGBGGGBBGGGBBBGGBGGBBBGBGBB\n",
"1 31\nG\n",
"2 2\nGB\n",
"6 5\nGGBBBG\n",
"50 7\nGGGBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\n",
"30 31\nBGGBBGBGGBGBGBBGBGGGGBGBGGBBBB\n",
"8 3\nBGBGBGBB\n",
"8 10\nGGGBGGBB\n",
"50 13\nBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBGB\n",
"20 35\nBBGGBGGGGBBBGBBGGGBB\n",
"31 24\nBBGGBBGGBGBBBBGGBGBBBGBGGBBGBBB\n",
"1 57\nB\n",
"46 11\nBGBGBGBGGGGGGGBGBBGBBGGBBGBBGBBGGGBGGBGBGGGGGB\n",
"17 42\nBGBBGBGGGGGGBBGGG\n",
"26 3\nGBBGGBGBGGGBGBGGGBBBBBGBBG\n",
"5 2\nGBGGB\n",
"4 1\nGBGG\n",
"46 5\nBBGBGBBBGGBGGBBBGGGBBGGGBGGGBBBBBGBGBBGGGGBBGG\n",
"1 31\nH\n",
"50 7\nGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGBGGG\n",
"1 57\nC\n",
"8 2\nBGBGBGBB\n",
"10 16\nBGBGBGBGBG\n",
"50 26\nGGGBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\n",
"34 20\nGBBGBGGGBBGGBBBBGGBGBGGGBGGGBGBBBB\n",
"50 96\nBBGBBBBBBBBBBBBGBBBGBBBBBBBGBBBBBBGBBBGBBGBBGBBBGG\n",
"8 2\nBBGBGBGB\n",
"50 11\nGGBBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGBBGGGGGGBG\n",
"46 2\nBGGGGGBGBGGBGGGBBGBBGBBGGBBGBBGBGGGGGGGBGBGBGB\n",
"2 1\nCB\n",
"50 50\nBBBBBBBBBGBBBBBBGBBBBBBBGBBBGBBBBBBBBBBBBBBGBBBBBB\n",
"26 2\nGBBGBBBBBGGGBGBGGGBGBGGBBG\n",
"6 1\nGGBBBG\n",
"46 3\nBGBGBGBGGGGGGGBGBBGBBGGBBGBBGBBGGGBGGBGBGGGGGB\n",
"26 5\nGBBGGBGBGGGBGBGGGBBBBBGBBG\n",
"46 5\nGGBGGGGGBBGBGBBBBBGGGBGGGBBGGGBBBGGBBGBBBGBGBB\n",
"6 1\nGBBBGG\n",
"26 2\nGBBGGBGBGGGBGBGGGBBBBBGBBG\n",
"50 2\nGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGBGGG\n",
"26 4\nGBBGGBGBGGGBGBGGGBBBBBGBBG\n",
"50 1\nGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGBGGG\n",
"30 15\nBGGBBGGGGGGGGBBGGGBBGGBBBGBBGG\n",
"30 103\nBGGBBGGGGGGGGBBGGGBBGGBBBGBBGG\n",
"6 5\nGBBBGG\n",
"8 4\nBGBGBGBB\n",
"8 20\nGGGBGGBB\n",
"1 18\nH\n",
"6 8\nGBBBGG\n",
"8 2\nGGGBGGBB\n",
"1 18\nG\n",
"1 5\nG\n",
"30 102\nBGGBBGGGGGGGGBBGGGBBGGBBBGBBGG\n",
"1 30\nG\n",
"20 63\nBBGGBGGGGBBBGBBGGGBB\n",
"1 70\nB\n",
"30 103\nGGGBBGGGGGGGGBBBGGBBGGBBBGBBGG\n",
"50 11\nGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGBGGG\n",
"8 5\nBGBGBGBB\n",
"1 50\nC\n",
"10 25\nBGBGBGBGBG\n",
"50 26\nGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGBGGG\n",
"50 47\nBBBBBBBBBGBBBBBBGBBBBBBBGBBBGBBBBBBBBBBBBBBGBBBBBB\n",
"30 23\nBGGBBGGGGGGGGBBGGGBBGGBBBGBBGG\n",
"20 40\nBBGGBGGGGBBBGBBGGGBB\n",
"30 68\nGGGBBGGGGGGGGBBBGGBBGGBBBGBBGG\n",
"1 66\nC\n",
"10 5\nBGBGBGBGBG\n",
"50 73\nBBBBBBBBBGBBBBBBGBBBBBBBGBBBGBBBBBBBBBBBBBBGBBBBBB\n",
"30 42\nBGGBBGGGGGGGGBBGGGBBGGBBBGBBGG\n",
"20 55\nBBGGBGGGGBBBGBBGGGBB\n",
"1 66\nB\n"
],
"output": [
"GBGGB\n",
"GGBGB\n",
"GGGB\n",
"GGGGGGGGGGGGGGGGGGBBBBBBBBBBBB\n",
"GBBBBBGBBB\n",
"G\n",
"GGGGBGBGGGBBBBBGBGBGBGGGBGGBGBGBGBGBGBGBGBBBBB\n",
"GGGGBBBBBGBGBGBGBBBGBBBBBBGBBBBBBBBBBBBBBBBBBBBBBB\n",
"G\n",
"GB\n",
"GGGGGGGBGBGBGGGGGBGBBBBBBBB\n",
"GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\n",
"GGGBBB\n",
"GGBGBGBGBGBGGGBBGBGBGBGBBBGBGBGBGBGBGBGBGBGBGGBGBB\n",
"GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGBBBBBBBBBBBBBBBBBBBB\n",
"GGGGGGGGBGGBGGBBBBBBBB\n",
"GGGGGBBBBB\n",
"GGGGGGGGGGGGGGGGBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\n",
"GGGGGGGGGGGGGGGGGBBBBBBBBBBBBBBBBB\n",
"GGGGGGGGGGGGGGGBBBBBBBBBBBBBBB\n",
"GGGGGGGGGGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\n",
"GGBGBBBB\n",
"GGGGGBBB\n",
"BBBBBBBBBB\n",
"BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBGBBBBBBBBBBB\n",
"B\n",
"GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGBBBBB\n",
"GBBGBB\n",
"GBBGBGBGBGBGBGBBBBGBBGBBBBBBBBBGBBGBBBBBBBBB\n",
"GGGGGGGGGGBBBBBBBBBB\n",
"GGGGGGGGGGGGBBBBBBBBBBBBBBBBBBB\n",
"B\n",
"GGGGGGGGGG\n",
"GGGGGGGGGGGGGGGGGGGGGBBBBBBBBBBBBB\n",
"GGGGGGGGGGGBGGGGGBBGBGBGBGBGBGBGBGBGBGBGBBBBBB\n",
"GGGGGGGGGGGBBBBBB\n",
"BB\n",
"GB\n",
"GGGGGGGGGGGGBGGBGBGBGBGBGGGGGGBGBGBGBGBGBGGBGGBGBB\n",
"GGGGGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\n",
"BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\n",
"GGBBBBGBGBGBGGGBGBGGGBGBBB\n",
"GGGGGGGGGGGGGGGGGGBBBBBBBBBBBB\n",
"GGGGGGBGBGBBBGBGBGBGBGBGGGBGGBGBGBGBGBGBBBBBBB\n",
"G\n",
"GB\n",
"GGGBBB\n",
"GGGGGGGGGGBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG\n",
"GGGGGGGGGGGGGGGBBBBBBBBBBBBBBB\n",
"GGGBBBBB\n",
"GGGGGBBB\n",
"BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBGBBBBBBBBBBBBBB\n",
"GGGGGGGGGGBBBBBBBBBB\n",
"GGGGGGGGGGGGBBBBBBBBBBBBBBBBBBB\n",
"B\n",
"GGGGGGGGGGGBGBGBGBGGGBGBGBGBGBGBGBGBGBGBGBBBBB\n",
"GGGGGGGGGGGBBBBBB\n",
"GGGBGBGGBGBGGGBGBBBGBBGBBB\n",
"GGGBB\n",
"GGBG\n",
"GGBGBGBGBGBGBGBGBGBGBGGBGBGBGBGBBGBGBGBGBGBGBB\n",
"H\n",
"GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGB\n",
"C\n",
"GGBGBBBB\n",
"GGGGGBBBBB\n",
"GGGGGGGGGGGGGGGGGGGGGGGGGGGGGBGGGGGGGGGGGGGGGGGGGG\n",
"GGGGGGGGGGGGGGGGGBBBBBBBBBBBBBBBBB\n",
"GGGGGGGGGGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\n",
"GBGBGBBB\n",
"GGGGGGGGGGGGBGBGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGBBB\n",
"GGBGGGGGBGBGGBGGBBGBBGBGBGBBGBGBGBGGGGGGGBGBBB\n",
"CB\n",
"GGGGGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\n",
"GGBBBBBGBGBGGGBGBGGGBGBGBB\n",
"GGBBGB\n",
"GGGBGBGBGBGGGGGGBBGBGBGBBGBBGBGBGBGGGBGGBGBGGB\n",
"GGGGGBGBGGBGBGGBBGBBGBBBBB\n",
"GGGGGGGBGGBBBGBGBGBGBGBGGGBGGBGBGBBBGBGBBBBBBB\n",
"GBBGBG\n",
"GGBGBGGBGBGGGBGBGBBBGBBGBB\n",
"GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGBG\n",
"GGGGBGBGGBGBGGGBBBGBBGBBBB\n",
"GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGBGG\n",
"GGGGGGGGGGGGGGGBGBGBGBBBBBBBBB\n",
"GGGGGGGGGGGGGGGGGGBBBBBBBBBBBB\n",
"GGGBBB\n",
"GGGBBBBB\n",
"GGGGGBBB\n",
"H\n",
"GGGBBB\n",
"GGGGGBBB\n",
"G\n",
"G\n",
"GGGGGGGGGGGGGGGGGGBBBBBBBBBBBB\n",
"G\n",
"GGGGGGGGGGBBBBBBBBBB\n",
"B\n",
"GGGGGGGGGGGGGGGGGGBBBBBBBBBBBB\n",
"GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGB\n",
"GGGBBBBB\n",
"C\n",
"GGGGGBBBBB\n",
"GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGB\n",
"GGGGGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\n",
"GGGGGGGGGGGGGGGGGGBBBBBBBBBBBB\n",
"GGGGGGGGGGBBBBBBBBBB\n",
"GGGGGGGGGGGGGGGGGGBBBBBBBBBBBB\n",
"C\n",
"GGGGGBBBBB\n",
"GGGGGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB\n",
"GGGGGGGGGGGGGGGGGGBBBBBBBBBBBB\n",
"GGGGGGGGGGBBBBBBBBBB\n",
"B\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
During the break the schoolchildren, boys and girls, formed a queue of n people in the canteen. Initially the children stood in the order they entered the canteen. However, after a while the boys started feeling awkward for standing in front of the girls in the queue and they started letting the girls move forward each second.
Let's describe the process more precisely. Let's say that the positions in the queue are sequentially numbered by integers from 1 to n, at that the person in the position number 1 is served first. Then, if at time x a boy stands on the i-th position and a girl stands on the (i + 1)-th position, then at time x + 1 the i-th position will have a girl and the (i + 1)-th position will have a boy. The time is given in seconds.
You've got the initial position of the children, at the initial moment of time. Determine the way the queue is going to look after t seconds.
Input
The first line contains two integers n and t (1 ≤ n, t ≤ 50), which represent the number of children in the queue and the time after which the queue will transform into the arrangement you need to find.
The next line contains string s, which represents the schoolchildren's initial arrangement. If the i-th position in the queue contains a boy, then the i-th character of string s equals "B", otherwise the i-th character equals "G".
Output
Print string a, which describes the arrangement after t seconds. If the i-th position has a boy after the needed time, then the i-th character a must equal "B", otherwise it must equal "G".
Examples
Input
5 1
BGGBG
Output
GBGGB
Input
5 2
BGGBG
Output
GGBGB
Input
4 1
GGGB
Output
GGGB
### Input:
5 1
BGGBG
### Output:
GBGGB
### Input:
5 2
BGGBG
### Output:
GGBGB
### Code:
n, t = map(int, input().split())
a = list(input())
for i in range(t):
j = 0
while j < n:
while j < n and a[j] == 'G':
j += 1
while j < n and a[j] == 'B':
j += 1
if j < n:
a[j - 1], a[j] = 'G', 'B'
j += 1
for i in a:
print(i, end = '')
|
28_B. pSort_10850
|
One day n cells of some array decided to play the following game. Initially each cell contains a number which is equal to it's ordinal number (starting from 1). Also each cell determined it's favourite number. On it's move i-th cell can exchange it's value with the value of some other j-th cell, if |i - j| = di, where di is a favourite number of i-th cell. Cells make moves in any order, the number of moves is unlimited.
The favourite number of each cell will be given to you. You will also be given a permutation of numbers from 1 to n. You are to determine whether the game could move to this state.
Input
The first line contains positive integer n (1 ≤ n ≤ 100) — the number of cells in the array. The second line contains n distinct integers from 1 to n — permutation. The last line contains n integers from 1 to n — favourite numbers of the cells.
Output
If the given state is reachable in the described game, output YES, otherwise NO.
