context
list | gen_kwargs
dict | repeat_idx
int64 | request_idx
int64 | task_name
string | metadata
dict | model_outputs
string |
|---|---|---|---|---|---|---|
[
{
"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 integer array nums that represents a circular array. Your task is to create a new array result of the same size, following these rules:\nFor each index i (where 0 <= i < nums.length), perform the following independent actions:\n\n\nIf nums[i] > 0: Start at index i and move nums[i] steps to the right in the circular array. Set result[i] to the value of the index where you land.\nIf nums[i] < 0: Start at index i and move abs(nums[i]) steps to the left in the circular array. Set result[i] to the value of the index where you land.\nIf nums[i] == 0: Set result[i] to nums[i].\n\nReturn the new array result.\nNote: Since nums is circular, moving past the last element wraps around to the beginning, and moving before the first element wraps back to the end.\n \nExample 1:\n\nInput: nums = [3,-2,1,1]\nOutput: [1,1,1,3]\nExplanation:\n\nFor nums[0] that is equal to 3, If we move 3 steps to right, we reach nums[3]. So result[0] should be 1.\nFor nums[1] that is equal to -2, If we move 2 steps to left, we reach nums[3]. So result[1] should be 1.\nFor nums[2] that is equal to 1, If we move 1 step to right, we reach nums[3]. So result[2] should be 1.\nFor nums[3] that is equal to 1, If we move 1 step to right, we reach nums[0]. So result[3] should be 3.\n\n\nExample 2:\n\nInput: nums = [-1,4,-1]\nOutput: [-1,-1,4]\nExplanation:\n\nFor nums[0] that is equal to -1, If we move 1 step to left, we reach nums[2]. So result[0] should be -1.\nFor nums[1] that is equal to 4, If we move 4 steps to right, we reach nums[2]. So result[1] should be -1.\nFor nums[2] that is equal to -1, If we move 1 step to left, we reach nums[1]. So result[2] should be 4.\n\n\n \nConstraints:\n\n1 <= nums.length <= 100\n-100 <= nums[i] <= 100",
"role": "user"
}
] |
{
"do_sample": false,
"max_new_tokens": 32768,
"seed": 0,
"temperature": 0.7
}
| 0 | 341 |
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.You are given a string S of length 3 consisting of uppercase English letters.\nDetermine whether it is possible to rearrange the characters in S to make it match the string ABC.\n\nInput\n\nThe input is given from Standard Input in the following format:\nS\n\nOutput\n\nPrint Yes if it is possible to rearrange the characters in S to make it match the string ABC, and No otherwise.\n\nConstraints\n\n\n- S is a string of length 3 consisting of uppercase English letters.\n\nSample Input 1\n\nBAC\n\nSample Output 1\n\nYes\n\nYou can make S match ABC by swapping the first and second characters of S.\n\nSample Input 2\n\nAAC\n\nSample Output 2\n\nNo\n\nYou cannot make S match ABC no matter how you rearrange the characters.\n\nSample Input 3\n\nABC\n\nSample Output 3\n\nYes\n\nSample Input 4\n\nARC\n\nSample Output 4\n\nNo",
"role": "user"
}
] |
{
"do_sample": false,
"max_new_tokens": 32768,
"seed": 2,
"temperature": 0.7
}
| 2 | 225 |
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. Let (i, j) denote the cell at the i-th row from the top and j-th column from the left.\nInitially, there is one wall in each cell.\nAfter processing Q queries explained below in the order they are given, find the number of remaining walls.\nIn the q-th query, you are given two integers R_q and C_q.\nYou place a bomb at (R_q, C_q) to destroy walls. As a result, the following process occurs.\n\n- If there is a wall at (R_q, C_q), destroy that wall and end the process.