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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.The definition of an 11/22 string in this problem is the same as in Problems C and E.\n\nA string T is called an 11/22 string when it satisfies all of the following conditions:\n\n- |T| is odd. Here, |T| denotes the length of T.\n- The 1-st through (\\frac{|T|+1}{2} - 1)-th characters are all 1.\n- The (\\frac{|T|+1}{2})-th character is /.\n- The (\\frac{|T|+1}{2} + 1)-th through |T|-th characters are all 2.\n\nFor example, 11/22, 111/222, and / are 11/22 strings, but 1122, 1/22, 11/2222, 22/11, and //2/2/211 are not.\nGiven a string S of length N consisting of 1, 2, and /, determine whether S is an 11/22 string.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\r\nS\n\nOutput\n\nIf S is an 11/22 string, print Yes; otherwise, print No.\n\nConstraints\n\n\n- 1 \\leq N \\leq 100\n- S is a string of length N consisting of 1, 2, and /.\n\nSample Input 1\n\n5\r\n11/22\n\nSample Output 1\n\nYes\r\n\n11/22 satisfies the conditions for an 11/22 string in the problem statement.\n\nSample Input 2\n\n1\r\n/\n\nSample Output 2\n\nYes\r\n\n/ satisfies the conditions for an 11/22 string.\n\nSample Input 3\n\n4\r\n1/22\n\nSample Output 3\n\nNo\r\n\n1/22 does not satisfy the conditions for an 11/22 string.\n\nSample Input 4\n\n5\r\n22/11\n\nSample Output 4\n\nNo",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.An integer sequence where no two adjacent elements are the same is called a good sequence.\nYou are given two good sequences of length N: A=(A_1,A_2,\\dots,A_N) and B=(B_1,B_2,\\dots,B_N). Each element of A and B is between 0 and M-1, inclusive.\nYou can perform the following operations on A any number of times, possibly zero:\n\n- Choose an integer i between 1 and N, inclusive, and perform one of the following:\n- Set A_i \\leftarrow (A_i + 1) \\bmod M.\n- Set A_i \\leftarrow (A_i - 1) \\bmod M. Here, (-1) \\bmod M = M - 1.\n\n\n\nHowever, you cannot perform an operation that makes A no longer a good sequence.\nDetermine if it is possible to make A equal to B, and if it is possible, find the minimum number of operations required to do so.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN M\nA_1 A_2 \\dots A_N\nB_1 B_2 \\dots B_N\n\nOutput\n\nIf the goal is unachievable, print -1.\nOtherwise, print the minimum number of operations required as an integer.\n\nConstraints\n\n\n- 2 \\leq N \\leq 2 \\times 10^5\n- 2 \\leq M \\leq 10^6\n- 0\\leq A_i,B_i< M(1\\leq i\\leq N)\n- A_i\\ne A_{i+1}(1\\leq i\\leq N-1)\n- B_i\\ne B_{i+1}(1\\leq i\\leq N-1)\n- All input values are integers.\n\nSample Input 1\n\n3 9\n2 0 1\n4 8 1\n\nSample Output 1\n\n3\n\nYou can achieve the goal in three operations as follows:\n\n- Set A_1 \\leftarrow (A_1 + 1) \\bmod M. Now A = (3, 0, 1).\n- Set A_2 \\leftarrow (A_2 - 1) \\bmod M. Now A = (3, 8, 1).\n- Set A_1 \\leftarrow (A_1 + 1) \\bmod M. Now A = (4, 8, 1).\n\nIt is impossible to achieve the goal in two or fewer operations, so the answer is 3.\nFor example, you cannot set A_2 \\leftarrow (A_2 + 1) \\bmod M in the first operation, because it would make A = (2, 1, 1), which is not a good sequence.\n\nSample Input 2\n\n3 9\n1 8 2\n1 8 2\n\nSample Output 2\n\n0\n\nA and B might be equal from the beginning.\n\nSample Input 3\n\n24 182\n128 115 133 52 166 92 164 119 143 99 54 162 86 2 59 166 24 78 81 5 109 67 172 99\n136 103 136 28 16 52 2 85 134 64 123 74 64 28 85 161 19 74 14 110 125 104 180 75\n\nSample Output 3\n\n811",
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|
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There is a graph with N + Q vertices, numbered 1, 2, \\ldots, N + Q. Initially, the graph has no edges.\nFor this graph, perform the following operation for i = 1, 2, \\ldots, Q in order:\n\n- For each integer j satisfying L_i \\leq j \\leq R_i, add an undirected edge with cost C_i between vertices N + i and j.\n\nDetermine if the graph is connected after all operations are completed. If it is connected, find the cost of a minimum spanning tree of the graph.\nA minimum spanning tree is a spanning tree with the smallest possible cost, and the cost of a spanning tree is the sum of the costs of the edges used in the spanning tree.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN Q\r\nL_1 R_1 C_1\r\nL_2 R_2 C_2\r\n\\vdots\r\nL_Q R_Q C_Q\n\nOutput\n\nIf the graph is connected, print the cost of a minimum spanning tree. Otherwise, print -1.\n\nConstraints\n\n\n- 1 \\leq N, Q \\leq 2 \\times 10^5\n- 1 \\leq L_i \\leq R_i \\leq N\n- 1 \\leq C_i \\leq 10^9\n- All input values are integers.\n\nSample Input 1\n\n4 3\r\n1 2 2\r\n1 3 4\r\n2 4 5\n\nSample Output 1\n\n22\r\n\nThe following edges form a minimum spanning tree:\n\n- An edge with cost 2 connecting vertices 1 and 5\n- An edge with cost 2 connecting vertices 2 and 5\n- An edge with cost 4 connecting vertices 1 and 6\n- An edge with cost 4 connecting vertices 3 and 6\n- An edge with cost 5 connecting vertices 3 and 7\n- An edge with cost 5 connecting vertices 4 and 7\n\nSince 2 + 2 + 4 + 4 + 5 + 5 = 22, print 22.\n\nSample Input 2\n\n6 2\r\n1 2 10\r\n4 6 10\n\nSample Output 2\n\n-1\r\n\nThe graph is disconnected.\n\nSample Input 3\n\n200000 4\r\n1 200000 1000000000\r\n1 200000 998244353\r\n1 200000 999999999\r\n1 200000 999999999\n\nSample Output 3\n\n199651870599998",
"role": "user"
}
] |
{
"do_sample": false,
"max_new_tokens": 32768,
"seed": 1,
"temperature": 0.7
}
| 1 | 44 |
LiveCodeBenchV5
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{
"expected_answer": "",
"problem_id": "",
"reference_solution": ""
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|
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
|
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given three integers n, x, and y.\nAn event is being held for n performers. When a performer arrives, they are assigned to one of the x stages. All performers assigned to the same stage will perform together as a band, though some stages might remain empty.\nAfter all performances are completed, the jury will award each band a score in the range [1, y].\nReturn the total number of possible ways the event can take place.\nSince the answer may be very large, return it modulo 10^9 + 7.\nNote that two events are considered to have been held differently if either of the following conditions is satisfied:\n\nAny performer is assigned a different stage.\nAny band is awarded a different score.\n\n \nExample 1:\n\nInput: n = 1, x = 2, y = 3\nOutput: 6\nExplanation:\n\nThere are 2 ways to assign a stage to the performer.\nThe jury can award a score of either 1, 2, or 3 to the only band.\n\n\nExample 2:\n\nInput: n = 5, x = 2, y = 1\nOutput: 32\nExplanation:\n\nEach performer will be assigned either stage 1 or stage 2.\nAll bands will be awarded a score of 1.\n\n\nExample 3:\n\nInput: n = 3, x = 3, y = 4\nOutput: 684\n\n \nConstraints:\n\n1 <= n, x, y <= 1000",
"role": "user"
}
] |
{
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
}
| 2 | 330 |
LiveCodeBenchV5
|
{
"expected_answer": "",
"problem_id": "",
"reference_solution": ""
}
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There is a grid with H rows and W columns.\r\nLet (i,j) denote the cell at the i-th row from the top and the j-th column from the left.\nThere are N horizontal bars numbered from 1 to N placed on the grid.\r\nBar i consists of L_i blocks of size 1 \\times 1 connected horizontally, and its leftmost block is initially at cell (R_i, C_i).\r\nThat is, initially, bar i occupies the cells (R_i, C_i), (R_i, C_i + 1), \\dots, (R_i, C_i + L_i - 1).\r\nIt is guaranteed that there is no cell occupied by two different bars.\nThe current time is t = 0.\r\nAt every time t = 0.5 + n for some non-negative integer n, the following occurs in order of i = 1, 2, \\dots, N:\n\n- If bar i is not on the bottom row (the H-th row), and none of the cells directly below the cells occupied by bar i is occupied by any bar, then bar i moves down by one cell. That is, if at that time bar i occupies the cells (r,C_i),(r,C_i+1),\\dots,(r,C_i+L_i-1)\\ (r < H), and the cell (r + 1, C_i + j) is not occupied by any bar for all j (0 \\leq j \\leq L_i - 1), then bar i now occupies (r + 1, C_i), (r + 1, C_i + 1), \\dots, (r + 1, C_i + L_i - 1).\n- Otherwise, nothing happens.\n\nLet (R'_i, C_i), (R'_i, C_i + 1), \\dots, (R'_i, C_i + L_i - 1) be the cells occupied by bar i at time t = 10^{100}. Find R'_1, R'_2, \\dots, R'_N.\n\nInput\n\nThe input is given from Standard Input in the following format:\nH W N\r\nR_1 C_1 L_1\r\nR_2 C_2 L_2\r\n\\vdots\r\nR_N C_N L_N\n\nOutput\n\nPrint N lines.\r\nThe i-th line (1 \\leq i \\leq N) should contain R'_i.\n\nConstraints\n\n\n- 1 \\leq H, W \\leq 2 \\times 10^5\n- 1 \\leq N \\leq 2 \\times 10^5\n- 1 \\leq R_i \\leq H\n- 1 \\leq C_i \\leq W\n- 1 \\leq L_i \\leq W - C_i + 1\n- In the initial state, there is no cell occupied by two different bars.\n- All input values are integers.\n\nSample Input 1\n\n4 4 4\r\n1 2 3\r\n3 2 2\r\n2 1 2\r\n2 4 1\n\nSample Output 1\n\n2\r\n4\r\n3\r\n4\r\n\nThe following three diagrams represent the grid at times t = 0, 1, and 2 from left to right.\r\nColored rectangles represent the bars, and the number inside each rectangle indicates its bar number.\n\nThe changes in the grid state are explained as follows:\n\n- At t = 0.5:\n- i = 1: The cells directly below bar 1 are (2,2),(2,3),(2,4). Among these, (2,2) is occupied by bar 3 and (2,4) is occupied by bar 4, so nothing happens.\n- i = 2: The cells directly below bar 2 are (4,2),(4,3), which are not occupied by any other bar, so bar 2 moves down by one cell.\n- i = 3: The cells directly below bar 3 are (3,1),(3,2), which are not occupied by any other bar, so bar 3 moves down by one cell.\n- i = 4: The cell directly below bar 4 is (3,4), which is not occupied by any other bar, so bar 4 moves down by one cell.\n\n\n- At t = 1.5:\n- i = 1: The cells directly below bar 1 are (2,2),(2,3),(2,4), which are not occupied by any other bar, so bar 1 moves down by one cell.\n- i = 2: Bar 2 is on the bottom row, so nothing happens.\n- i = 3: The cells directly below bar 3 are (4,1),(4,2). Among these, (4,2) is occupied by bar 2, so nothing happens.