Examples
Input
5
5 4 3 2 1
1 1 1 1 1
Output
YES
Input
7
4 3 5 1 2 7 6
4 6 6 1 6 6 1
Output
NO
Input
7
4 2 5 1 3 7 6
4 6 6 1 6 6 1
Output
YES
|
n=int(input())
a=list(map(int,input().split()))
b=list(map(int,input().split()))
c=[[] for i in range(n)]
for i in range(n):
if i-b[i]>=0:
c[i].append(i-b[i])
c[i-b[i]].append(i)
if i+b[i]<n:
c[i].append(i+b[i])
c[i+b[i]].append(i)
v=[1]*n
def dfs(u):
global v,c
v[u]=0
for i in c[u]:
if v[i]:
dfs(i)
for i in range(n):
v=[1]*n
dfs(a[i]-1)
if v[i]:
print('NO')
break
else:
print('YES')
|
{
"input": [
"7\n4 3 5 1 2 7 6\n4 6 6 1 6 6 1\n",
"5\n5 4 3 2 1\n1 1 1 1 1\n",
"7\n4 2 5 1 3 7 6\n4 6 6 1 6 6 1\n",
"80\n39 2 33 16 36 27 65 62 40 17 44 6 13 10 43 31 66 64 63 20 59 72 9 24 12 29 77 47 71 79 50 32 55 4 35 60 7 69 14 54 3 42 15 11 75 22 28 30 49 18 46 56 51 68 5 38 25 58 73 26 61 21 37 80 19 45 53 1 70 67 23 52 41 74 34 76 57 8 48 78\n6 23 42 42 13 72 14 45 66 76 74 44 49 10 14 64 17 15 4 68 14 34 42 56 50 65 17 52 15 26 1 42 27 22 6 52 25 47 76 45 48 67 18 44 74 48 62 58 59 79 13 5 12 14 5 13 51 21 57 59 49 43 8 34 7 16 34 29 38 74 40 72 18 46 47 43 2 4 17 1\n",
"1\n1\n1\n",
"68\n1 2 3 46 5 6 7 8 9 63 11 57 13 14 15 16 40 18 19 20 21 22 23 24 25 26 27 28 29 35 31 32 33 34 30 36 37 64 39 17 41 12 43 52 58 4 47 44 49 50 51 48 53 54 55 56 42 59 45 60 61 62 10 38 65 66 67 68\n13 48 67 55 4 39 47 8 4 35 50 28 28 30 63 60 52 29 2 33 48 57 40 43 25 34 62 50 60 5 3 66 32 15 7 51 51 26 47 23 67 30 27 53 40 42 5 4 60 67 11 4 31 10 62 46 45 13 14 13 24 66 53 25 22 60 14 42\n",
"17\n1 11 3 4 5 6 7 8 9 10 2 12 13 14 15 16 17\n13 9 16 5 16 12 11 4 4 7 12 16 2 7 14 6 3\n",
"2\n2 1\n2 2\n",
"2\n2 1\n1 1\n",
"76\n44 47 38 4 31 6 33 8 50 69 35 26 73 14 74 16 41 9 59 75 46 7 23 52 58 10 17 49 29 64 42 19 12 36 65 34 3 37 39 1 30 76 27 2 22 55 61 48 24 5 54 11 51 28 68 18 57 60 56 71 63 25 15 66 62 32 67 53 43 70 45 72 13 40 20 21\n54 63 9 55 65 59 4 1 42 31 63 5 28 26 19 35 50 21 39 23 40 64 45 36 74 74 70 67 53 20 19 27 13 2 71 62 6 51 2 65 61 58 55 55 32 75 54 75 48 45 40 45 7 43 72 75 54 9 32 52 8 36 33 59 57 58 68 32 71 21 63 69 7 40 28 68\n",
"10\n6 2 9 4 8 7 5 10 3 1\n2 9 7 9 4 5 1 5 3 2\n",
"2\n1 2\n1 1\n",
"13\n13 1 12 4 6 10 7 8 9 3 11 5 2\n6 12 12 7 11 7 10 3 1 5 2 2 1\n",
"19\n7 2 17 18 4 16 1 9 12 10 8 11 6 13 14 19 3 5 15\n12 4 9 1 13 18 14 10 18 2 17 16 12 3 16 6 5 7 7\n",
"71\n1 63 3 4 5 6 7 8 9 44 29 12 13 14 55 34 42 18 52 20 21 33 23 24 25 26 27 28 19 30 47 32 15 71 37 36 69 38 39 40 41 17 43 10 45 58 35 48 49 11 51 50 53 54 22 56 57 46 59 60 61 62 2 64 65 66 67 68 31 70 16\n21 45 8 62 56 53 25 22 65 34 39 43 30 63 18 18 25 10 31 64 70 33 49 70 34 21 69 25 21 4 38 41 4 36 4 28 6 48 6 25 57 11 62 48 62 69 12 14 12 70 41 2 49 30 40 37 67 12 13 22 50 35 61 42 33 30 10 47 10 65 37\n",
"4\n1 2 3 4\n1 1 1 1\n",
"50\n5 2 4 31 1 10 44 24 9 38 20 27 35 14 37 46 8 18 41 34 7 22 25 45 32 43 6 47 39 15 26 48 30 23 16 36 17 21 50 40 3 11 12 19 42 29 28 49 33 13\n27 15 18 20 19 23 49 18 28 32 29 2 16 23 23 2 17 25 27 43 32 31 11 3 49 46 22 44 14 48 35 15 32 35 2 49 10 22 5 36 49 16 43 46 33 11 31 15 45 23\n",
"8\n5 2 3 4 8 6 1 7\n6 7 7 7 7 7 2 7\n",
"2\n1 2\n2 2\n",
"52\n17 35 19 41 21 51 46 45 13 10 15 43 37 30 34 12 39 20 14 48 49 3 23 6 4 26 47 18 16 5 31 36 27 29 24 11 52 38 33 42 1 8 9 32 44 7 28 22 40 50 2 25\n47 6 50 13 49 22 17 18 3 11 2 43 35 8 25 38 19 41 17 5 7 8 10 51 17 30 34 48 41 8 46 10 11 45 15 28 42 32 37 33 43 31 38 13 43 19 32 19 2 47 42 46\n",
"82\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 59 17 18 19 20 21 22 23 24 25 26 27 28 29 61 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 16 60 30 79 63 64 65 66 67 68 69 70 71 72 73 74 75 76 82 78 62 80 81 77\n8 79 66 53 45 15 70 17 53 28 30 70 14 49 51 43 45 14 27 30 37 51 29 55 6 5 24 6 61 31 64 47 71 60 79 64 28 64 17 38 11 13 3 72 24 70 16 14 30 72 52 33 31 71 32 66 29 45 55 32 48 14 63 60 50 50 61 2 47 26 4 26 72 3 56 19 1 47 17 26 66 5\n",
"6\n3 2 1 4 6 5\n3 6 1 6 6 1\n",
"79\n1 2 3 67 5 6 7 60 9 71 63 12 31 57 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 64 32 79 34 35 45 37 38 39 40 41 42 43 44 36 46 47 48 11 50 51 52 74 54 55 56 14 58 59 8 61 62 49 13 65 66 4 68 72 70 10 69 73 53 75 76 77 78 33\n17 46 68 35 48 11 78 40 65 61 52 45 51 66 13 56 53 63 61 43 22 60 13 67 34 16 64 19 11 27 33 8 9 1 68 9 17 62 65 23 50 1 55 20 70 61 65 55 38 47 9 45 55 70 39 31 43 47 40 52 20 5 20 75 25 25 63 2 36 12 60 3 35 21 78 38 39 25 46\n",