\n- If there is no wall at (R_q, C_q), destroy the first walls that appear when looking up, down, left, and right from (R_q, C_q). More precisely, the following four processes occur simultaneously:\n- If there exists an i \\lt R_q such that a wall exists at (i, C_q) and no wall exists at (k, C_q) for all i \\lt k \\lt R_q, destroy the wall at (i, C_q).\n- If there exists an i \\gt R_q such that a wall exists at (i, C_q) and no wall exists at (k, C_q) for all R_q \\lt k \\lt i, destroy the wall at (i, C_q).\n- If there exists a j \\lt C_q such that a wall exists at (R_q, j) and no wall exists at (R_q, k) for all j \\lt k \\lt C_q, destroy the wall at (R_q, j).\n- If there exists a j \\gt C_q such that a wall exists at (R_q, j) and no wall exists at (R_q, k) for all C_q \\lt k \\lt j, destroy the wall at (R_q, j).\n\nInput\n\nThe input is given from Standard Input in the following format:\nH W Q\nR_1 C_1\nR_2 C_2\n\\vdots\nR_Q C_Q\n\nOutput\n\nPrint the number of remaining walls after processing all queries.\n\nConstraints\n\n\n- 1 \\leq H, W\n- H \\times W \\leq 4 \\times 10^5\n- 1 \\leq Q \\leq 2 \\times 10^5\n- 1 \\leq R_q \\leq H\n- 1 \\leq C_q \\leq W\n- All input values are integers.\n\nSample Input 1\n\n2 4 3\n1 2\n1 2\n1 3\n\nSample Output 1\n\n2\n\nThe process of handling the queries can be explained as follows:\n\n- In the 1st query, (R_1, C_1) = (1, 2). There is a wall at (1, 2), so the wall at (1, 2) is destroyed.\n- In the 2nd query, (R_2, C_2) = (1, 2). There is no wall at (1, 2), so the walls at (2,2),(1,1),(1,3), which are the first walls that appear when looking up, down, left, and right from (1, 2), are destroyed.\n- In the 3rd query, (R_3, C_3) = (1, 3). There is no wall at (1, 3), so the walls at (2,3),(1,4), which are the first walls that appear when looking up, down, left, and right from (1, 3), are destroyed.\n\nAfter processing all queries, there are two remaining walls, at (2, 1) and (2, 4).\n\nSample Input 2\n\n5 5 5\n3 3\n3 3\n3 2\n2 2\n1 2\n\nSample Output 2\n\n10\n\nSample Input 3\n\n4 3 10\n2 2\n4 1\n1 1\n4 2\n2 1\n3 1\n1 3\n1 2\n4 3\n4 2\n\nSample Output 3\n\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.There is one humidifier in the AtCoder company office. The current time is 0, and the humidifier has no water inside.\nYou will add water to this humidifier N times. The i-th addition of water (1 \\leq i \\leq N) takes place at time T_i, and you add V_i liters of water. It is guaranteed that T_i < T_{i+1} for all 1 \\leq i \\leq N-1.\nHowever, the humidifier has a leak, and as long as there is water inside, the amount of water decreases by 1 liter per unit time.\nFind the amount of water remaining in the humidifier immediately after you finish adding water at time T_N.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\r\nT_1 V_1\r\nT_2 V_2\r\n\\vdots\r\nT_N V_N\n\nOutput\n\nPrint the answer.\n\nConstraints\n\n\n- 1 \\leq N \\leq 100\n- 1 \\leq T_i \\leq 100 (1 \\leq i \\leq N)\n- 1 \\leq V_i \\leq 100 (1 \\leq i \\leq N)\n- T_i < T_{i+1} (1 \\leq i \\leq N-1)\n- All input values are integers.\n\nSample Input 1\n\n4\r\n1 3\r\n3 1\r\n4 4\r\n7 1\n\nSample Output 1\n\n3\r\n\nAt each point in time, water is added as follows:\n\n- Time 1: Before adding, the humidifier has 0 liters. After adding 3 liters, it has 3 liters.\n- Time 3: Before adding, it has 1 liter. After adding 1 liter, it has 2 liters total.\n- Time 4: Before adding, it has 1 liter. After adding 4 liters, it has 5 liters total.\n- Time 7: Before adding, it has 2 liters. After adding 1 liter, it has 3 liters total.\n\nAfter finishing the addition at time 7, the humidifier contains 3 liters. Thus, the answer is 3.\n\nSample Input 2\n\n3\r\n1 8\r\n10 11\r\n21 5\n\nSample Output 2\n\n5\n\nSample Input 3\n\n10\r\n2 1\r\n22 10\r\n26 17\r\n29 2\r\n45 20\r\n47 32\r\n72 12\r\n75 1\r\n81 31\r\n97 7\n\nSample Output 3\n\n57",