\n- i = 4: The cell directly below bar 4 is (4,4), which is not occupied by any other bar, so bar 4 moves down by one cell.\n\n\n\nAt times t = 2.5, 3.5, \\dots, there is no bar such that the cells directly below it are all unoccupied, so nothing happens. Thus, the grid at time t = 10^{100} is the same as at t = 2 (the rightmost diagram above).\nTherefore, R'_1 = 2, R'_2 = 4, R'_3 = 3, R'_4 = 4.\n\nSample Input 2\n\n382 382 3\r\n3 3 3\r\n8 8 8\r\n2 2 2\n\nSample Output 2\n\n382\r\n382\r\n381\n\nSample Input 3\n\n5 10 8\r\n2 2 1\r\n4 3 1\r\n4 8 2\r\n1 2 2\r\n2 5 3\r\n5 4 3\r\n4 5 2\r\n1 5 2\n\nSample Output 3\n\n5\r\n5\r\n5\r\n4\r\n3\r\n5\r\n4\r\n2",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.We call a positive integer n a good integer if and only if the sum of its positive divisors is divisible by 3.\nYou are given two positive integers N and M. Find the number, modulo 998244353, of length-M sequences A of positive integers such that the product of the elements in A is a good integer not exceeding N.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN M\n\nOutput\n\nPrint the answer.\n\nConstraints\n\n\n- 1 \\leq N \\leq 10^{10}\n- 1 \\leq M \\leq 10^5\n- N and M are integers.\n\nSample Input 1\n\n10 1\n\nSample Output 1\n\n5\n\nThere are five sequences that satisfy the conditions:\n\n- (2)\n- (5)\n- (6)\n- (8)\n- (10)\n\nSample Input 2\n\n4 2\n\nSample Output 2\n\n2\n\nThere are two sequences that satisfy the conditions:\n\n- (1, 2)\n- (2, 1)\n\nSample Input 3\n\n370 907\n\nSample Output 3\n\n221764640\n\nSample Input 4\n\n10000000000 100000\n\nSample Output 4\n\n447456146",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Mr. Ball and Mr. Box will play a game with balls and boxes.\nInitially, Mr. Ball has 10^{100} balls of each of M different types, and Mr. Box has 10^{100} yen.\nThere are N boxes, where the i-th box has capacity V_i and costs P_i yen. During the game, Mr. Box can buy any box at any time.\nIn this game, the following operations are repeated until the game ends:\n\n- Mr. Ball chooses one ball and gives it to Mr. Box.\n- Mr. Box either accepts the ball or ends the game without accepting it.\n- If Mr. Box accepts the ball, he chooses one of his purchased boxes and puts the ball in it.\n- If the box with the ball satisfies the following conditions, Mr. Box receives 1 yen. Otherwise, the game ends.\n- The number of balls in the box does not exceed its capacity.\n- All balls in the box are of the same type.\n\n\n\nMr. Ball will play optimally to minimize Mr. Box's final money, while Mr. Box will play optimally to maximize it.\nHow much will Mr. Box's money increase throughout the game?\nHere, both players have access to all information. In particular, Mr. Ball can see the capacity, price, and contents (type and number of balls) of each box.\nAlso, note that Mr. Box's initial money is large enough that he will never run out of money to buy boxes.\nSolve T test cases for each input file.\n\nInput\n\nThe input is given from Standard Input in the following format, where \\mathrm{case}_i represents the i-th test case:\nT\n\\mathrm{case}_1\n\\mathrm{case}_2\n\\vdots\n\\mathrm{case}_T\n\nEach test case is given in the following format:\nN M\nV_1 P_1\nV_2 P_2\n\\vdots\nV_N P_N\n\nOutput\n\nPrint the difference between Mr. Box's final and initial money when both players play optimally.\n\nConstraints\n\n\n- 1\\le T,N,M\\le 3\\times 10^5\n- 1\\le V_i,P_i \\le 10^9\n- The sum of N over the T test cases is at most 3\\times 10^5.\n- All input values are integers.\n\nSample Input 1\n\n3\n3 2\n1 1000000000\n3 1\n3 1\n1 300000\n1000000000 1\n10 4\n22 5\n26 45\n72 21\n47 39\n97 2\n75 35\n82 24\n17 46\n32 22\n28 67\n\nSample Output 1\n\n2\n0\n28\n\nIn the first test case, there are two types of balls and three boxes.\nLet us call the two types of balls white and black balls, and call the i-th box box i.\nHere is an example of how the game could proceed where the money increases by 2 yen.\n\n- Mr. Ball chooses and gives a white ball.\n- Mr. Box accepts the ball, buys box 2 for 1 yen, and puts the white ball in it.\n- Box 2 contains 1 white ball. This satisfies the conditions, so Mr. Box receives 1 yen.\n\n\n- Mr. Ball chooses and gives a white ball.\n- Mr. Box accepts the ball and puts it in box 2.\n- Box 2 contains 2 white balls. This satisfies the conditions, so Mr. Box receives 1 yen.\n\n\n- Mr. Ball chooses and gives a black ball.\n- Mr. Box accepts the ball, buys box 3 for 1 yen, and puts the black ball in it.\n- Box 3 contains 1 black ball. This satisfies the conditions, so Mr. Box receives 1 yen.\n\n\n- Mr. Ball chooses and gives a white ball.\n- Mr. Box accepts the ball and puts it in box 2.\n- Box 2 contains 3 white balls. This satisfies the conditions, so Mr. Box receives 1 yen.\n\n\n- Mr. Ball chooses and gives a white ball.\n- Mr. Box chooses to end the game without accepting it.\n\nFinally, box 2 contains 3 white balls and box 3 contains 1 black ball.\nMr. Box spent 2 yen and received 4 yen, so his money increased by 2 yen.\nIn the second test case, Mr. Ball can play in a way that prevents Mr. Box from earning any money.",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There is a village with N villagers numbered from 1 to N.\nEach villager is honest or a liar. Additionally, some villagers are confused.\nYou have obtained M testimonies from the villagers. Each testimony is given by A_i, B_i, C_i for i=1,2,\\ldots,M, representing:\n\n- If C_i=0, villager A_i testified that villager B_i is honest.\n- If C_i=1, villager A_i testified that villager B_i is a liar.\n\nAll villagers know whether every other villager is honest or a liar, and you know that they made their testimonies to you according to the following rules:\n\n- An honest villager who is not confused always tells the truth.\n- A liar who is not confused always tells lies.\n- A confused honest villager always tells lies.\n- A confused liar always tells the truth.\n\nIn other words, if they are not confused, honest villagers always tell the truth, and liars always tell lies, but if they are confused, it is reversed.\nYou have decided to guess the set of villagers who are confused.\nGiven a choice of villagers who are confused, whether the set of testimonies \"contradicts\" or not is determined.\nHere, a set of testimonies is said to contradict if, no matter how you assign honest or liar statuses to the villagers, there is at least one testimony that violates the villagers' testimony rules.\nFind a set of confused villagers such that the given set of testimonies does not contradict.\nIf no such set of confused villagers exists, indicate that fact.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN M\nA_1 B_1 C_1\nA_2 B_2 C_2\n\\vdots\nA_M B_M C_M\n\nOutput\n\nIf there exists a set of confused villagers such that the given set of testimonies does not contradict, print a string of length N representing the set of confused villagers. In this string, the i-th character should be 1 if villager i is confused, and 0 otherwise.\nIf no such set of confused villagers exists, print -1.\n\nConstraints\n\n\n- 2 \\leq N \\leq 2 \\times 10^5\n- 0 \\leq M \\leq \\mathrm{min} \\lbrace 2 \\times 10^5,N(N-1) \\rbrace \n- 1 \\leq A_i, B_i \\leq N, A_i \\neq B_i\n- A_i \\neq A_j or B_i \\neq B_j for i \\neq j.\n- C_i = 0 or 1.\n- All input values are integers.\n\nSample Input 1\n\n3 3\n1 2 1\n1 3 0\n2 3 0\n\nSample Output 1\n\n010\n\nSuppose villager 1 is an honest villager who is not confused, villager 2 is a confused liar, and villager 3 is an honest villager who is not confused.\nIn this case, villager 1 correctly testifies that villager 2 is a liar and villager 3 is honest.\nAlso, villager 2, who is a liar but confused, tells the truth and testifies that villager 3 is honest.\nTherefore, all given testimonies are consistent with the villagers' testimony rules, so 010, indicating that only villager 2 is confused, is one valid output.\n\nSample Input 2\n\n3 6\n1 2 1\n1 3 0\n2 1 1\n2 3 0\n3 1 1\n3 2 0\n\nSample Output 2\n\n-1\n\nSuppose villagers 2 and 3 are confused.\nIn this case, there are 2^3=8 possible combinations for whether each villager is honest or a liar.\nAmong them, for example, if villager 1 is an honest villager who is not confused, villager 2 is a confused liar, and villager 3 is a confused honest villager, then according to the rules, villager 2 should tell the truth, but they falsely testify that villager 1 is a liar.\nYou can confirm that also in other combinations, there will be some testimonies that violate the rules.\nTherefore, if villagers 2 and 3 are confused, the given set of testimonies contradicts.\nIn fact, in this test case, no matter which villagers are confused, the given set of testimonies contradicts.\n\nSample Input 3\n\n3 0\n\nSample Output 3\n\n000\n\nThere may be any number of confused villagers, possibly zero or all.",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Note: This problem has almost the same setting as Problem F. Only the parts in bold in the main text and constraints differ.\nYou are holding a ring with both hands.\nThis ring consists of N\\ (N \\geq 3) parts numbered 1,2,\\dots,N, where parts i and i+1 (1 \\leq i \\leq N-1) are adjacent, and parts 1 and N are also adjacent.\nInitially, your left hand is holding part 1, and your right hand is holding part 2.\nIn one operation, you can do the following:\n\n- Move one of your hands to an adjacent part of the part it is currently holding. However, you can do this only if the other hand is not on the destination part.\n\nThe following figure shows the initial state and examples of operations that can and cannot be made from there. The number written on each part of the ring represents the part number, and the circles labeled L and R represent your left and right hands, respectively.\n\nYou need to follow Q instructions given to you in order.\nThe i-th (1 \\leq i \\leq Q) instruction is represented by a character H_i and an integer T_i, meaning the following:\n\n- Perform some number of operations (possibly zero) so that your left hand (if H_i is L) or your right hand (if H_i is R) is holding part T_i.