"60\n1 2 17 4 27 6 43 26 32 10 11 12 29 14 15 16 3 44 56 20 21 22 53 24 25 8 5 28 58 7 31 9 33 57 48 36 37 38 39 30 41 50 40 35 45 46 13 18 47 55 51 52 23 54 42 19 34 49 59 60\n59 25 14 52 1 24 36 16 42 8 59 22 41 47 49 33 36 35 37 30 25 6 30 8 50 2 25 3 29 10 52 20 8 45 13 43 53 45 10 33 54 53 47 26 32 4 2 38 33 45 19 4 56 22 13 40 45 45 24 14\n",
"6\n3 5 1 4 6 2\n3 6 1 6 6 1\n",
"5\n1 3 2 4 5\n1 4 1 2 4\n",
"47\n1 32 29 9 47 6 8 36 37 10 11 16 2 14 38 40 15 44 19 35 18 22 23 12 17 41 5 31 26 25 4 27 33 34 42 7 24 28 45 20 46 13 43 30 21 3 39\n38 28 41 46 28 20 36 9 4 10 44 28 9 39 12 36 32 38 43 3 13 33 34 35 22 23 1 4 39 2 11 34 20 19 25 13 20 26 45 36 36 43 45 13 31 9 5\n",
"80\n39 2 33 16 36 27 65 62 40 17 44 6 13 10 43 31 66 64 63 20 59 72 9 24 12 29 77 47 71 79 50 32 55 4 35 60 7 69 14 54 3 42 15 11 75 22 28 30 49 18 46 23 51 68 5 38 25 58 73 26 61 21 37 80 19 45 53 1 70 67 23 52 41 74 34 76 57 8 48 78\n6 23 42 42 13 72 14 45 66 76 74 44 49 10 14 64 17 15 4 68 14 34 42 56 50 65 17 52 15 26 1 42 27 22 6 52 25 47 76 45 48 67 18 44 74 48 62 58 59 79 13 5 12 14 5 13 51 21 57 59 49 43 8 34 7 16 34 29 38 74 40 72 18 46 47 43 2 4 17 1\n",
"1\n1\n2\n",
"2\n2 1\n1 2\n",
"76\n44 47 38 4 31 6 33 8 50 69 35 26 73 14 74 16 41 9 59 75 46 7 23 52 58 10 17 49 29 64 42 19 12 36 65 34 3 37 39 1 30 76 27 2 22 55 61 48 24 5 54 11 51 28 68 18 57 60 56 71 63 25 15 66 62 32 67 53 43 70 45 72 13 40 20 21\n54 63 9 55 65 59 4 1 42 31 63 5 28 26 19 35 50 21 39 23 40 64 45 36 74 74 70 67 53 20 19 27 13 2 71 62 6 51 2 65 61 58 55 55 32 75 54 75 48 45 40 45 7 43 72 75 80 9 32 52 8 36 33 59 57 58 68 32 71 21 63 69 7 40 28 68\n",
"10\n6 2 9 4 8 7 5 10 3 1\n2 9 7 16 4 5 1 5 3 2\n",
"13\n13 1 12 4 6 10 7 8 9 3 4 5 2\n6 12 12 7 11 7 10 3 1 5 2 2 1\n",
"19\n7 2 17 18 4 16 1 9 12 10 8 11 6 13 14 19 4 5 15\n12 4 9 1 13 18 14 10 18 2 17 16 12 3 16 6 5 7 7\n",
"71\n1 63 3 4 5 6 7 8 9 44 29 12 13 14 55 34 42 18 52 20 21 33 23 24 25 26 27 28 19 30 47 32 15 71 37 36 69 38 39 40 41 17 43 10 45 58 35 48 49 11 51 50 53 54 22 56 57 46 59 60 61 62 2 64 65 66 67 68 31 70 16\n21 45 8 62 56 53 25 22 65 34 39 43 30 63 18 18 25 10 31 64 70 33 49 70 34 21 69 25 21 4 38 41 4 36 4 28 6 48 6 25 57 11 62 48 62 69 12 14 12 70 41 2 49 30 40 37 67 12 13 18 50 35 61 42 33 30 10 47 10 65 37\n",
"50\n5 2 4 31 1 10 44 24 9 38 20 27 35 14 37 46 8 18 41 34 7 22 25 45 32 43 6 47 39 15 26 48 30 23 16 36 17 21 50 40 3 11 12 19 42 29 28 49 33 13\n27 15 18 20 19 23 49 18 28 32 29 2 16 23 23 2 17 25 27 43 32 31 11 3 49 46 22 44 14 48 35 15 32 35 0 49 10 22 5 36 49 16 43 46 33 11 31 15 45 23\n",
"8\n5 2 3 4 8 6 1 7\n6 7 7 8 7 7 2 7\n",
"52\n17 35 19 41 21 51 46 45 13 10 15 43 37 30 15 12 39 20 14 48 49 3 23 6 4 26 47 18 16 5 31 36 27 29 24 11 52 38 33 42 1 8 9 32 44 7 28 22 40 50 2 25\n47 6 50 13 49 22 17 18 3 11 2 43 35 8 25 38 19 41 17 5 7 8 10 51 17 30 34 48 41 8 46 10 11 45 15 28 42 32 37 33 43 31 38 13 43 19 32 19 2 47 42 46\n",
"82\n1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 59 17 18 19 20 21 22 23 24 25 26 27 28 29 61 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 16 60 30 79 63 64 65 66 67 68 69 70 71 72 73 74 75 76 82 78 62 80 81 77\n8 79 66 53 45 15 70 17 53 28 30 70 14 49 51 43 45 14 27 30 37 51 29 55 6 5 24 6 61 31 64 47 71 60 79 64 28 64 17 38 11 13 3 72 24 87 16 14 30 72 52 33 31 71 32 66 29 45 55 32 48 14 63 60 50 50 61 2 47 26 4 26 72 3 56 19 1 47 17 26 66 5\n",
"60\n1 2 17 4 27 6 43 26 32 10 11 12 29 14 15 16 3 44 56 20 21 22 53 24 25 8 5 28 58 7 31 9 33 57 48 36 37 38 39 30 41 50 40 35 45 46 13 18 47 55 51 52 23 54 42 19 34 49 59 60\n59 25 14 52 1 24 36 16 42 8 59 22 41 47 49 33 36 35 37 30 25 6 30 8 50 2 25 3 29 10 52 20 8 45 13 43 53 45 10 33 54 53 47 26 32 4 2 38 33 45 19 4 56 22 1 40 45 45 24 14\n",
"6\n1 5 1 4 6 2\n3 6 1 6 6 1\n",
"5\n1 3 2 4 5\n1 4 1 3 4\n",
"47\n1 32 29 9 16 6 8 36 37 10 11 16 2 14 38 40 15 44 19 35 18 22 23 12 17 41 5 31 26 25 4 27 33 34 42 7 24 28 45 20 46 13 43 30 21 3 39\n38 28 41 46 28 20 36 9 4 10 44 28 9 39 12 36 32 38 43 3 13 33 34 35 22 23 1 4 39 2 11 34 20 19 25 13 20 26 45 36 36 43 45 13 31 9 5\n",
"7\n4 3 5 1 2 7 6\n4 6 6 1 11 6 1\n",