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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 j-th column from the left.\nCell (i, j) is empty if C_{i, j} is ., and not empty if C_{i, j} is #.\nTakahashi is currently at cell (S_i, S_j), and he will act according to the following rules for i = 1, 2, \\ldots, |X| in order.\n\n- If the i-th character of X is L, and the cell to the left of his current cell exists and is empty, he moves to the cell to the left. Otherwise, he stays in the current cell.\n- If the i-th character of X is R, and the cell to the right of his current cell exists and is empty, he moves to the cell to the right. Otherwise, he stays in the current cell.\n- If the i-th character of X is U, and the cell above his current cell exists and is empty, he moves to the cell above. Otherwise, he stays in the current cell.\n- If the i-th character of X is D, and the cell below his current cell exists and is empty, he moves to the cell below. Otherwise, he stays in the current cell.\n\nPrint the cell where he is after completing the series of actions.\n\nInput\n\nThe input is given from Standard Input in the following format:\nH W\r\nS_i S_j\r\nC_{1, 1}C_{1, 2}\\ldotsC_{1, W}\r\nC_{2, 1}C_{2, 2}\\ldotsC_{2, W}\r\n\\vdots\r\nC_{H, 1}C_{H, 2}\\ldotsC_{H, W}\r\nX\n\nOutput\n\nLet (x, y) be the cell where Takahashi is after completing the series of actions. Print x and y, separated by a space.\n\nConstraints\n\n\n- 1 \\leq H, W \\leq 50\n- 1 \\leq S_i \\leq H\n- 1 \\leq S_j \\leq W\n- H, W, S_i, S_j are integers.\n- C_{i, j} is . or #.\n- C_{S_i, S_j} = .\n- X is a string of length between 1 and 50, inclusive, consisting of L, R, U, D.\n\nSample Input 1\n\n2 3\r\n2 1\r\n.#.\r\n...\r\nULDRU\n\nSample Output 1\n\n2 2\r\n\nTakahashi starts at cell (2, 1). His series of actions are as follows:\n\n- The 1st character of X is U, and the cell above (2, 1) exists and is an empty cell, so he moves to the cell above, which is (1, 1).\n- The 2nd character of X is L, and the cell to the left of (1, 1) does not exist, so he stays at (1, 1).\n- The 3rd character of X is D, and the cell below (1, 1) exists and is an empty cell, so he moves to the cell below, which is (2, 1).\n- The 4th character of X is R, and the cell to the right of (2, 1) exists and is an empty cell, so he moves to the cell to the right, which is (2, 2).\n- The 5th character of X is U, and the cell above (2, 2) exists but is not an empty cell, so he stays at (2, 2).\n\nTherefore, after completing the series of actions, he is at cell (2, 2).\n\nSample Input 2\n\n4 4\r\n4 2\r\n....\r\n.#..\r\n...#\r\n....\r\nDUUUURULRD\n\nSample Output 2\n\n2 4\n\nSample Input 3\n\n6 6\r\n1 1\r\n.#####\r\n######\r\n######\r\n######\r\n######\r\n######\r\nRURLDLULLRULRDL\n\nSample Output 3\n\n1 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.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. Return the function body without invoking it at the final solution.You are given two integers, n and k, along with two 2D integer arrays, stayScore and travelScore.\nA tourist is visiting a country with n cities, where each city is directly connected to every other city. The tourist's journey consists of exactly k 0-indexed days, and they can choose any city as their starting point.