\n Here, you must not move the other hand not specified by H_i.\n\nIt is guaranteed that only achievable instructions are given.\n\nDetails\nUnder the settings of this problem, it can be proved that the positions of both hands are uniquely determined just before following the i-th instruction for each i.\nAt that time, if we denote the positions of the left and right hands as parts l_i and r_i, respectively, it is guaranteed that T_i \\neq r_i when H_i is L, and T_i \\neq l_i when H_i is R.\n\n\nFind the minimum total number of operations required to follow all the instructions.\n\nInput\n\nThe Input is given from Standard Input in the following format:\nN Q\nH_1 T_1\nH_2 T_2\n\\vdots\nH_Q T_Q\n\nOutput\n\nPrint the minimum total number of operations required to follow all the instructions.\n\nConstraints\n\n\n- 3 \\leq N \\leq 100\n- 1 \\leq Q \\leq 100\n- H_i is L or R.\n- 1 \\leq T_i \\leq N\n- N, Q, and T_i are integers.\n- Only achievable instructions are given (see the problem statement for details).\n\nSample Input 1\n\n6 3\nR 4\nL 5\nR 6\n\nSample Output 1\n\n8\n\n\nBy performing the following operations, you can follow all Q instructions in order.\n\n- Move your right hand as part 2 \\rightarrow 3 \\rightarrow 4 to follow the first instruction.\n- Move your left hand as part 1 \\rightarrow 6 \\rightarrow 5 to follow the second instruction.\n- Move your right hand as part 4 \\rightarrow 3 \\rightarrow 2 \\rightarrow 1 \\rightarrow 6 to follow the third instruction.\n\nIn this case, the total number of operations is 2+2+4=8, which is the minimum.\n(Note that when following the third instruction, you cannot move your right hand as part 4 \\rightarrow 5 \\rightarrow 6.)\n\nSample Input 2\n\n100 2\nL 1\nR 2\n\nSample Output 2\n\n0\n\nThere are cases where you can follow the instructions without performing any operations.\n\nSample Input 3\n\n30 8\nR 23\nR 26\nR 29\nL 20\nR 29\nR 19\nL 7\nL 16\n\nSample Output 3\n\n92",
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"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given an array nums consisting of n prime integers.\nYou need to construct an array ans of length n, such that, for each index i, the bitwise OR of ans[i] and ans[i] + 1 is equal to nums[i], i.e. ans[i] OR (ans[i] + 1) == nums[i].\nAdditionally, you must minimize each value of ans[i] in the resulting array.\nIf it is not possible to find such a value for ans[i] that satisfies the condition, then set ans[i] = -1.\n \nExample 1:\n\nInput: nums = [2,3,5,7]\nOutput: [-1,1,4,3]\nExplanation:\n\nFor i = 0, as there is no value for ans[0] that satisfies ans[0] OR (ans[0] + 1) = 2, so ans[0] = -1.\nFor i = 1, the smallest ans[1] that satisfies ans[1] OR (ans[1] + 1) = 3 is 1, because 1 OR (1 + 1) = 3.\nFor i = 2, the smallest ans[2] that satisfies ans[2] OR (ans[2] + 1) = 5 is 4, because 4 OR (4 + 1) = 5.\nFor i = 3, the smallest ans[3] that satisfies ans[3] OR (ans[3] + 1) = 7 is 3, because 3 OR (3 + 1) = 7.\n\n\nExample 2:\n\nInput: nums = [11,13,31]\nOutput: [9,12,15]\nExplanation:\n\nFor i = 0, the smallest ans[0] that satisfies ans[0] OR (ans[0] + 1) = 11 is 9, because 9 OR (9 + 1) = 11.\nFor i = 1, the smallest ans[1] that satisfies ans[1] OR (ans[1] + 1) = 13 is 12, because 12 OR (12 + 1) = 13.\nFor i = 2, the smallest ans[2] that satisfies ans[2] OR (ans[2] + 1) = 31 is 15, because 15 OR (15 + 1) = 31.\n\n\n \nConstraints:\n\n1 <= nums.length <= 100\n2 <= nums[i] <= 1000\nnums[i] is a prime number.",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Note: This problem has almost the same setting as Problem B. Only the parts in bold in the main text and constraints differ.\nYou are holding a ring with both hands.\nThis ring consists of N\\ (N \\geq 3) parts numbered 1,2,\\dots,N, where parts i and i+1 (1 \\leq i \\leq N-1) are adjacent, and parts 1 and N are also adjacent.\nInitially, your left hand is holding part 1, and your right hand is holding part 2.\nIn one operation, you can do the following:\n\n- Move one of your hands to an adjacent part of the part it is currently holding. However, you can do this only if the other hand is not on the destination part.\n\nThe following figure shows the initial state and examples of operations that can and cannot be made from there. The number written on each part of the ring represents the part number, and the circles labeled L and R represent your left and right hands, respectively.\n\nYou need to follow Q instructions given to you in order.\nThe i-th (1 \\leq i \\leq Q) instruction is represented by a character H_i and an integer T_i, meaning the following:\n\n- Perform some number of operations (possibly zero) so that your left hand (if H_i is L) or your right hand (if H_i is R) is holding part T_i.\n Here, you may move the other hand not specified by H_i.\n\nUnder the settings and constraints of this problem, it can be proved that any instructions are achievable.\nFind the minimum total number of operations required to follow all the instructions.\n\nInput\n\nThe Input is given from Standard Input in the following format:\nN Q\nH_1 T_1\nH_2 T_2\n\\vdots\nH_Q T_Q\n\nOutput\n\nPrint the minimum total number of operations required to follow all the instructions.\n\nConstraints\n\n\n- 3\\leq N \\leq 3000\n- 1\\leq Q \\leq 3000\n- H_i is L or R.\n- 1 \\leq T_i \\leq N\n- N, Q, and T_i are integers.\n\nSample Input 1\n\n6 3\nR 4\nL 5\nR 5\n\nSample Output 1\n\n6\n\n\nBy performing the following operations, you can follow all Q instructions in order.\n\n- Move your right hand as part 2 \\rightarrow 3 \\rightarrow 4 to follow the first instruction.\n- Move your left hand as part 1 \\rightarrow 6 \\rightarrow 5 to follow the second instruction.\n- Move your left hand as part 5 \\rightarrow 6, then move your right hand as part 4 \\rightarrow 5 to follow the third instruction.\n\nIn this case, the total number of operations is 2+2+1+1=6, which is the minimum.\n\nSample Input 2\n\n100 2\nL 1\nR 2\n\nSample Output 2\n\n0\n\nThere are cases where you can follow the instructions without performing any operations.\n\nSample Input 3\n\n30 8\nR 23\nR 26\nR 29\nL 20\nR 29\nR 19\nL 7\nL 16\n\nSample Output 3\n\n58",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given a permutation P of (1,2,\\dots,N) and an integer K. \nFind the expected value, modulo 998244353, of the inversion number of P after performing the following operation:\n\n- First, choose an integer i uniformly at random between 1 and N - K + 1, inclusive.\n- Then, shuffle P_i, P_{i+1}, \\dots, P_{i+K-1} uniformly at random.\n\n\nWhat is the inversion number?\r\nThe inversion number of a sequence (A_1, A_2, \\dots, A_N) is the number of integer pairs (i, j) satisfying 1 \\le i < j \\le N and A_i > A_j.\r\n\n\nWhat does \"expected value modulo 998244353\" mean?\r\nIt can be proved that the sought expected value is always rational. Under the constraints of this problem, when this value is represented as an irreducible fraction \\frac{P}{Q}, it can also be proved that Q \\not\\equiv 0 \\pmod{998244353}. Thus, there is a unique integer R satisfying R \\times Q \\equiv P \\pmod{998244353}, \\ 0 \\le R < 998244353. Report this integer R.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN K\r\nP_1 P_2 \\dots P_N\n\nOutput\n\nPrint the answer in one line.\n\nConstraints\n\n\n- All input values are integers.\n- 1 \\le K \\le N \\le 2 \\times 10^5\n- P is a permutation of (1,2,\\dots,N).\n\nSample Input 1\n\n4 2\r\n1 4 2 3\n\nSample Output 1\n\n166374061\r\n\nThe operation changes the permutation P into the following:\n\n- (1,4,2,3) ... probability 1/2\n- (4,1,2,3) ... probability 1/6\n- (1,2,4,3) ... probability 1/6\n- (1,4,3,2) ... probability 1/6\n\nThe expected value of the inversion number is \\displaystyle 2 \\times \\frac{1}{2} + 3 \\times \\frac{1}{6} + 1 \\times \\frac{1}{6} + 3 \\times \\frac{1}{6} = \\frac{13}{6}.\n\\displaystyle \\frac{13}{6} modulo 998244353 is 166374061, so print this number.\n\nSample Input 2\n\n1 1\r\n1\n\nSample Output 2\n\n0\n\nSample Input 3\n\n10 6\r\n7 4 10 5 6 1 8 2 3 9\n\nSample Output 3\n\n499122200",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There is a grid with H rows and W columns. Let (i,j) denote the cell at the i-th row from the top and the j-th column from the left.\nIf S_{i,j} is #, the cell (i,j) is impassable; if it is ., the cell is passable and contains no house; if it is @, the cell is passable and contains a house.\nInitially, Santa Claus is in cell (X,Y). He will act according to the string T as follows.\n\n- Let |T| be the length of the string T. For i=1,2,\\ldots,|T|, he moves as follows.\n- Let (x,y) be the cell he is currently in.\n- If T_i is U and cell (x-1,y) is passable, move to cell (x-1,y).\n- If T_i is D and cell (x+1,y) is passable, move to cell (x+1,y).\n- If T_i is L and cell (x,y-1) is passable, move to cell (x,y-1).\n- If T_i is R and cell (x,y+1) is passable, move to cell (x,y+1).\n- Otherwise, stay in cell (x,y).\n\n\n\n\n\nFind the cell where he is after completing all actions, and the number of distinct houses that he passed through or arrived at during his actions. If the same house is passed multiple times, it is only counted once.\n\nInput\n\nThe Input is given from Standard Input in the following format:\nH W X Y\nS_{1,1}S_{1,2}\\ldots S_{1,W}\n\\dots\nS_{H,1}S_{H,2}\\ldots S_{H,W}\nT\n\nOutput\n\nLet (X,Y) be the cell where he is after completing all actions, and C be the number of distinct houses he passed through or arrived at during his actions. Print X,Y,C in this order separated by spaces.\n\nConstraints\n\n\n- 3 \\leq H,W \\leq 100\n- 1 \\leq X \\leq H\n- 1 \\leq Y \\leq W\n- All given numbers are integers.\n- Each S_{i,j} is one of #, ., @.\n- S_{i,1} and S_{i,W} are # for every 1 \\leq i \\leq H.\n- S_{1,j} and S_{H,j} are # for every 1 \\leq j \\leq W.\n- S_{X,Y}= .\n- T is a string of length at least 1 and at most 10^4, consisting of U, D, L, R.\n\nSample Input 1\n\n5 5 3 4\n#####\n#...#\n#.@.#\n#..@#\n#####\nLLLDRUU\n\nSample Output 1\n\n2 3 1\n\nSanta Claus behaves as follows:\n\n\n- T_1= L, so he moves from (3,4) to (3,3). A house is passed.\n- T_2= L, so he moves from (3,3) to (3,2).\n- T_3= L, but cell (3,1) is impassable, so he stays at (3,2).\n- T_4= D, so he moves from (3,2) to (4,2).\n- T_5= R, so he moves from (4,2) to (4,3).\n- T_6= U, so he moves from (4,3) to (3,3). A house is passed, but it has already been passed.\n- T_7= U, so he moves from (3,3) to (2,3).\n\nThe number of houses he passed or arrived during his actions is 1.\n\nSample Input 2\n\n6 13 4 6\n#############\n#@@@@@@@@@@@#\n#@@@@@@@@@@@#\n#@@@@.@@@@@@#\n#@@@@@@@@@@@#\n#############\nUURUURLRLUUDDURDURRR\n\nSample Output 2\n\n3 11 11\n\nSample Input 3\n\n12 35 7 10\n###################################\n#.................................#\n#..........@......................#\n#......@................@.........#\n#.............##............@.....#\n#...##........##....##............#\n#...##........##....##.......##...#\n#....##......##......##....##.....#\n#....##......##......##..##.......#\n#.....#######.........###.........#\n#.................................#\n###################################\nLRURRRUUDDULUDUUDLRLRDRRLULRRUDLDRU\n\nSample Output 3\n\n4 14 1",