"80\n39 2 33 16 36 27 65 62 40 17 44 6 13 10 43 31 66 64 63 20 59 72 9 24 12 29 77 47 71 79 50 32 55 4 35 60 7 69 14 54 3 42 15 11 75 22 44 30 49 18 46 23 51 68 5 38 25 58 73 26 61 21 37 80 19 45 53 1 70 67 23 52 41 74 34 76 57 8 48 78\n6 23 42 42 13 72 14 45 66 76 74 44 49 10 14 64 17 15 4 68 14 34 42 56 50 65 17 52 15 26 1 42 27 22 6 52 25 47 76 45 48 67 18 44 74 48 62 58 59 79 13 5 12 14 5 13 51 21 57 59 49 43 8 34 7 16 34 29 38 74 40 72 18 46 47 43 2 4 17 1\n",
"76\n44 47 38 4 31 6 33 8 50 69 35 26 73 14 74 16 41 9 59 75 46 7 23 52 58 10 17 49 29 64 42 19 12 36 65 34 3 37 39 1 30 76 27 2 22 55 61 48 24 5 54 11 51 28 68 18 57 60 56 71 63 25 15 66 62 51 67 53 43 70 45 72 13 40 20 21\n54 63 9 55 65 59 4 1 42 31 63 5 28 26 19 35 50 21 39 23 40 64 45 36 74 74 70 67 53 20 19 27 13 2 71 62 6 51 2 65 61 58 55 55 32 75 54 75 48 45 40 45 7 43 72 75 80 9 32 52 8 36 33 59 57 58 68 32 71 21 63 69 7 40 28 68\n",
"10\n6 2 9 4 8 7 5 10 3 1\n2 9 7 16 4 5 1 3 3 2\n",
"13\n13 1 12 4 6 10 7 8 9 3 4 5 2\n6 12 12 7 11 7 10 3 1 5 2 1 1\n",
"19\n7 2 17 18 4 16 1 9 12 10 8 11 6 13 14 19 4 5 15\n12 4 9 1 13 18 14 10 18 2 17 16 12 3 16 6 5 7 14\n",
"71\n1 63 3 4 5 6 7 8 9 44 29 12 13 14 55 34 42 18 52 20 21 33 23 24 25 26 27 28 19 30 47 32 15 71 37 36 69 38 39 40 41 17 43 10 45 58 35 48 49 11 51 50 53 54 22 56 57 46 59 60 61 62 2 64 65 66 67 68 31 70 16\n21 45 8 62 56 53 25 28 65 34 39 43 30 63 18 18 25 10 31 64 70 33 49 70 34 21 69 25 21 4 38 41 4 36 4 28 6 48 6 25 57 11 62 48 62 69 12 14 12 70 41 2 49 30 40 37 67 12 13 18 50 35 61 42 33 30 10 47 10 65 37\n",
"50\n5 2 4 31 1 10 44 24 9 38 20 27 35 14 37 46 8 18 41 34 7 22 25 45 32 43 6 47 39 15 26 48 30 23 16 36 17 21 50 40 3 11 12 19 42 29 28 49 33 13\n27 15 18 20 19 23 49 18 28 32 29 2 16 23 23 2 17 25 27 43 32 31 11 3 49 46 22 44 14 48 35 15 32 35 -1 49 10 22 5 36 49 16 43 46 33 11 31 15 45 23\n",
"8\n5 2 3 4 8 6 1 7\n6 7 7 8 7 7 2 10\n",
"52\n17 35 19 41 21 51 46 45 13 10 15 43 37 30 15 12 39 20 14 48 49 3 23 6 4 26 47 18 16 5 31 36 27 29 24 11 52 38 33 42 1 8 9 32 44 7 28 22 40 50 2 25\n47 6 50 13 49 22 17 18 3 11 2 43 35 8 25 38 19 41 17 5 7 8 10 51 17 30 34 48 41 8 46 10 11 45 15 28 42 32 37 26 43 31 38 13 43 19 32 19 2 47 42 46\n",
"60\n1 2 17 4 27 6 43 26 32 10 11 12 29 14 15 16 3 44 56 20 21 22 53 24 25 8 5 28 58 7 31 9 33 57 48 36 37 38 39 30 41 50 40 35 45 46 13 18 47 55 51 52 23 54 42 19 34 49 59 60\n59 25 14 52 1 24 36 16 42 8 59 8 41 47 49 33 36 35 37 30 25 6 30 8 50 2 25 3 29 10 52 20 8 45 13 43 53 45 10 33 54 53 47 26 32 4 2 38 33 45 19 4 56 22 1 40 45 45 24 14\n",
"6\n1 5 1 4 6 1\n3 6 1 6 6 1\n",
"47\n1 32 29 9 16 6 8 36 37 10 11 16 2 14 38 40 15 44 19 35 18 22 23 12 17 41 5 31 26 25 4 27 33 34 42 7 24 28 45 20 46 13 43 30 21 3 39\n38 28 41 46 28 20 36 9 4 10 44 44 9 39 12 36 32 38 43 3 13 33 34 35 22 23 1 4 39 2 11 34 20 19 25 13 20 26 45 36 36 43 45 13 31 9 5\n",
"80\n39 2 33 16 36 27 65 62 40 17 44 6 13 10 43 31 66 64 63 20 59 72 9 24 12 29 77 47 71 79 50 32 55 4 35 60 7 69 14 54 3 42 15 11 75 22 44 30 49 18 46 23 51 68 5 38 25 58 73 26 61 21 37 80 19 45 53 1 70 67 23 52 41 74 34 76 57 8 48 78\n6 23 42 42 13 72 14 45 66 76 74 44 49 10 14 64 17 15 4 68 14 34 42 56 50 65 17 52 15 26 1 42 27 22 6 52 25 47 76 10 48 67 18 44 74 48 62 58 59 79 13 5 12 14 5 13 51 21 57 59 49 43 8 34 7 16 34 29 38 74 40 72 18 46 47 43 2 4 17 1\n",
"76\n44 47 38 4 31 6 33 8 41 69 35 26 73 14 74 16 41 9 59 75 46 7 23 52 58 10 17 49 29 64 42 19 12 36 65 34 3 37 39 1 30 76 27 2 22 55 61 48 24 5 54 11 51 28 68 18 57 60 56 71 63 25 15 66 62 51 67 53 43 70 45 72 13 40 20 21\n54 63 9 55 65 59 4 1 42 31 63 5 28 26 19 35 50 21 39 23 40 64 45 36 74 74 70 67 53 20 19 27 13 2 71 62 6 51 2 65 61 58 55 55 32 75 54 75 48 45 40 45 7 43 72 75 80 9 32 52 8 36 33 59 57 58 68 32 71 21 63 69 7 40 28 68\n",
"10\n6 2 9 4 8 7 5 10 3 1\n2 9 7 16 4 10 1 3 3 2\n",
"13\n13 1 12 4 6 10 7 8 9 3 4 5 2\n6 12 12 7 11 7 10 3 1 5 0 1 1\n",
"19\n7 2 17 18 4 16 1 9 12 10 8 11 6 13 14 19 4 5 15\n12 4 9 1 1 18 14 10 18 2 17 16 12 3 16 6 5 7 14\n",
"50\n5 2 4 31 1 10 44 24 9 38 20 27 35 14 37 46 8 18 41 34 7 22 25 45 32 43 6 47 19 15 26 48 30 23 16 36 17 21 50 40 3 11 12 19 42 29 28 49 33 13\n27 15 18 20 19 23 49 18 28 32 29 2 16 23 23 2 17 25 27 43 32 31 11 3 49 46 22 44 14 48 35 15 32 35 -1 49 10 22 5 36 49 16 43 46 33 11 31 15 45 23\n",