\nEach day, the tourist has two choices:\n\nStay in the current city: If the tourist stays in their current city curr during day i, they will earn stayScore[i][curr] points.\nMove to another city: If the tourist moves from their current city curr to city dest, they will earn travelScore[curr][dest] points.\n\nReturn the maximum possible points the tourist can earn.\n \nExample 1:\n\nInput: n = 2, k = 1, stayScore = [[2,3]], travelScore = [[0,2],[1,0]]\nOutput: 3\nExplanation:\nThe tourist earns the maximum number of points by starting in city 1 and staying in that city.\n\nExample 2:\n\nInput: n = 3, k = 2, stayScore = [[3,4,2],[2,1,2]], travelScore = [[0,2,1],[2,0,4],[3,2,0]]\nOutput: 8\nExplanation:\nThe tourist earns the maximum number of points by starting in city 1, staying in that city on day 0, and traveling to city 2 on day 1.\n\n \nConstraints:\n\n1 <= n <= 200\n1 <= k <= 200\nn == travelScore.length == travelScore[i].length == stayScore[i].length\nk == stayScore.length\n1 <= stayScore[i][j] <= 100\n0 <= travelScore[i][j] <= 100\ntravelScore[i][i] == 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 permutations P = (P_1, P_2, \\ldots, P_N) and A = (A_1, A_2, \\ldots, A_N) of (1,2,\\ldots,N).\nYou can perform the following operation any number of times, possibly zero:\n\n- replace A_i with A_{P_i} simultaneously for all i=1,2,\\ldots,N.\n\nPrint the lexicographically smallest A that can be obtained.\nWhat is lexicographical order?\n For sequences of length N, A = (A_1, A_2, \\ldots, A_N) and B = (B_1, B_2, \\ldots, B_N), A is lexicographically smaller than B if and only if:\n\n- there exists an integer i\\ (1\\leq i\\leq N) such that A_i < B_i, and A_j = B_j for all 1\\leq j < i.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\r\nP_1 P_2 \\ldots P_N\r\nA_1 A_2 \\ldots A_N\n\nOutput\n\nLet (A_1, A_2, \\ldots, A_N) be the lexicographically smallest A that can be obtained. Print A_1, A_2, \\ldots, A_N in this order, separated by spaces, in one line.\n\nConstraints\n\n\n- 1\\leq N\\leq2\\times10^5\n- 1\\leq P_i\\leq N\\ (1\\leq i\\leq N)\n- P_i\\neq P_j\\ (1\\leq i<j\\leq N)\n- 1\\leq A_i\\leq N\\ (1\\leq i\\leq N)\n- A_i\\neq A_j\\ (1\\leq i<j\\leq N)\n- All input values are integers.\n\nSample Input 1\n\n6\r\n3 1 5 6 2 4\r\n4 3 1 6 2 5\n\nSample Output 1\n\n1 4 2 5 3 6\r\n\nInitially, A = (4, 3, 1, 6, 2, 5).\nRepeating the operation yields the following.\n\n- A = (1, 4, 2, 5, 3, 6)\n- A = (2, 1, 3, 6, 4, 5)\n- A = (3, 2, 4, 5, 1, 6)\n- A = (4, 3, 1, 6, 2, 5)\n\nAfter this, A will revert to the original state every four operations.\nTherefore, print the lexicographically smallest among these, which is 1 4 2 5 3 6.\n\nSample Input 2\n\n8\r\n3 5 8 7 2 6 1 4\r\n1 2 3 4 5 6 7 8\n\nSample Output 2\n\n1 2 3 4 5 6 7 8\r\n\nYou may choose to perform no operations.\n\nSample Input 3\n\n26\r\n24 14 4 20 15 19 16 11 23 22 12 18 21 3 6 8 26 2 25 7 13 1 5 9 17 10\r\n15 3 10 1 13 19 22 24 20 4 14 23 7 26 25 18 11 6 9 12 2 21 5 16 8 17\n\nSample Output 3\n\n4 1 22 18 20 13 14 6 15 11 3 26 2 12 5 23 9 10 25 24 7 17 16 21 19 8",
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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 10^{100} flower pots. Initially, he is not growing any plants.\nYou are given Q queries to process in order.\nThere are three types of queries as follows.\n\n- 1: Prepare one empty flower pot and put a plant in it. Here, the plant's height is 0.\n- 2 T: Wait for T days. During this time, the height of every existing plants increases by T.\n- 3 H: Harvest all plants with a height of at least H, and output the number of plants harvested. The harvested plants are removed from their flower pots.