"role": "user"
}
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"temperature": 0.7
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"expected_answer": "",
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!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"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a tree rooted at node 0, consisting of n nodes numbered from 0 to n - 1. The tree is represented by an array parent of size n, where parent[i] is the parent of node i. Since node 0 is the root, parent[0] == -1.\nYou are also given a string s of length n, where s[i] is the character assigned to node i.\nConsider an empty string dfsStr, and define a recursive function dfs(int x) that takes a node x as a parameter and performs the following steps in order:\n\nIterate over each child y of x in increasing order of their numbers, and call dfs(y).\nAdd the character s[x] to the end of the string dfsStr.\n\nNote that dfsStr is shared across all recursive calls of dfs.\nYou need to find a boolean array answer of size n, where for each index i from 0 to n - 1, you do the following:\n\nEmpty the string dfsStr and call dfs(i).\nIf the resulting string dfsStr is a palindrome, then set answer[i] to true. Otherwise, set answer[i] to false.\n\nReturn the array answer.\n \nExample 1:\n\n\nInput: parent = [-1,0,0,1,1,2], s = \"aababa\"\nOutput: [true,true,false,true,true,true]\nExplanation:\n\nCalling dfs(0) results in the string dfsStr = \"abaaba\", which is a palindrome.\nCalling dfs(1) results in the string dfsStr = \"aba\", which is a palindrome.\nCalling dfs(2) results in the string dfsStr = \"ab\", which is not a palindrome.\nCalling dfs(3) results in the string dfsStr = \"a\", which is a palindrome.\nCalling dfs(4) results in the string dfsStr = \"b\", which is a palindrome.\nCalling dfs(5) results in the string dfsStr = \"a\", which is a palindrome.\n\n\nExample 2:\n\n\nInput: parent = [-1,0,0,0,0], s = \"aabcb\"\nOutput: [true,true,true,true,true]\nExplanation:\nEvery call on dfs(x) results in a palindrome string.\n\n \nConstraints:\n\nn == parent.length == s.length\n1 <= n <= 10^5\n0 <= parent[i] <= n - 1 for all i >= 1.\nparent[0] == -1\nparent represents a valid tree.\ns consists only of lowercase English letters.",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There are N pieces placed on a number line. Initially, all pieces are placed at distinct coordinates.\r\nThe initial coordinates of the pieces are X_1, X_2, \\ldots, X_N.\r\nTakahashi can repeat the following operation any number of times, possibly zero.\n\nChoose an integer i such that 1 \\leq i \\leq N-3, and let M be the midpoint between the positions of the i-th and (i+3)-rd pieces in ascending order of coordinate.\r\nThen, move each of the (i+1)-th and (i+2)-th pieces in ascending order of coordinate to positions symmetric to M.\r\nUnder the constraints of this problem, it can be proved that all pieces always occupy distinct coordinates, no matter how one repeatedly performs the operation.\n\nHis goal is to minimize the sum of the coordinates of the N pieces.\r\nFind the minimum possible sum of the coordinates of the N pieces after repeating the operations.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\r\nX_1 X_2 \\ldots X_N\n\nOutput\n\nPrint the minimum possible sum of the coordinates of the N pieces after repeating the operations.\n\nConstraints\n\n\n- 4 \\leq N \\leq 2 \\times 10^5\n- 0 \\leq X_1 < X_2 < \\cdots < X_N \\leq 10^{12}\n- All input values are integers.\n\nSample Input 1\n\n4\r\n1 5 7 10\n\nSample Output 1\n\n21\r\n\nIf Takahashi chooses i = 1, the operation is performed as follows:\n\n- The coordinates of the 1st and 4th pieces in ascending order of coordinate are 1 and 10, so the coordinate of M in this operation is (1 + 10)/2 = 5.5.\n- The 2nd piece from the left moves from coordinate 5 to 5.5 + (5.5 - 5) = 6.\n- The 3rd piece from the left moves from coordinate 7 to 5.5 - (7 - 5.5) = 4.\n\nAfter this operation, the sum of the coordinates of the four pieces is 1 + 4 + 6 + 10 = 21, which is minimal. Thus, print 21.\n\nSample Input 2\n\n6\r\n0 1 6 10 14 16\n\nSample Output 2\n\n41",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.A string T is called a 1122 string if and only if it satisfies all of the following three conditions:\n\n- \\lvert T \\rvert is even. Here, \\lvert T \\rvert denotes the length of T.\n- For each integer i satisfying 1\\leq i\\leq \\frac{|T|}{2}, the (2i-1)-th and 2i-th characters of T are equal.\n- Each character appears in T exactly zero or two times. That is, every character contained in T appears exactly twice in T.\n\nGiven a string S consisting of lowercase English letters, print Yes if S is a 1122 string, and No otherwise.\n\nInput\n\nThe input is given from Standard Input in the following format:\nS\n\nOutput\n\nIf S is a 1122 string, print Yes; otherwise, print No.\n\nConstraints\n\n\n- S is a string of length between 1 and 100, inclusive, consisting of lowercase English letters.\n\nSample Input 1\n\naabbcc\n\nSample Output 1\n\nYes\n\nS=aabbcc satisfies all the conditions for a 1122 string, so print Yes.\n\nSample Input 2\n\naab\n\nSample Output 2\n\nNo\n\nS=aab has an odd length and does not satisfy the first condition, so print No.\n\nSample Input 3\n\nzzzzzz\n\nSample Output 3\n\nNo\n\nS=zzzzzz contains six zs and does not satisfy the third condition, so print No.",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given integers A, B, and M.\nHow many permutations P = (P_1, \\dots, P_{AB-1}) of (1, 2, \\ldots, AB - 1) satisfy all of the following conditions? Find the count modulo M.\n\n- The length of a longest increasing subsequence of P is A.\n- The length of a longest decreasing subsequence of P is B.\n- There exists an integer n such that appending n + 0.5 to the end of P does not change either of the lengths of a longest increasing subsequence and a longest decreasing subsequence.\n\nInput\n\nThe input is given from Standard Input in the following format:\nA B M\n\nOutput\n\nPrint the number of permutations satisfying the conditions, modulo M.\n\nConstraints\n\n\n- All input values are integers.\n- 2 \\leq A, B\n- AB \\leq 120\n- 10^8 \\leq M \\leq 10^9\n- M is a prime.\n\nSample Input 1\n\n3 2 998244353\n\nSample Output 1\n\n10\n\nFor example, P = (2, 4, 5, 1, 3) satisfies the conditions. This can be confirmed as follows:\n\n- The length of a longest increasing subsequence of P is 3.\n- The length of a longest decreasing subsequence of P is 2.\n- For n = 4, the lengths of longest increasing and decreasing subsequences of (2, 4, 5, 1, 3, 4.5) are 3 and 2, respectively.\n\nThere are 10 permutations of (1, 2, 3, 4, 5) that satisfy the conditions.\n\nSample Input 2\n\n10 12 924844033\n\nSample Output 2\n\n623378361\n\nPrint the count modulo M.",
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"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given two strings s and t of the same length, and two integer arrays nextCost and previousCost.\nIn one operation, you can pick any index i of s, and perform either one of the following actions:\n\nShift s[i] to the next letter in the alphabet. If s[i] == 'z', you should replace it with 'a'. This operation costs nextCost[j] where j is the index of s[i] in the alphabet.\nShift s[i] to the previous letter in the alphabet. If s[i] == 'a', you should replace it with 'z'. This operation costs previousCost[j] where j is the index of s[i] in the alphabet.\n\nThe shift distance is the minimum total cost of operations required to transform s into t.\nReturn the shift distance from s to t.\n \nExample 1:\n\nInput: s = \"abab\", t = \"baba\", nextCost = [100,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0], previousCost = [1,100,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]\nOutput: 2\nExplanation:\n\nWe choose index i = 0 and shift s[0] 25 times to the previous character for a total cost of 1.\nWe choose index i = 1 and shift s[1] 25 times to the next character for a total cost of 0.\nWe choose index i = 2 and shift s[2] 25 times to the previous character for a total cost of 1.\nWe choose index i = 3 and shift s[3] 25 times to the next character for a total cost of 0.\n\n\nExample 2:\n\nInput: s = \"leet\", t = \"code\", nextCost = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1], previousCost = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]\nOutput: 31\nExplanation:\n\nWe choose index i = 0 and shift s[0] 9 times to the previous character for a total cost of 9.\nWe choose index i = 1 and shift s[1] 10 times to the next character for a total cost of 10.\nWe choose index i = 2 and shift s[2] 1 time to the previous character for a total cost of 1.\nWe choose index i = 3 and shift s[3] 11 times to the next character for a total cost of 11.\n\n\n \nConstraints:\n\n1 <= s.length == t.length <= 10^5\ns and t consist only of lowercase English letters.\nnextCost.length == previousCost.length == 26\n0 <= nextCost[i], previousCost[i] <= 10^9",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There is an N \\times N grid. Takahashi wants to color each cell black or white so that all of the following conditions are satisfied:\n\n- For every row, the following condition holds:\n\n- There exists an integer i\\ (0\\leq i\\leq N) such that the leftmost i cells are colored black, and the rest are colored white.