"52\n17 35 19 41 21 51 46 45 13 10 15 43 37 30 15 12 39 20 14 48 49 3 23 6 4 26 47 18 16 5 31 36 27 2 24 11 52 38 33 42 1 8 9 32 44 7 28 22 40 50 2 25\n47 6 50 13 49 22 17 18 3 11 2 43 35 8 25 38 19 41 17 5 7 8 10 51 17 30 34 48 41 8 46 10 11 45 15 28 42 32 37 26 43 31 38 13 43 19 32 19 2 47 42 46\n",
"6\n1 5 1 4 6 1\n3 6 1 6 6 0\n",
"47\n1 32 29 9 16 6 8 36 37 10 11 16 2 14 38 40 15 44 19 35 18 22 23 12 30 41 5 31 26 25 4 27 33 34 42 7 24 28 45 20 46 13 43 30 21 3 39\n38 28 41 46 28 20 36 9 4 10 44 44 9 39 12 36 32 38 43 3 13 33 34 35 22 23 1 4 39 2 11 34 20 19 25 13 20 26 45 36 36 43 45 13 31 9 5\n",
"80\n39 2 33 16 36 27 65 62 40 17 44 6 13 10 43 31 66 64 63 20 59 72 9 24 12 29 77 47 71 79 50 32 55 4 35 60 7 69 14 47 3 42 15 11 75 22 44 30 49 18 46 23 51 68 5 38 25 58 73 26 61 21 37 80 19 45 53 1 70 67 23 52 41 74 34 76 57 8 48 78\n6 23 42 42 13 72 14 45 66 76 74 44 49 10 14 64 17 15 4 68 14 34 42 56 50 65 17 52 15 26 1 42 27 22 6 52 25 47 76 10 48 67 18 44 74 48 62 58 59 79 13 5 12 14 5 13 51 21 57 59 49 43 8 34 7 16 34 29 38 74 40 72 18 46 47 43 2 4 17 1\n",
"76\n44 47 38 4 31 6 33 8 41 69 35 26 73 14 74 16 41 9 59 75 46 7 23 52 58 10 17 49 29 64 42 19 12 36 65 34 3 37 39 1 30 76 27 2 22 55 61 48 24 5 54 11 51 28 68 18 57 60 56 71 63 25 15 66 62 51 67 53 43 70 45 72 13 40 20 21\n54 63 9 55 65 59 4 1 42 31 63 5 38 26 19 35 50 21 39 23 40 64 45 36 74 74 70 67 53 20 19 27 13 2 71 62 6 51 2 65 61 58 55 55 32 75 54 75 48 45 40 45 7 43 72 75 80 9 32 52 8 36 33 59 57 58 68 32 71 21 63 69 7 40 28 68\n",
"19\n7 2 17 18 4 16 1 9 12 10 8 11 6 13 14 19 4 5 15\n12 4 11 1 1 18 14 10 18 2 17 16 12 3 16 6 5 7 14\n",
"50\n5 2 4 31 1 10 44 24 9 38 20 27 35 14 37 46 8 18 41 34 7 22 25 45 32 43 6 47 19 15 26 48 30 23 16 36 17 21 50 40 3 11 12 19 42 29 28 49 33 13\n27 15 18 20 19 23 55 18 28 32 29 2 16 23 23 2 17 25 27 43 32 31 11 3 49 46 22 44 14 48 35 15 32 35 -1 49 10 22 5 36 49 16 43 46 33 11 31 15 45 23\n",
"52\n17 35 19 41 21 51 46 45 13 10 15 43 37 30 15 12 39 20 14 48 49 3 23 6 4 26 47 18 16 5 31 36 27 2 24 11 52 38 33 42 1 8 9 32 44 7 28 22 40 50 2 25\n47 6 50 13 49 22 17 18 3 11 2 43 35 8 25 38 19 41 17 5 7 8 10 51 17 30 34 48 41 8 46 10 11 45 15 28 42 32 37 26 43 31 38 13 43 19 32 19 2 14 42 46\n",
"80\n39 2 33 16 36 27 65 62 40 1 44 6 13 10 43 31 66 64 63 20 59 72 9 24 12 29 77 47 71 79 50 32 55 4 35 60 7 69 14 47 3 42 15 11 75 22 44 30 49 18 46 23 51 68 5 38 25 58 73 26 61 21 37 80 19 45 53 1 70 67 23 52 41 74 34 76 57 8 48 78\n6 23 42 42 13 72 14 45 66 76 74 44 49 10 14 64 17 15 4 68 14 34 42 56 50 65 17 52 15 26 1 42 27 22 6 52 25 47 76 10 48 67 18 44 74 48 62 58 59 79 13 5 12 14 5 13 51 21 57 59 49 43 8 34 7 16 34 29 38 74 40 72 18 46 47 43 2 4 17 1\n",
"76\n44 47 38 4 31 6 33 8 41 69 35 26 73 14 74 6 41 9 59 75 46 7 23 52 58 10 17 49 29 64 42 19 12 36 65 34 3 37 39 1 30 76 27 2 22 55 61 48 24 5 54 11 51 28 68 18 57 60 56 71 63 25 15 66 62 51 67 53 43 70 45 72 13 40 20 21\n54 63 9 55 65 59 4 1 42 31 63 5 38 26 19 35 50 21 39 23 40 64 45 36 74 74 70 67 53 20 19 27 13 2 71 62 6 51 2 65 61 58 55 55 32 75 54 75 48 45 40 45 7 43 72 75 80 9 32 52 8 36 33 59 57 58 68 32 71 21 63 69 7 40 28 68\n",
"19\n7 2 17 18 4 16 1 9 12 10 8 11 2 13 14 19 4 5 15\n12 4 11 1 1 18 14 10 18 2 17 16 12 3 16 6 5 7 14\n",
"50\n5 2 4 31 1 10 44 24 9 38 20 27 35 14 37 46 8 18 41 34 7 22 25 45 32 43 6 47 19 15 31 48 30 23 16 36 17 21 50 40 3 11 12 19 42 29 28 49 33 13\n27 15 18 20 19 23 55 18 28 32 29 2 16 23 23 2 17 25 27 43 32 31 11 3 49 46 22 44 14 48 35 15 32 35 -1 49 10 22 5 36 49 16 43 46 33 11 31 15 45 23\n",
"52\n17 35 19 41 21 51 46 45 13 10 15 43 37 30 15 12 39 20 14 48 49 3 23 6 4 26 47 18 16 5 31 36 27 2 24 11 52 38 33 42 1 8 9 32 44 7 28 22 40 50 2 25\n47 6 50 0 49 22 17 18 3 11 2 43 35 8 25 38 19 41 17 5 7 8 10 51 17 30 34 48 41 8 46 10 11 45 15 28 42 32 37 26 43 31 38 13 43 19 32 19 2 14 42 46\n",
"80\n39 1 33 16 36 27 65 62 40 1 44 6 13 10 43 31 66 64 63 20 59 72 9 24 12 29 77 47 71 79 50 32 55 4 35 60 7 69 14 47 3 42 15 11 75 22 44 30 49 18 46 23 51 68 5 38 25 58 73 26 61 21 37 80 19 45 53 1 70 67 23 52 41 74 34 76 57 8 48 78\n6 23 42 42 13 72 14 45 66 76 74 44 49 10 14 64 17 15 4 68 14 34 42 56 50 65 17 52 15 26 1 42 27 22 6 52 25 47 76 10 48 67 18 44 74 48 62 58 59 79 13 5 12 14 5 13 51 21 57 59 49 43 8 34 7 16 34 29 38 74 40 72 18 46 47 43 2 4 17 1\n",