\n\nAssume that performing queries of the first and third types takes zero time.\n\nInput\n\nThe input is given from Standard Input in the following format:\nQ\n\\text{query}_1\n\\text{query}_2\n\\vdots\n\\text{query}_Q\n\nEach query is given in one of the following formats:\n1\n\n2 T\n\n3 H\n\nOutput\n\nLet there be K queries of the third type, and print K lines.\nThe i-th line (1 \\leq i \\leq K) should contain the answer to the i-th query of type 3.\n\nConstraints\n\n\n- 1 \\leq Q \\leq 2 \\times 10^{5}\n- 1 \\leq T,H \\leq 10^{9}\n- There is at least one query of the third type.\n- All input values are integers.\n\nSample Input 1\n\n6\n1\n2 15\n1\n3 10\n2 20\n3 20\n\nSample Output 1\n\n1\n1\n\nQueries are processed in the following order:\n\n- In the first query, a plant of height 0 is planted.\n- In the second query, the height of the plant increases to 15.\n- In the third query, another plant of height 0 is planted. Now there is one plant of height 15 and one plant of height 0.\n- In the fourth query, all plants with height at least 10 are harvested. Here, one plant of height 15 gets harvested, and one plant of height 0 remains. Since one plant was harvested, print 1 on the first line.\n- In the fifth query, the height of the remaining plant increases to 20.\n- In the sixth query, all plants with height at least 20 are harvested. Here, one plant of height 20 gets harvested. Thus, print 1 on the second line.\n\nSample Input 2\n\n15\n1\n1\n2 226069413\n3 1\n1\n1\n2 214168203\n1\n3 214168203\n1\n1\n1\n2 314506461\n2 245642315\n3 1\n\nSample Output 2\n\n2\n2\n4",
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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 have an empty bag.\r\nYou are given Q queries, which must be processed in order.\nThere are three types of queries.\n\n- 1 x : Put one ball with the integer x written on it into the bag.\n- 2 x : Remove one ball with the integer x written on it from the bag and discard it. It is guaranteed that the bag has a ball with the integer x written on it when this query is given.\n- 3 : Print the number of different integers written on the balls in the bag.\n\nInput\n\nThe input is given from Standard Input in the following format:\nQ\r\n\\text{query}_1\r\n\\text{query}_2\r\n\\vdots\r\n\\text{query}_Q\r\n\nThe i-th query \\text{query}_i is given in one of the following three formats:\n1 x\r\n\n2 x\r\n\n3\n\nOutput\n\nIf there are K queries of the third type, print K lines.\r\nThe i-th line (1 \\leq i \\leq K) should contain the answer to the i-th query of the third type.\n\nConstraints\n\n\n- 1 \\leq Q \\leq 2 \\times 10^{5}\n- 1 \\leq x \\leq 10^{6}\n- When a query of the second type is given, the bag has a ball with the integer x written on it.\n- There is at least one query of the third type.\n- All input values are integers.\n\nSample Input 1\n\n8\r\n1 3\r\n1 1\r\n1 4\r\n3\r\n2 1\r\n3\r\n1 5\r\n3\n\nSample Output 1\n\n3\r\n2\r\n3\r\n\nInitially, the bag is empty.\nFor the first query 1 3, a ball with the integer 3 written on it enters the bag.\nFor the second query 1 1, a ball with the integer 1 written on it enters the bag.\nFor the third query 1 4, a ball with the integer 4 written on it enters the bag.\nFor the fourth query 3, the bag has balls with the integers 1, 3, 4, so print 3.\nFor the fifth query 2 1, a ball with the integer 1 written on it is removed from the bag.\nFor the sixth query 3, the bag has balls with the integers 3, 4, so print 2.\nFor the seventh query 1 5, a ball with the integer 5 written on it enters the bag.\nFor the eighth query 3, the bag has balls with the integers 3, 4, 5, so print 3.\n\nSample Input 2\n\n8\r\n1 2\r\n1 2\r\n3\r\n2 2\r\n1 4\r\n1 4\r\n2 2\r\n3\n\nSample Output 2\n\n1\r\n1",