\n\n- For every column, the following condition holds:\n\n- There exists an integer i\\ (0\\leq i\\leq N) such that the topmost i cells are colored black, and the rest are colored white.\n\n\nOut of these N^2 cells, M of them have already been colored. Among them, the i-th one is at the X_i-th row from the top and the Y_i-th column from the left, and it is colored black if C_i is B and white if C_i is W.\nDetermine whether he can color the remaining uncolored N^2 - M cells so that all the conditions are satisfied.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN M\r\nX_1 Y_1 C_1\r\n\\vdots\r\nX_M Y_M C_M\n\nOutput\n\nIf it is possible to satisfy the conditions, print Yes; otherwise, print No.\n\nConstraints\n\n\n- 1\\leq N\\leq 10^9\n- 1\\leq M\\leq \\min(N^2,2\\times 10^5)\n- 1\\leq X_i,Y_i\\leq N\n- (X_i,Y_i)\\neq (X_j,Y_j)\\ (i\\neq j)\n- C_i is B or W.\n- All input numbers are integers.\n\nSample Input 1\n\n4 3\r\n4 1 B\r\n3 2 W\r\n1 3 B\n\nSample Output 1\n\nYes\r\n\nFor example, one can color the grid as in the following figure to satisfy the conditions. The cells already colored are surrounded by red borders.\n\nSample Input 2\n\n2 2\r\n1 2 W\r\n2 2 B\n\nSample Output 2\n\nNo\r\n\nNo matter how the remaining two cells are colored, the conditions cannot be satisfied.\n\nSample Input 3\n\n1 1\r\n1 1 W\n\nSample Output 3\n\nYes\n\nSample Input 4\n\n2289 10\r\n1700 1083 W\r\n528 967 B\r\n1789 211 W\r\n518 1708 W\r\n1036 779 B\r\n136 657 B\r\n759 1497 B\r\n902 1309 B\r\n1814 712 B\r\n936 763 B\n\nSample Output 4\n\nNo",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.The definition of an 11/22 string in this problem is the same as in Problems A and C.\n\nA string T is called an 11/22 string when it satisfies all of the following conditions:\n\n- |T| is odd. Here, |T| denotes the length of T.\n- The 1-st through (\\frac{|T|+1}{2} - 1)-th characters are all 1.\n- The (\\frac{|T|+1}{2})-th character is /.\n- The (\\frac{|T|+1}{2} + 1)-th through |T|-th characters are all 2.\n\nFor example, 11/22, 111/222, and / are 11/22 strings, but 1122, 1/22, 11/2222, 22/11, and //2/2/211 are not.\nGiven a string S of length N consisting of 1, 2, and /, process Q queries.\nEach query provides two integers L and R. Let T be the (contiguous) substring of S from the L-th through R-th character. Find the maximum length of a subsequence (not necessarily contiguous) of T that is an 11/22 string. If no such subsequence exists, print 0.\n\nInput\n\nThe input is given from Standard Input in the following format. Here, \\mathrm{query}_i denotes the i-th query.\nN Q\nS\n\\mathrm{query}_1\n\\mathrm{query}_2\n\\vdots\n\\mathrm{query}_Q\n\nEach query is given in the following format:\nL R\n\nOutput\n\nPrint Q lines. The i-th line should contain the answer to the i-th query.\n\nConstraints\n\n\n- 1 \\leq N \\leq 10^5\n- 1 \\leq Q \\leq 10^5\n- S is a string of length N consisting of 1, 2, and /.\n- 1 \\leq L \\leq R \\leq N\n- N, Q, L, and R are integers.\n\nSample Input 1\n\n12 5\n111/212/1122\n1 7\n9 12\n3 6\n4 10\n1 12\n\nSample Output 1\n\n5\n0\n3\n1\n7\n\nFor the first query, the substring from the 1-st to 7-th character of S is 111/212. This string contains 11/22 as a subsequence, which is the longest subsequence that is an 11/22 string. Therefore, the answer is 5.\nFor the second query, the substring from the 9-th to 12-th character of S is 1122. This string does not contain any subsequence that is an 11/22 string, so the answer is 0.",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given two strings S and T consisting of lowercase English letters.\nDetermine if there exists a pair of integers c and w such that 1 \\leq c \\leq w < |S| and the following condition is satisfied. Here, |S| denotes the length of the string S. Note that w must be less than |S|.\n\n- If S is split at every w characters from the beginning, the concatenation of the c-th characters of the substrings of length at least c in order equals T.\n\nInput\n\nThe input is given from Standard Input in the following format:\nS T\n\nOutput\n\nPrint Yes if there exists a pair of integers c and w such that 1 \\leq c \\leq w < |S| and the condition is satisfied, and No otherwise.\n\nConstraints\n\n\n- S and T are strings consisting of lowercase English letters.\n- 1 \\leq |T| \\leq |S| \\leq 100\n\nSample Input 1\n\natcoder toe\n\nSample Output 1\n\nYes\n\nIf S is split at every two characters, it looks like this:\nat\nco\nde\nr\n\nThen, the concatenation of the 2nd characters of the substrings of length at least 2 is toe, which equals T. Thus, print Yes.\n\nSample Input 2\n\nbeginner r\n\nSample Output 2\n\nNo\n\nw=|S| is not allowed, and no pair of integers 1 \\leq c \\leq w < |S| satisfies the condition. Thus, print No.\n\nSample Input 3\n\nverticalreading agh\n\nSample Output 3\n\nNo",
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"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.There is a circle of red and blue tiles. You are given an array of integers colors. The color of tile i is represented by colors[i]:\n\ncolors[i] == 0 means that tile i is red.\ncolors[i] == 1 means that tile i is blue.\n\nEvery 3 contiguous tiles in the circle with alternating colors (the middle tile has a different color from its left and right tiles) is called an alternating group.\nReturn the number of alternating groups.\nNote that since colors represents a circle, the first and the last tiles are considered to be next to each other.\n \nExample 1:\n\nInput: colors = [1,1,1]\nOutput: 0\nExplanation:\n\n\nExample 2:\n\nInput: colors = [0,1,0,0,1]\nOutput: 3\nExplanation:\n\nAlternating groups:\n\n\n \nConstraints:\n\n3 <= colors.length <= 100\n0 <= colors[i] <= 1",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There is a rooted tree with N + 1 vertices numbered from 0 to N. Vertex 0 is the root, and the parent of vertex i is vertex p_i.\r\nOne of the vertices among vertex 1, vertex 2, ..., vertex N hides a treasure. The probability that the treasure is at vertex i is \\frac{a_i}{\\sum_{j=1}^N a_j}.\r\nAlso, each vertex is in one of the two states: \"searched\" and \"unsearched\". Initially, vertex 0 is searched, and all other vertices are unsearched.\r\nUntil the vertex containing the treasure becomes searched, you perform the following operation:\n\n- Choose an unsearched vertex whose parent is searched, and mark it as searched.\n\nFind the expected number of operations required when you act to minimize the expected number of operations, modulo 998244353.\nYou are given T test cases; solve each of them.\n\nHow to find an expected value modulo 998244353\r\n\r\nIt can be proved that the expected value is always a rational number. Under the constraints of this problem, it can also be proved that when the expected value is expressed as an irreducible fraction \\frac{P}{Q}, we have Q \\not\\equiv 0 \\pmod{998244353}. In this case, there is a unique integer R satisfying R \\times Q \\equiv P \\pmod{998244353},\\ 0 \\leq R < 998244353. Report this R.\n\nInput\n\nThe input is given from Standard Input in the following format. Here, \\mathrm{case}_i denotes the i-th test case.\nT\r\n\\mathrm{case}_1\r\n\\mathrm{case}_2\r\n\\vdots\r\n\\mathrm{case}_T\r\n\nEach test case is given in the following format:\nN\r\np_1 p_2 \\dots p_N\r\na_1 a_2 \\dots a_N\n\nOutput\n\nPrint T lines. The i-th line should contain the answer for the i-th test case.\n\nConstraints\n\n\n- 1 \\leq T \\leq 2 \\times 10^5\n- 1 \\leq N \\leq 2 \\times 10^5\n- 0 \\leq p_i < i\n- 1 \\leq a_i\n- \\sum_{i=1}^N a_i \\leq 10^8\n- The sum of N over all test cases is at most 2 \\times 10^5.\n- All input values are integers.\n\nSample Input 1\n\n3\r\n3\r\n0 0 1\r\n1 2 3\r\n5\r\n0 1 0 0 0\r\n8 6 5 1 7\r\n10\r\n0 1 1 3 3 1 4 7 5 4\r\n43 39 79 48 92 90 76 30 16 30\n\nSample Output 1\n\n166374061\r\n295776107\r\n680203339\r\n\nIn the first test case, the expected number of operations is \\frac{13}{6}.",
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[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.There exist two undirected trees with n and m nodes, numbered from 0 to n - 1 and from 0 to m - 1, respectively. You are given two 2D integer arrays edges1 and edges2 of lengths n - 1 and m - 1, respectively, where edges1[i] = [a_i, b_i] indicates that there is an edge between nodes a_i and b_i in the first tree and edges2[i] = [u_i, v_i] indicates that there is an edge between nodes u_i and v_i in the second tree.\nYou must connect one node from the first tree with another node from the second tree with an edge.\nReturn the minimum possible diameter of the resulting tree.\nThe diameter of a tree is the length of the longest path between any two nodes in the tree.\n \nExample 1:\n\nInput: edges1 = [[0,1],[0,2],[0,3]], edges2 = [[0,1]]\nOutput: 3\nExplanation:\nWe can obtain a tree of diameter 3 by connecting node 0 from the first tree with any node from the second tree.\n\nExample 2:\n\n\nInput: edges1 = [[0,1],[0,2],[0,3],[2,4],[2,5],[3,6],[2,7]], edges2 = [[0,1],[0,2],[0,3],[2,4],[2,5],[3,6],[2,7]]\nOutput: 5\nExplanation:\nWe can obtain a tree of diameter 5 by connecting node 0 from the first tree with node 0 from the second tree.\n\n \nConstraints:\n\n1 <= n, m <= 10^5\nedges1.length == n - 1\nedges2.length == m - 1\nedges1[i].length == edges2[i].length == 2\nedges1[i] = [a_i, b_i]\n0 <= a_i, b_i < n\nedges2[i] = [u_i, v_i]\n0 <= u_i, v_i < m\nThe input is generated such that edges1 and edges2 represent valid trees.",
"role": "user"
}
] |
{
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
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| 2 | 67 |
LiveCodeBenchV5
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"expected_answer": "",
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!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|