"76\n44 47 38 4 31 6 33 8 41 69 35 26 73 14 74 6 41 9 59 75 46 7 23 52 58 10 17 49 29 64 42 19 12 36 65 34 3 37 39 1 30 26 27 2 22 55 61 48 24 5 54 11 51 28 68 18 57 60 56 71 63 25 15 66 62 51 67 53 43 70 45 72 13 40 20 21\n54 63 9 55 65 59 4 1 42 31 63 5 38 26 19 35 50 21 39 23 40 64 45 36 74 74 70 67 53 20 19 27 13 2 71 62 6 51 2 65 61 58 55 55 32 75 54 75 48 45 40 45 7 43 72 75 80 9 32 52 8 36 33 59 57 58 68 32 71 21 63 69 7 40 28 68\n",
"19\n7 2 17 18 4 16 1 9 12 10 8 11 2 13 14 19 4 5 15\n12 4 11 1 1 18 14 10 26 2 17 16 12 3 16 6 5 7 14\n",
"50\n5 2 4 31 1 10 44 24 9 38 20 27 35 14 37 46 8 18 41 34 7 22 25 45 32 43 6 47 19 15 31 48 30 23 16 36 17 21 50 40 3 11 12 19 42 29 28 49 33 13\n27 15 18 20 19 23 55 18 28 27 29 2 16 23 23 2 17 25 27 43 32 31 11 3 49 46 22 44 14 48 35 15 32 35 -1 49 10 22 5 36 49 16 43 46 33 11 31 15 45 23\n",
"52\n17 35 19 41 21 51 46 45 13 10 15 43 37 30 15 12 39 20 14 48 49 3 23 6 4 26 47 18 16 5 31 36 27 2 24 11 52 38 33 42 1 8 9 32 44 7 28 22 40 50 2 25\n47 6 50 0 49 22 17 18 3 11 2 43 35 8 25 38 19 41 17 5 7 8 10 51 17 30 34 48 41 8 46 15 11 45 15 28 42 32 37 26 43 31 38 13 43 19 32 19 2 14 42 46\n",
"80\n39 1 33 16 36 27 65 62 40 1 44 6 13 10 43 31 66 64 63 20 59 72 9 24 12 29 77 47 71 79 50 32 55 4 35 60 7 69 14 47 3 42 15 11 75 22 44 30 49 18 46 23 51 68 5 38 25 58 73 26 61 21 37 80 19 45 53 1 70 67 23 52 41 74 34 76 57 8 48 78\n6 23 42 42 13 72 14 45 66 76 74 44 49 10 14 64 17 15 4 68 14 34 42 56 50 65 17 52 15 26 1 42 27 22 6 52 25 47 76 10 91 67 18 44 74 48 62 58 59 79 13 5 12 14 5 13 51 21 57 59 49 43 8 34 7 16 34 29 38 74 40 72 18 46 47 43 2 4 17 1\n",
"76\n44 47 38 4 31 6 33 8 41 69 35 26 73 14 74 6 41 9 21 75 46 7 23 52 58 10 17 49 29 64 42 19 12 36 65 34 3 37 39 1 30 26 27 2 22 55 61 48 24 5 54 11 51 28 68 18 57 60 56 71 63 25 15 66 62 51 67 53 43 70 45 72 13 40 20 21\n54 63 9 55 65 59 4 1 42 31 63 5 38 26 19 35 50 21 39 23 40 64 45 36 74 74 70 67 53 20 19 27 13 2 71 62 6 51 2 65 61 58 55 55 32 75 54 75 48 45 40 45 7 43 72 75 80 9 32 52 8 36 33 59 57 58 68 32 71 21 63 69 7 40 28 68\n",
"19\n7 2 17 18 4 16 1 9 12 10 8 11 2 13 14 19 4 5 15\n12 4 11 1 1 18 14 10 26 2 17 16 12 3 31 6 5 7 14\n",
"50\n5 2 4 31 1 10 44 24 9 38 20 27 35 14 37 46 8 18 41 34 7 22 25 45 32 43 6 47 19 15 31 48 30 23 16 36 17 21 50 40 3 11 12 19 42 29 28 49 33 13\n27 15 18 20 19 23 55 18 28 27 29 2 16 23 23 2 17 25 27 43 32 31 11 3 49 46 22 44 14 48 23 15 32 35 -1 49 10 22 5 36 49 16 43 46 33 11 31 15 45 23\n",
"52\n17 35 19 41 21 51 46 45 13 10 15 43 37 30 15 12 39 20 14 48 49 3 23 6 4 26 47 18 16 5 31 36 27 2 24 11 52 38 33 42 1 8 9 32 44 7 28 22 40 50 2 25\n47 6 50 0 49 22 17 18 3 11 2 43 35 8 25 38 19 41 17 5 7 8 10 51 17 30 34 48 41 8 46 15 11 45 15 28 42 32 37 26 5 31 38 13 43 19 32 19 2 14 42 46\n",
"80\n39 1 33 16 36 27 65 62 40 1 44 6 13 10 43 31 66 64 63 20 59 72 9 24 12 29 77 47 71 79 50 32 55 4 35 60 7 69 14 47 3 42 15 11 75 22 44 30 49 18 46 23 51 68 5 38 25 58 73 26 61 21 37 80 19 45 53 1 70 67 23 52 12 74 34 76 57 8 48 78\n6 23 42 42 13 72 14 45 66 76 74 44 49 10 14 64 17 15 4 68 14 34 42 56 50 65 17 52 15 26 1 42 27 22 6 52 25 47 76 10 91 67 18 44 74 48 62 58 59 79 13 5 12 14 5 13 51 21 57 59 49 43 8 34 7 16 34 29 38 74 40 72 18 46 47 43 2 4 17 1\n",
"19\n7 2 17 18 4 16 1 9 12 10 8 11 2 13 14 19 4 5 15\n12 5 11 1 1 18 14 10 26 2 17 16 12 3 31 6 5 7 14\n",
"50\n5 2 4 31 1 10 44 24 9 38 20 27 35 14 37 46 8 18 41 34 7 22 25 18 32 43 6 47 19 15 31 48 30 23 16 36 17 21 50 40 3 11 12 19 42 29 28 49 33 13\n27 15 18 20 19 23 55 18 28 27 29 2 16 23 23 2 17 25 27 43 32 31 11 3 49 46 22 44 14 48 23 15 32 35 -1 49 10 22 5 36 49 16 43 46 33 11 31 15 45 23\n",
"52\n17 35 19 41 21 51 46 45 13 10 15 43 37 30 15 12 39 20 14 48 49 3 23 6 4 26 47 18 16 5 31 36 27 2 24 11 52 38 33 42 1 8 9 32 44 7 28 22 40 50 1 25\n47 6 50 0 49 22 17 18 3 11 2 43 35 8 25 38 19 41 17 5 7 8 10 51 17 30 34 48 41 8 46 15 11 45 15 28 42 32 37 26 5 31 38 13 43 19 32 19 2 14 42 46\n",
"80\n39 1 33 16 36 27 65 62 40 1 44 6 13 10 43 31 66 64 63 20 59 72 9 24 12 29 77 47 71 79 50 32 55 4 35 60 7 69 14 47 3 42 15 11 75 22 44 30 49 18 46 23 51 68 5 38 25 58 73 26 61 21 37 80 19 45 53 1 70 67 23 52 12 74 34 76 57 8 48 78\n6 23 42 42 13 72 14 45 66 76 74 44 49 10 14 64 17 15 4 68 14 34 42 56 50 65 17 52 15 26 1 42 27 22 6 52 25 47 76 10 91 67 18 44 74 48 62 58 59 79 13 5 12 14 5 13 51 21 57 59 49 43 8 34 7 16 34 29 38 74 49 72 18 46 47 43 2 4 17 1\n",