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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 positive integers N, M, K, and a sequence of non-negative integers: A=(A_1,A_2,\\ldots,A_N).\nFor a non-empty non-negative integer sequence B=(B_1,B_2,\\ldots,B_{|B|}), we define its score as follows.\n\n- If the length of B is a multiple of M: (B_1 \\oplus B_2 \\oplus \\dots \\oplus B_{|B|})^K\n- Otherwise: 0\n\nHere, \\oplus represents the bitwise XOR.\nFind the sum, modulo 998244353, of the scores of the 2^N-1 non-empty subsequences of A.\nWhat is bitwise XOR? The bitwise XOR of non-negative integers A and B, denoted as A \\oplus B, is defined as follows: - In the binary representation of A \\oplus B, the digit at position 2^k (k \\geq 0) is 1 if exactly one of A and B has a 1 in that position in their binary representations, and 0 otherwise. For example, 3 \\oplus 5 = 6 (in binary: 011 \\oplus 101 = 110). In general, the XOR of k integers p_1, \\dots, p_k is defined as (\\cdots ((p_1 \\oplus p_2) \\oplus p_3) \\oplus \\cdots \\oplus p_k), and it can be proved that this is independent of the order of p_1, \\dots, p_k.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN M K\r\nA_1 A_2 \\ldots A_N\n\nOutput\n\nPrint the answer.\n\nConstraints\n\n\n- 1 \\leq N,K \\leq 2 \\times 10^5\n- 1 \\leq M \\leq 100\n- 0 \\leq A_i < 2^{20}\n- All input values are integers.\n\nSample Input 1\n\n3 2 2\r\n1 2 3\n\nSample Output 1\n\n14\r\n\nHere are the scores of the 2^3-1=7 non-empty subsequences of A.\n\n- (1): 0\n- (2): 0\n- (3): 0\n- (1,2): (1\\oplus2)^2=9\n- (1,3): (1\\oplus3)^2=4\n- (2,3): (2\\oplus3)^2=1\n- (1,2,3): 0\n\nTherefore, the sought sum is 0+0+0+9+4+1+0=14.\n\nSample Input 2\n\n10 5 3\r\n100 100 100 100 100 100 100 100 100 100\n\nSample Output 2\n\n252000000\n\nSample Input 3\n\n16 4 100\r\n7053 3876 3178 8422 7802 5998 2334 6757 6889 6637 7365 9495 7848 9026 7312 6558\n\nSample Output 3\n\n432440016",
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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 an integer Y between 1583 and 2023.\nFind the number of days in the year Y of the Gregorian calendar.\nWithin the given range, the year Y has the following number of days:\n\n- \r\nif Y is not a multiple of 4, then 365 days;\n\n- \r\nif Y is a multiple of 4 but not a multiple of 100, then 366 days;\n\n- \r\nif Y is a multiple of 100 but not a multiple of 400, then 365 days;\n\n- \r\nif Y is a multiple of 400, then 366 days.\n\nInput\n\nThe input is given from Standard Input in the following format:\nY\n\nOutput\n\nPrint the number of days in the year Y as an integer.\n\nConstraints\n\n\n- Y is an integer between 1583 and 2023, inclusive.\n\nSample Input 1\n\n2023\n\nSample Output 1\n\n365\r\n\n2023 is not a multiple of 4, so it has 365 days.\n\nSample Input 2\n\n1992\n\nSample Output 2\n\n366\r\n\n1992 is a multiple of 4 but not a multiple of 100, so it has 366 days.\n\nSample Input 3\n\n1800\n\nSample Output 3\n\n365\r\n\n1800 is a multiple of 100 but not a multiple of 400, so it has 365 days.\n\nSample Input 4\n\n1600\n\nSample Output 4\n\n366\r\n\n1600 is a multiple of 400, so it has 366 days.",
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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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"do_sample": false,
"max_new_tokens": 32768,
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"temperature": 0.7