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given a string S of length N consisting of digits from 1 through 9.\nFor each pair of integers (i,j) \\ (1\\leq i\\leq j\\leq N), define f(i, j) as the value obtained by interpreting the substring of S from the i-th through the j-th character as a decimal integer. Find \\displaystyle \\sum_{i=1}^N \\sum_{j=i}^N f(i, j).\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\r\nS\n\nOutput\n\nPrint the answer.\n\nConstraints\n\n\n- 1 \\leq N \\leq 2 \\times 10^5\n- N is an integer.\n- S is a string of length N consisting of digits from 1 through 9.\n\nSample Input 1\n\n3\r\n379\n\nSample Output 1\n\n514\r\n\nThe answer is f(1,1) + f(1,2) + f(1,3) + f(2,2) + f(2,3) + f(3,3) = 3 + 37 + 379 + 7 + 79 + 9 = 514.\n\nSample Input 2\n\n30\r\n314159265358979323846264338327\n\nSample Output 2\n\n369673254065355789035427227741",
"role": "user"
}
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{
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| 1 | 238 |
LiveCodeBenchV5
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"expected_answer": "",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Whether a non-empty sequence of non-negative integers (V_1, V_2, \\dots, V_M) is Polish or not is recursively defined as follows:\n\n- We say (V_1, V_2, \\dots, V_M) is Polish if there exist V_1 Polish sequences W_1, W_2, \\dots, W_{V_1} such that the concatenation of sequences (V_1), W_1, W_2, \\dots, W_{V_1} in this order equals (V_1, V_2, \\dots, V_M).\n\nIn particular, the sequence (0) is Polish.\nGiven a sequence of non-negative integers (A_1, A_2, \\dots, A_N) of length N, find the number of Polish sequences of length N that are lexicographically not greater than (A_1, A_2, \\dots, A_N), modulo 998244353.\n What is lexicographical order on sequences?\nWe say that sequence S = (S_1,S_2,\\ldots,S_{|S|}) is lexicographically less than sequence T = (T_1,T_2,\\ldots,T_{|T|}) if either condition 1. or 2. below holds.\nHere, |S|, |T| represent the lengths of S, T respectively.\n\n- |S| \\lt |T| and (S_1,S_2,\\ldots,S_{|S|}) = (T_1,T_2,\\ldots,T_{|S|}). \n- There exists an integer 1 \\leq i \\leq \\min\\lbrace |S|, |T| \\rbrace such that both of the following hold:\n\n- (S_1,S_2,\\ldots,S_{i-1}) = (T_1,T_2,\\ldots,T_{i-1})\n- S_i is (numerically) less than T_i.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\nA_1 A_2 \\dots A_N\n\nOutput\n\nPrint the number of sequences satisfying the conditions, modulo 998244353.\n\nConstraints\n\n\n- 1\\leq N \\leq 3\\times 10^5\n- 0\\leq A_i \\lt N\n- All input values are integers.\n\nSample Input 1\n\n6\n1 1 1 2 0 0\n\nSample Output 1\n\n2\n\n(1, 1, 1, 1, 1, 0) and (1, 1, 1, 2, 0, 0) satisfy the conditions.\nWe can verify that (1, 1, 1, 2, 0, 0) is Polish as follows.\n\n- As stated in the problem statement, (0) is Polish.\n- (2, 0, 0) is Polish because it equals the concatenation of (2) and two Polish sequences (0) and (0) in this order.\n- (1, 2, 0, 0) is Polish because it equals the concatenation of (1) and one Polish sequence (2, 0, 0) in this order.\n- (1, 1, 2, 0, 0) is Polish because it equals the concatenation of (1) and one Polish sequence (1, 2, 0, 0) in this order.\n- (1, 1, 1, 2, 0, 0) is Polish because it equals the concatenation of (1) and one Polish sequence (1, 1, 2, 0, 0) in this order.\n\nSample Input 2\n\n11\n3 3 4 4 5 5 6 6 7 7 8\n\nSample Output 2\n\n13002\n\nSample Input 3\n\n19\n18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18 18\n\nSample Output 3\n\n477638700\n\nSample Input 4\n\n4\n1 1 0 0\n\nSample Output 4\n\n0",
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"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.A competition consists of n players numbered from 0 to n - 1.\nYou are given an integer array skills of size n and a positive integer k, where skills[i] is the skill level of player i. All integers in skills are unique.\nAll players are standing in a queue in order from player 0 to player n - 1.\nThe competition process is as follows:\n\nThe first two players in the queue play a game, and the player with the higher skill level wins.\nAfter the game, the winner stays at the beginning of the queue, and the loser goes to the end of it.\n\nThe winner of the competition is the first player who wins k games in a row.\nReturn the initial index of the winning player.\n \nExample 1:\n\nInput: skills = [4,2,6,3,9], k = 2\nOutput: 2\nExplanation:\nInitially, the queue of players is [0,1,2,3,4]. The following process happens:\n\nPlayers 0 and 1 play a game, since the skill of player 0 is higher than that of player 1, player 0 wins. The resulting queue is [0,2,3,4,1].\nPlayers 0 and 2 play a game, since the skill of player 2 is higher than that of player 0, player 2 wins. The resulting queue is [2,3,4,1,0].\nPlayers 2 and 3 play a game, since the skill of player 2 is higher than that of player 3, player 2 wins. The resulting queue is [2,4,1,0,3].\n\nPlayer 2 won k = 2 games in a row, so the winner is player 2.\n\nExample 2:\n\nInput: skills = [2,5,4], k = 3\nOutput: 1\nExplanation:\nInitially, the queue of players is [0,1,2]. The following process happens:\n\nPlayers 0 and 1 play a game, since the skill of player 1 is higher than that of player 0, player 1 wins. The resulting queue is [1,2,0].\nPlayers 1 and 2 play a game, since the skill of player 1 is higher than that of player 2, player 1 wins. The resulting queue is [1,0,2].\nPlayers 1 and 0 play a game, since the skill of player 1 is higher than that of player 0, player 1 wins. The resulting queue is [1,2,0].\n\nPlayer 1 won k = 3 games in a row, so the winner is player 1.\n\n \nConstraints:\n\nn == skills.length\n2 <= n <= 10^5\n1 <= k <= 10^9\n1 <= skills[i] <= 10^6\nAll integers in skills are unique.",
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"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given an array of integers nums.\nYour task is to find the length of the longest subsequence seq of nums, such that the absolute differences between consecutive elements form a non-increasing sequence of integers. In other words, for a subsequence seq_0, seq_1, seq_2, ..., seq_m of nums, |seq_1 - seq_0| >= |seq_2 - seq_1| >= ... >= |seq_m - seq_m - 1|.\nReturn the length of such a subsequence.\nA subsequence is an non-empty array that can be derived from another array by deleting some or no elements without changing the order of the remaining elements.\n \nExample 1:\n\nInput: nums = [16,6,3]\nOutput: 3\nExplanation: \nThe longest subsequence is [16, 6, 3] with the absolute adjacent differences [10, 3].\n\nExample 2:\n\nInput: nums = [6,5,3,4,2,1]\nOutput: 4\nExplanation:\nThe longest subsequence is [6, 4, 2, 1] with the absolute adjacent differences [2, 2, 1].\n\nExample 3:\n\nInput: nums = [10,20,10,19,10,20]\nOutput: 5\nExplanation: \nThe longest subsequence is [10, 20, 10, 19, 10] with the absolute adjacent differences [10, 10, 9, 9].\n\n \nConstraints:\n\n2 <= nums.length <= 10^4\n1 <= nums[i] <= 300",
"role": "user"
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"do_sample": false,
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"seed": 0,
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LiveCodeBenchV5
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"expected_answer": "",
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!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|
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There are N people divided into three teams.\nThe people are numbered 1, 2, \\ldots, N, and the teams are numbered 1, 2, 3. Currently, person i belongs to team A_i.\nEach person has a value called strength; person i has a strength of B_i. The strength of a team is defined as the sum of the strengths of its members.\nDetermine whether it is possible for zero or more people to switch teams so that all teams have equal strength. If it is possible, find the minimum number of people who need to switch teams to achieve this.\nYou cannot create new teams other than teams 1, 2, 3.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\r\nA_1 B_1\r\nA_2 B_2\r\n\\vdots\r\nA_N B_N\n\nOutput\n\nIf it is possible to make all teams have equal strength, print the minimum number of people who need to switch teams. Otherwise, print -1.\n\nConstraints\n\n\n- 3 \\leq N \\leq 100\n- A_i \\in \\lbrace 1, 2, 3 \\rbrace\n- For each x \\in \\lbrace 1, 2, 3 \\rbrace, there exists some i with A_i = x.\n- 1 \\leq B_i\n- \\displaystyle\\sum_{i = 1}^{N} B_i \\leq 1500 \n- All input values are integers.\n\nSample Input 1\n\n6\r\n1 2\r\n2 5\r\n1 5\r\n3 3\r\n1 3\r\n3 6\n\nSample Output 1\n\n2\r\n\nIf person 1 switches to team 3 and person 4 switches to team 2, all teams will have a strength of 8.\n\nSample Input 2\n\n4\r\n1 1\r\n1 2\r\n2 3\r\n3 4\n\nSample Output 2\n\n-1\n\nSample Input 3\n\n3\r\n1 1\r\n2 1\r\n3 1\n\nSample Output 3\n\n0\n\nSample Input 4\n\n12\r\n2 5\r\n1 4\r\n3 3\r\n2 3\r\n3 9\r\n1 2\r\n2 2\r\n3 9\r\n2 6\r\n1 9\r\n1 1\r\n3 1\n\nSample Output 4\n\n3",
"role": "user"
}
] |
{
"do_sample": false,
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"seed": 2,
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LiveCodeBenchV5
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"expected_answer": "",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given integers A, B, and M.\nHow many permutations P = (P_1, \\dots, P_{AB-1}) of (1, 2, \\ldots, AB - 1) satisfy all of the following conditions? Find the count modulo M.\n\n- The length of a longest increasing subsequence of P is A.\n- The length of a longest decreasing subsequence of P is B.\n- There exists an integer n such that appending n + 0.5 to the end of P does not change either of the lengths of a longest increasing subsequence and a longest decreasing subsequence.\n\nInput\n\nThe input is given from Standard Input in the following format:\nA B M\n\nOutput\n\nPrint the number of permutations satisfying the conditions, modulo M.\n\nConstraints\n\n\n- All input values are integers.\n- 2 \\leq A, B\n- AB \\leq 120\n- 10^8 \\leq M \\leq 10^9\n- M is a prime.\n\nSample Input 1\n\n3 2 998244353\n\nSample Output 1\n\n10\n\nFor example, P = (2, 4, 5, 1, 3) satisfies the conditions. This can be confirmed as follows:\n\n- The length of a longest increasing subsequence of P is 3.\n- The length of a longest decreasing subsequence of P is 2.\n- For n = 4, the lengths of longest increasing and decreasing subsequences of (2, 4, 5, 1, 3, 4.5) are 3 and 2, respectively.\n\nThere are 10 permutations of (1, 2, 3, 4, 5) that satisfy the conditions.\n\nSample Input 2\n\n10 12 924844033\n\nSample Output 2\n\n623378361\n\nPrint the count modulo M.",