"19\n7 2 17 18 4 16 1 9 12 10 8 11 2 13 14 19 4 5 15\n22 5 11 1 1 18 14 10 26 2 17 16 12 3 31 6 5 7 14\n",
"50\n5 2 4 31 1 10 44 24 9 38 20 27 35 14 37 46 8 18 41 34 7 22 25 18 32 43 6 47 19 15 31 48 30 23 16 36 17 21 50 40 2 11 12 19 42 29 28 49 33 13\n27 15 18 20 19 23 55 18 28 27 29 2 16 23 23 2 17 25 27 43 32 31 11 3 49 46 22 44 14 48 23 15 32 35 -1 49 10 22 5 36 49 16 43 46 33 11 31 15 45 23\n",
"52\n17 35 19 41 21 51 46 45 13 10 9 43 37 30 15 12 39 20 14 48 49 3 23 6 4 26 47 18 16 5 31 36 27 2 24 11 52 38 33 42 1 8 9 32 44 7 28 22 40 50 1 25\n47 6 50 0 49 22 17 18 3 11 2 43 35 8 25 38 19 41 17 5 7 8 10 51 17 30 34 48 41 8 46 15 11 45 15 28 42 32 37 26 5 31 38 13 43 19 32 19 2 14 42 46\n",
"80\n39 1 33 16 36 27 65 62 40 1 44 6 13 10 43 31 66 64 63 20 59 72 9 24 12 29 77 47 71 79 50 32 55 4 35 60 7 69 14 47 3 42 15 11 75 22 44 30 49 18 46 23 51 68 5 38 25 58 73 26 61 21 37 80 19 45 53 1 70 67 23 52 12 74 34 76 57 8 48 78\n6 23 42 42 13 72 14 45 66 76 74 44 49 10 14 64 17 15 4 68 14 34 42 56 50 65 17 52 15 26 1 42 27 22 6 52 25 47 76 10 91 67 18 44 74 48 62 58 59 79 13 5 12 14 5 13 51 21 57 59 49 43 8 34 7 16 34 55 38 74 49 72 18 46 47 43 2 4 17 1\n",
"19\n7 1 17 18 4 16 1 9 12 10 8 11 2 13 14 19 4 5 15\n22 5 11 1 1 18 14 10 26 2 17 16 12 3 31 6 5 7 14\n",
"50\n5 2 4 31 1 10 44 24 9 38 20 27 35 14 37 46 8 18 41 34 7 22 25 18 32 43 6 47 19 15 31 48 30 23 16 36 17 21 50 40 2 11 12 19 42 29 28 49 33 13\n27 15 18 20 19 23 55 18 28 27 29 2 16 23 23 2 17 25 27 43 32 31 11 3 49 46 22 44 14 27 23 15 32 35 -1 49 10 22 5 36 49 16 43 46 33 11 31 15 45 23\n",
"52\n17 7 19 41 21 51 46 45 13 10 9 43 37 30 15 12 39 20 14 48 49 3 23 6 4 26 47 18 16 5 31 36 27 2 24 11 52 38 33 42 1 8 9 32 44 7 28 22 40 50 1 25\n47 6 50 0 49 22 17 18 3 11 2 43 35 8 25 38 19 41 17 5 7 8 10 51 17 30 34 48 41 8 46 15 11 45 15 28 42 32 37 26 5 31 38 13 43 19 32 19 2 14 42 46\n"
],
"output": [
"NO\n",
"YES\n",
"YES\n",
"NO\n",
"YES\n",
"YES\n",
"YES\n",
"NO\n",
"YES\n",
"NO\n",
"YES\n",
"YES\n",
"NO\n",
"NO\n",
"YES\n",
"YES\n",
"NO\n",
"YES\n",
"YES\n",
"NO\n",
"YES\n",
"YES\n",
"YES\n",
"YES\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"YES\n",
"YES\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"YES\n",
"NO\n",
"YES\n",
"YES\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"YES\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n",
"NO\n"
]
}
| 2CODEFORCES
|
Below is a problem description that describes the problem. Write code in Python that appropriately solves the problem.
### Description:
One day n cells of some array decided to play the following game. Initially each cell contains a number which is equal to it's ordinal number (starting from 1). Also each cell determined it's favourite number. On it's move i-th cell can exchange it's value with the value of some other j-th cell, if |i - j| = di, where di is a favourite number of i-th cell. Cells make moves in any order, the number of moves is unlimited.
The favourite number of each cell will be given to you. You will also be given a permutation of numbers from 1 to n. You are to determine whether the game could move to this state.
Input
The first line contains positive integer n (1 ≤ n ≤ 100) — the number of cells in the array. The second line contains n distinct integers from 1 to n — permutation. The last line contains n integers from 1 to n — favourite numbers of the cells.
Output
If the given state is reachable in the described game, output YES, otherwise NO.
Examples
Input
5
5 4 3 2 1
1 1 1 1 1
Output
YES
Input
7
4 3 5 1 2 7 6
4 6 6 1 6 6 1
Output
NO
Input
7
4 2 5 1 3 7 6
4 6 6 1 6 6 1
Output
YES
### Input:
7
4 3 5 1 2 7 6
4 6 6 1 6 6 1
### Output:
NO
### Input:
5
5 4 3 2 1
1 1 1 1 1
### Output:
YES
### Code:
n=int(input())
a=list(map(int,input().split()))
b=list(map(int,input().split()))
c=[[] for i in range(n)]
for i in range(n):
if i-b[i]>=0:
c[i].append(i-b[i])
c[i-b[i]].append(i)
if i+b[i]<n:
c[i].append(i+b[i])
c[i+b[i]].append(i)
v=[1]*n
def dfs(u):
global v,c
v[u]=0
for i in c[u]:
if v[i]:
dfs(i)
for i in range(n):
v=[1]*n
dfs(a[i]-1)
if v[i]:
print('NO')
break
else:
print('YES')
|
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