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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 a tree with N vertices.\r\nThe vertices are numbered 1, 2, \\ldots, N.\r\nThe i-th edge (1\\leq i\\leq N-1) connects vertices U_i and V_i, with a length of L_i.\nFor each K=1,2,\\ldots, N, solve the following problem.\n\nTakahashi and Aoki play a game. The game proceeds as follows.\n\n- First, Aoki specifies K distinct vertices on the tree.\n- Then, Takahashi constructs a walk that starts and ends at vertex 1, and passes through all the vertices specified by Aoki.\n\nThe score is defined as the length of the walk constructed by Takahashi. Takahashi wants to minimize the score, while Aoki wants to maximize it.\r\nFind the score when both players play optimally.\n\n\nDefinition of a walk\r\n A walk on an undirected graph (possibly a tree) is a sequence of k vertices and k-1 edges v_1,e_1,v_2,\\ldots,v_{k-1},e_{k-1},v_k (where k is a positive integer)\r\n such that edge e_i connects vertices v_i and v_{i+1}. The same vertex or edge can appear multiple times in the sequence. \r\n A walk is said to pass through vertex x if there exists at least one i (1\\leq i\\leq k) such that v_i=x. (There can be multiple such i.) \r\n The walk is said to start and end at v_1 and v_k, respectively, and the length of the walk is the sum of the lengths of e_1, e_2, \\ldots, e_{k-1}.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\r\nU_1 V_1 L_1\r\nU_2 V_2 L_2\r\n\\vdots\r\nU_{N-1} V_{N-1} L_{N-1}\n\nOutput\n\nPrint N lines.\r\nThe i-th line (1\\leq i\\leq N) should contain the answer to the problem for K=i.\n\nConstraints\n\n\n- 2\\leq N\\leq 2\\times 10^5\n- 1\\leq U_i<V_i\\leq N\n- 1\\leq L_i\\leq 10^9\n- All input values are integers.\n- The given graph is a tree.\n\nSample Input 1\n\n5\r\n1 2 3\r\n2 3 5\r\n2 4 2\r\n1 5 3\n\nSample Output 1\n\n16\r\n22\r\n26\r\n26\r\n26\r\n\nFor K=1, Aoki's optimal move is to specify vertex 3, and Takahashi's optimal move is to construct a path vertex 1 \\to vertex 2 \\to vertex 3 \\to vertex 2 \\to vertex 1, resulting in a score of 16.\nFor K=2, Aoki's optimal move is to specify vertices 3 and 5, and Takahashi's optimal move is to construct a path such as vertex 1 \\to vertex 5 \\to vertex 1 \\to vertex 2 \\to vertex 3 \\to vertex 2 \\to vertex 1, resulting in a score of 22.\nFor K\\geq 3, the score when both players play optimally is 26.\n\nSample Input 2\n\n3\r\n1 2 1000000000\r\n2 3 1000000000\n\nSample Output 2\n\n4000000000\r\n4000000000\r\n4000000000\r\n\nBeware that the answer may not fit in a 32-bit integer.",
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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. The function should take stdin as input and print the output. Simply call the function after the definition.There is a road extending east and west, and N persons are on the road.\nThe road extends infinitely long to the east and west from a point called the origin.\nThe i-th person (1\\leq i\\leq N) is initially at a position X_i meters east from the origin.\nThe persons can move along the road to the east or west.\nSpecifically, they can perform the following movement any number of times.\n\n- Choose one person. If there is no other person at the destination, move the chosen person 1 meter east or west.\n\nThey have Q tasks in total, and the i-th task (1\\leq i\\leq Q) is as follows.\n\n- The T_i-th person arrives at coordinate G_i.\n\nFind the minimum total number of movements required to complete all Q tasks in order.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\nX_1 X_2 \\ldots X_N\nQ\nT_1 G_1\nT_2 G_2\n\\vdots\nT_Q G_Q\n\nOutput\n\nPrint the answer.