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"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a string s. Simulate events at each second i:\n\nIf s[i] == 'E', a person enters the waiting room and takes one of the chairs in it.\nIf s[i] == 'L', a person leaves the waiting room, freeing up a chair.\n\nReturn the minimum number of chairs needed so that a chair is available for every person who enters the waiting room given that it is initially empty.\n \nExample 1:\n\nInput: s = \"EEEEEEE\"\nOutput: 7\nExplanation:\nAfter each second, a person enters the waiting room and no person leaves it. Therefore, a minimum of 7 chairs is needed.\n\nExample 2:\n\nInput: s = \"ELELEEL\"\nOutput: 2\nExplanation:\nLet's consider that there are 2 chairs in the waiting room. The table below shows the state of the waiting room at each second.\n\n\n\n\nSecond\nEvent\nPeople in the Waiting Room\nAvailable Chairs\n\n\n0\nEnter\n1\n1\n\n\n1\nLeave\n0\n2\n\n\n2\nEnter\n1\n1\n\n\n3\nLeave\n0\n2\n\n\n4\nEnter\n1\n1\n\n\n5\nEnter\n2\n0\n\n\n6\nLeave\n1\n1\n\n\n\nExample 3:\n\nInput: s = \"ELEELEELLL\"\nOutput: 3\nExplanation:\nLet's consider that there are 3 chairs in the waiting room. The table below shows the state of the waiting room at each second.\n\n\n\n\nSecond\nEvent\nPeople in the Waiting Room\nAvailable Chairs\n\n\n0\nEnter\n1\n2\n\n\n1\nLeave\n0\n3\n\n\n2\nEnter\n1\n2\n\n\n3\nEnter\n2\n1\n\n\n4\nLeave\n1\n2\n\n\n5\nEnter\n2\n1\n\n\n6\nEnter\n3\n0\n\n\n7\nLeave\n2\n1\n\n\n8\nLeave\n1\n2\n\n\n9\nLeave\n0\n3\n\n\n\n \nConstraints:\n\n1 <= s.length <= 50\ns consists only of the letters 'E' and 'L'.\ns represents a valid sequence of entries and exits.",
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"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given positive integers n and target.\nAn array nums is beautiful if it meets the following conditions:\n\nnums.length == n.\nnums consists of pairwise distinct positive integers.\nThere doesn't exist two distinct indices, i and j, in the range [0, n - 1], such that nums[i] + nums[j] == target.\n\nReturn the minimum possible sum that a beautiful array could have modulo 10^9 + 7.\n \nExample 1:\n\nInput: n = 2, target = 3\nOutput: 4\nExplanation: We can see that nums = [1,3] is beautiful.\n- The array nums has length n = 2.\n- The array nums consists of pairwise distinct positive integers.\n- There doesn't exist two distinct indices, i and j, with nums[i] + nums[j] == 3.\nIt can be proven that 4 is the minimum possible sum that a beautiful array could have.\n\nExample 2:\n\nInput: n = 3, target = 3\nOutput: 8\nExplanation: We can see that nums = [1,3,4] is beautiful.\n- The array nums has length n = 3.\n- The array nums consists of pairwise distinct positive integers.\n- There doesn't exist two distinct indices, i and j, with nums[i] + nums[j] == 3.\nIt can be proven that 8 is the minimum possible sum that a beautiful array could have.\n\nExample 3:\n\nInput: n = 1, target = 1\nOutput: 1\nExplanation: We can see, that nums = [1] is beautiful.\n\n \nConstraints:\n\n1 <= n <= 10^9\n1 <= target <= 10^9",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Takahashi and Aoki will play a game using cards with numbers written on them.\nInitially, Takahashi has N cards with numbers A_1, \\ldots, A_N in his hand, Aoki has M cards with numbers B_1, \\ldots, B_M in his hand, and there are L cards with numbers C_1, \\ldots, C_L on the table.\r\nThroughout the game, both Takahashi and Aoki know all the numbers on all the cards, including the opponent's hand.\nStarting with Takahashi, they take turns performing the following action:\n\n- Choose one card from his hand and put it on the table. Then, if there is a card on the table with a number less than the number on the card he just played, he may take one such card from the table into his hand.\n\nThe player who cannot make a move first loses, and the other player wins. Determine who wins if both players play optimally.\nIt can be proved that the game always ends in a finite number of moves.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN M L\r\nA_1 \\ldots A_N\r\nB_1 \\ldots B_M\r\nC_1 \\ldots C_L\n\nOutput\n\nPrint Takahashi if Takahashi wins, and Aoki if Aoki wins.\n\nConstraints\n\n\n- 1 \\leq N, M, L\n- N + M + L \\leq 12\n- 1 \\leq A_i, B_i, C_i \\leq 10^9\n- All input values are integers.\n\nSample Input 1\n\n1 1 2\r\n2\r\n4\r\n1 3\n\nSample Output 1\n\nAoki\r\n\nThe game may proceed as follows (not necessarily optimal moves):\n\n- Takahashi plays 2 from his hand to the table, and takes 1 from the table into his hand. Now, Takahashi's hand is (1), Aoki's hand is (4), and the table cards are (2,3).\n- Aoki plays 4 from his hand to the table, and takes 2 into his hand. Now, Takahashi's hand is (1), Aoki's hand is (2), and the table cards are (3,4).\n- Takahashi plays 1 from his hand to the table. Now, Takahashi's hand is (), Aoki's hand is (2), and the table cards are (1,3,4).\n- Aoki plays 2 from his hand to the table. Now, Takahashi's hand is (), Aoki's hand is (), and the table cards are (1,2,3,4).\n- Takahashi cannot make a move and loses; Aoki wins.\n\nSample Input 2\n\n4 4 4\r\n98 98765 987654 987654321\r\n987 9876 9876543 98765432\r\n123 12345 1234567 123456789\n\nSample Output 2\n\nTakahashi\n\nSample Input 3\n\n1 1 8\r\n10\r\n10\r\n1 2 3 4 5 6 7 8\n\nSample Output 3\n\nAoki",
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"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a string initialCurrency, and you start with 1.0 of initialCurrency.\nYou are also given four arrays with currency pairs (strings) and rates (real numbers):\n\npairs1[i] = [startCurrency_i, targetCurrency_i] denotes that you can convert from startCurrency_i to targetCurrency_i at a rate of rates1[i] on day 1.\npairs2[i] = [startCurrency_i, targetCurrency_i] denotes that you can convert from startCurrency_i to targetCurrency_i at a rate of rates2[i] on day 2.\nAlso, each targetCurrency can be converted back to its corresponding startCurrency at a rate of 1 / rate.\n\nYou can perform any number of conversions, including zero, using rates1 on day 1, followed by any number of additional conversions, including zero, using rates2 on day 2.\nReturn the maximum amount of initialCurrency you can have after performing any number of conversions on both days in order.\nNote: Conversion rates are valid, and there will be no contradictions in the rates for either day. The rates for the days are independent of each other.\n \nExample 1:\n\nInput: initialCurrency = \"EUR\", pairs1 = [[\"EUR\",\"USD\"],[\"USD\",\"JPY\"]], rates1 = [2.0,3.0], pairs2 = [[\"JPY\",\"USD\"],[\"USD\",\"CHF\"],[\"CHF\",\"EUR\"]], rates2 = [4.0,5.0,6.0]\nOutput: 720.00000\nExplanation:\nTo get the maximum amount of EUR, starting with 1.0 EUR:\n\nOn Day 1:\n\t\nConvert EUR to USD to get 2.0 USD.\nConvert USD to JPY to get 6.0 JPY.\n\n\nOn Day 2:\n\t\nConvert JPY to USD to get 24.0 USD.\nConvert USD to CHF to get 120.0 CHF.\nFinally, convert CHF to EUR to get 720.0 EUR.\n\n\n\n\nExample 2:\n\nInput: initialCurrency = \"NGN\", pairs1 = [[\"NGN\",\"EUR\"]], rates1 = [9.0], pairs2 = [[\"NGN\",\"EUR\"]], rates2 = [6.0]\nOutput: 1.50000\nExplanation:\nConverting NGN to EUR on day 1 and EUR to NGN using the inverse rate on day 2 gives the maximum amount.\n\nExample 3:\n\nInput: initialCurrency = \"USD\", pairs1 = [[\"USD\",\"EUR\"]], rates1 = [1.0], pairs2 = [[\"EUR\",\"JPY\"]], rates2 = [10.0]\nOutput: 1.00000\nExplanation:\nIn this example, there is no need to make any conversions on either day.\n\n \nConstraints:\n\n1 <= initialCurrency.length <= 3\ninitialCurrency consists only of uppercase English letters.\n1 <= n == pairs1.length <= 10\n1 <= m == pairs2.length <= 10\npairs1[i] == [startCurrency_i, targetCurrency_i]\npairs2[i] == [startCurrency_i, targetCurrency_i]\n1 <= startCurrency_i.length, targetCurrency_i.length <= 3\nstartCurrency_i and targetCurrency_i consist only of uppercase English letters.\nrates1.length == n\nrates2.length == m\n1.0 <= rates1[i], rates2[i] <= 10.0\nThe input is generated such that there are no contradictions or cycles in the conversion graphs for either day.\nThe input is generated such that the output is at most 5 * 10^10.",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Takahashi has a piano with 100 keys arranged in a row.\r\nThe i-th key from the left is called key i.\nHe will play music by pressing N keys one by one.\r\nFor the i-th press, he will press key A_i, using his left hand if S_i= L, and his right hand if S_i= R.\nBefore starting to play, he can place both of his hands on any keys he likes, and his fatigue level at this point is 0.\r\nDuring the performance, if he moves one hand from key x to key y, the fatigue level increases by |y-x| (conversely, the fatigue level does not increase for any reason other than moving hands).\r\nTo press a certain key with a hand, that hand must be placed on that key.\nFind the minimum possible fatigue level at the end of the performance.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\r\nA_1 S_1\r\nA_2 S_2\r\n\\vdots\r\nA_N S_N\n\nOutput\n\nPrint the minimum fatigue level at the end of the performance.\n\nConstraints\n\n\n- 1 \\leq N \\leq 100\n- 1 \\leq A_i \\leq 100\n- N and A_i are integers.\n- S_i is L or R.\n\nSample Input 1\n\n4\r\n3 L\r\n6 R\r\n9 L\r\n1 R\n\nSample Output 1\n\n11\r\n\nFor example, the performance can be done as follows:\n\n- Initially, place the left hand on key 3 and the right hand on key 6.\n- Press key 3 with the left hand.\n- Press key 6 with the right hand.\n- Move the left hand from key 3 to key 9. The fatigue level increases by |9-3| = 6.\n- Move the right hand from key 6 to key 1. The fatigue level increases by |1-6| = 5.\n- Press key 9 with the left hand.\n- Press key 1 with the right hand.\n\nIn this case, the fatigue level at the end of the performance is 6+5 = 11, which is the minimum possible.\n\nSample Input 2\n\n3\r\n2 L\r\n2 L\r\n100 L\n\nSample Output 2\n\n98\n\nSample Input 3\n\n8\r\n22 L\r\n75 L\r\n26 R\r\n45 R\r\n72 R\r\n81 R\r\n47 L\r\n29 R\n\nSample Output 3\n\n188",
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"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given a string s.\nYou can perform the following process on s any number of times:\n\nChoose an index i in the string such that there is at least one character to the left of index i that is equal to s[i], and at least one character to the right that is also equal to s[i].\nDelete the closest character to the left of index i that is equal to s[i].\nDelete the closest character to the right of index i that is equal to s[i].\n\nReturn the minimum length of the final string s that you can achieve.\n \nExample 1:\n\nInput: s = \"abaacbcbb\"\nOutput: 5\nExplanation:\nWe do the following operations:\n\nChoose index 2, then remove the characters at indices 0 and 3. The resulting string is s = \"bacbcbb\".\nChoose index 3, then remove the characters at indices 0 and 5. The resulting string is s = \"acbcb\".\n\n\nExample 2:\n\nInput: s = \"aa\"\nOutput: 2\nExplanation:\nWe cannot perform any operations, so we return the length of the original string.\n\n \nConstraints:\n\n1 <= s.length <= 2 * 10^5\ns consists only of lowercase English letters.",
"role": "user"
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"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given 2 positive integers l and r. For any number x, all positive divisors of x except x are called the proper divisors of x.\nA number is called special if it has exactly 2 proper divisors. For example:\n\nThe number 4 is special because it has proper divisors 1 and 2.\nThe number 6 is not special because it has proper divisors 1, 2, and 3.\n\nReturn the count of numbers in the range [l, r] that are not special.\n \nExample 1:\n\nInput: l = 5, r = 7\nOutput: 3\nExplanation:\nThere are no special numbers in the range [5, 7].\n\nExample 2:\n\nInput: l = 4, r = 16\nOutput: 11\nExplanation:\nThe special numbers in the range [4, 16] are 4 and 9.\n\n \nConstraints:\n\n1 <= l <= r <= 10^9",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There are N cells numbered from 1 to N in a row. Initially, M cells contain stones, and cell X_i contains A_i stones (1 \\leq i \\leq M).\nYou can perform the following operation any number of times (possibly zero):\n\n- If cell i (1 \\leq i \\leq N-1) contains a stone, move one stone from cell i to cell i+1.\n\nFind the minimum number of operations required to reach a state where each of the N cells contains exactly one stone. If it is impossible, print -1.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN M\r\nX_1 X_2 \\ldots X_M\r\nA_1 A_2 \\ldots A_M\n\nOutput\n\nPrint the answer.\n\nConstraints\n\n\n- 2 \\leq N \\leq 2 \\times 10^{9}\n- 1 \\leq M \\leq 2 \\times 10^{5}\n- M \\leq N\n- 1 \\leq X_i \\leq N (1 \\leq i \\leq M)\n- X_i \\neq X_j (1 \\leq i < j \\leq M)\n- 1 \\leq A_i \\leq 2 \\times 10^{9} (1 \\leq i \\leq M)\n- All input values are integers.\n\nSample Input 1\n\n5 2\r\n1 4\r\n3 2\n\nSample Output 1\n\n4\r\n\nYou can reach a state where each of the five cells contains exactly one stone with four operations as follows:\n\n- Move one stone from cell 1 to cell 2.\n- Move one stone from cell 2 to cell 3.\n- Move one stone from cell 4 to cell 5.\n- Move one stone from cell 1 to cell 2.\n\nIt is impossible to achieve the goal in three or fewer operations. Therefore, print 4.\n\nSample Input 2\n\n10 3\r\n1 4 8\r\n4 2 4\n\nSample Output 2\n\n-1\r\n\nNo matter how you perform the operations, you cannot reach a state where all ten cells contain exactly one stone. Therefore, print -1.",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There is a calculator with the buttons 00, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.\nWhen a string x is displayed on this calculator and you press a button b, the resulting displayed string becomes the string x with b appended to its end.\nInitially, the calculator displays the empty string (a string of length 0).\nFind the minimum number of button presses required to display the string S on this calculator.\n\nInput\n\nThe input is given from Standard Input in the following format:\nS\n\nOutput\n\nPrint the answer as an integer.\n\nConstraints\n\n\n- S is a string of length at least 1 and at most 1000, consisting of 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.\n- The first character of S is not 0.\n\nSample Input 1\n\n1000000007\n\nSample Output 1\n\n6\n\nTo display 1000000007, you can press the buttons 1, 00, 00, 00, 00, 7 in this order. The total number of button presses is 6, and this is the minimum possible.\n\nSample Input 2\n\n998244353\n\nSample Output 2\n\n9\n\nSample Input 3\n\n32000\n\nSample Output 3\n\n4",
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!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|
[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.This problem fully contains Problem C (Operate 1), with K \\le 20.\nYou can solve Problem C by submitting a correct solution to this problem for Problem C.\nDetermine whether it is possible to perform the following operation on string S between 0 and K times, inclusive, to make it identical to string T.\n\n- Choose one of the following three operations and execute it.\n- Insert any one character at any position in S (possibly the beginning or end).\n- Delete one character from S.\n- Choose one character in S and replace it with another character.\n\nInput\n\nThe input is given from Standard Input in the following format:\nK\r\nS\r\nT\n\nOutput\n\nIf S can be made identical to T with at most K operations, print Yes; otherwise, print No.\n\nConstraints\n\n\n- Each of S and T is a string of length between 1 and 500000, inclusive, consisting of lowercase English letters.\n- K is an integer satisfying \\color{red}{1 \\le K \\le 20}.\n\nSample Input 1\n\n3\r\nabc\r\nawtf\n\nSample Output 1\n\nYes\r\n\nFor example, here is a way to convert abc to awtf with three operations:\n\n- Replace the second character b with w. After the operation, the string becomes awc.\n- Replace the third character c with f. After the operation, the string becomes awf.\n- Insert t between the second and third characters. After the operation, the string becomes awtf.\n\nSample Input 2\n\n2\r\nabc\r\nawtf\n\nSample Output 2\n\nNo\r\n\nabc cannot be converted to awtf with two or fewer operations.\n\nSample Input 3\n\n17\r\ntwothousandtwentyfour\r\nhappynewyear\n\nSample Output 3\n\nYes",
"role": "user"
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] |
{
"do_sample": false,
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"seed": 0,
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LiveCodeBenchV5
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|
[
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given N length-M sequences, where each element is 0 or 1. The i-th sequence is A_i = (A_{i, 1}, A_{i, 2}, \\dots, A_{i, M}).\nFor integers i, j \\ (1 \\leq i, j \\leq N), define f(i, j) as follows:\n\n- \nf(i, j) := The smallest non-negative integer x such that A_i and A_j become identical after performing the following operation x times, or 0 if such x does not exist.\n\n- \nFor all integers k \\ (1 \\leq k \\leq M) simultaneously, replace A_{i, k} with \\displaystyle \\left (\\sum_{l=1}^{k} A_{i, l} \\right ) \\bmod 2.\n\n\n\n\nFind \\displaystyle \\sum_{i=1}^{N} \\sum_{j=i}^{N} f(i, j), modulo 998244353.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN M\nA_{1, 1} A_{1, 2} \\cdots A_{1, M}\nA_{2, 1} A_{2, 2} \\cdots A_{2, M}\n\\vdots\nA_{N, 1} A_{N, 2} \\cdots A_{N, M}\n\nOutput\n\nPrint the answer in one line.\n\nConstraints\n\n\n- 1 \\leq N \\times M \\leq 10^6\n- A_{i, j} \\in \\{0, 1\\}\n\nSample Input 1\n\n4 3\n1 0 0\n1 1 0\n1 0 1\n0 1 1\n\nSample Output 1\n\n8\n\nf(1, 1) = 0, f(1, 2) = 3, f(1, 3) = 2, f(1, 4) = 0, f(2, 2) = 0, f(2, 3) = 3, f(2, 4) = 0, f(3, 3) = 0, f(3, 4) = 0, f(4, 4) = 0, so print their sum, 8.\n\nSample Input 2\n\n7 6\n1 0 0 0 0 0\n1 1 1 0 0 0\n1 0 1 1 0 0\n1 0 0 0 1 1\n1 0 0 0 0 1\n1 0 0 0 0 0\n1 1 1 1 1 1\n\nSample Output 2\n\n6",
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"seed": 2,
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!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[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are playing a game.\nThere are N enemies lined up in a row, and the i-th enemy from the front has a health of H_i.\nYou will repeat the following action until the healths of all enemies become 0 or less, using a variable T initialized to 0.\n\n- Increase T by 1. Then, attack the frontmost enemy with health 1 or more. If T is a multiple of 3, the enemy's health decreases by 3; otherwise, it decreases by 1.\n\nFind the value of T when the healths of all enemies become 0 or less.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\r\nH_1 H_2 \\ldots H_N\n\nOutput\n\nPrint the answer.\n\nConstraints\n\n\n- 1 \\leq N \\leq 2\\times 10^5\n- 1 \\leq H_i \\leq 10^9\n- All input values are integers.\n\nSample Input 1\n\n3\r\n6 2 2\n\nSample Output 1\n\n8\r\n\nThe actions are performed as follows:\n\n- T becomes 1. Attack the 1st enemy, and its health becomes 6-1=5.\n- T becomes 2. Attack the 1st enemy, and its health becomes 5-1=4.\n- T becomes 3. Attack the 1st enemy, and its health becomes 4-3=1.\n- T becomes 4. Attack the 1st enemy, and its health becomes 1-1=0.\n- T becomes 5. Attack the 2nd enemy, and its health becomes 2-1=1.\n- T becomes 6. Attack the 2nd enemy, and its health becomes 1-3=-2.\n- T becomes 7. Attack the 3rd enemy, and its health becomes 2-1=1.\n- T becomes 8. Attack the 3rd enemy, and its health becomes 1-1=0.\n\nSample Input 2\n\n9\r\n1 12 123 1234 12345 123456 1234567 12345678 123456789\n\nSample Output 2\n\n82304529\n\nSample Input 3\n\n5\r\n1000000000 1000000000 1000000000 1000000000 1000000000\n\nSample Output 3\n\n3000000000\r\n\nBeware of integer overflow.",
"role": "user"
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Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.