\n\nConstraints\n\n\n- 1\\leq N\\leq2\\times10^5\n- 0\\leq X_1 < X_2 < \\dotsb < X_N \\leq10^8\n- 1\\leq Q\\leq2\\times10^5\n- 1\\leq T_i\\leq N\\ (1\\leq i\\leq Q)\n- 0\\leq G_i\\leq10^8\\ (1\\leq i\\leq Q)\n- All input values are integers.\n\nSample Input 1\n\n5\n10 20 30 40 50\n4\n3 45\n4 20\n1 35\n2 60\n\nSample Output 1\n\n239\n\nAn optimal sequence of movements for the persons is as follows (the positions of the persons are not necessarily drawn to scale):\n\nFor each task, the persons move as follows.\n\n- The 4th person moves 6 steps east, and the 3rd person moves 15 steps east.\n- The 2nd person moves 2 steps west, the 3rd person moves 26 steps west, and the 4th person moves 26 steps west.\n- The 4th person moves 18 steps east, the 3rd person moves 18 steps east, the 2nd person moves 18 steps east, and the 1st person moves 25 steps east.\n- The 5th person moves 13 steps east, the 4th person moves 24 steps east, the 3rd person moves 24 steps east, and the 2nd person moves 24 steps east.\n\nThe total number of movements is 21+54+79+85=239.\nYou cannot complete all tasks with a total movement count of 238 or less, so print 239.\n\nSample Input 2\n\n8\n0 1 2 3 4 5 6 100000000\n6\n1 100000000\n8 0\n1 100000000\n8 4\n1 100000000\n5 21006578\n\nSample Output 2\n\n4294967297\n\nNote that some persons may need to move to the west of the origin or more than 10^8 meters to the east of it.\nAlso, note that the answer may exceed 2^{32}.\n\nSample Input 3\n\n12\n1558 3536 3755 3881 4042 4657 5062 7558 7721 8330 8542 9845\n8\n9 1694\n7 3296\n12 5299\n5 5195\n5 5871\n1 2491\n8 1149\n8 2996\n\nSample Output 3\n\n89644",
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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 strings.\nThe i-th string S_i (1 \\leq i \\leq N) is either Takahashi or Aoki.\nHow many i are there such that S_i is equal to Takahashi?\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\r\nS_1\r\nS_2\r\n\\vdots\r\nS_N\n\nOutput\n\nPrint the count of i such that S_i is equal to Takahashi as an integer in a single line.\n\nConstraints\n\n\n- 1 \\leq N \\leq 100\n- N is an integer.\n- Each S_i is Takahashi or Aoki. (1 \\leq i \\leq N)\n\nSample Input 1\n\n3\r\nAoki\r\nTakahashi\r\nTakahashi\n\nSample Output 1\n\n2\r\n\nS_2 and S_3 are equal to Takahashi, while S_1 is not.\nTherefore, print 2.\n\nSample Input 2\n\n2\r\nAoki\r\nAoki\n\nSample Output 2\n\n0\r\n\nIt is possible that no S_i is equal to Takahashi.\n\nSample Input 3\n\n20\r\nAoki\r\nTakahashi\r\nTakahashi\r\nAoki\r\nAoki\r\nAoki\r\nAoki\r\nTakahashi\r\nAoki\r\nAoki\r\nAoki\r\nTakahashi\r\nTakahashi\r\nAoki\r\nTakahashi\r\nAoki\r\nAoki\r\nAoki\r\nAoki\r\nTakahashi\n\nSample Output 3\n\n7",
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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=(P_1,P_2,\\dots,P_N) of (1,2,\\dots,N).\nYou want to satisfy P_i=i for all i=1,2,\\dots,N by performing the following operation zero or more times:\n\n- Choose an integer k such that 1 \\leq k \\leq N. If k \\geq 2, sort the 1-st through (k-1)-th terms of P in ascending order. Then, if k \\leq N-1, sort the (k+1)-th through N-th terms of P in ascending order.\n\nIt can be proved that under the constraints of this problem, it is possible to satisfy P_i=i for all i=1,2,\\dots,N with a finite number of operations for any P. Find the minimum number of operations required.\nYou have T test cases to solve.\n\nInput\n\nThe input is given from Standard Input in the following format:\nT\r\n\\mathrm{case}_1\r\n\\vdots\r\n\\mathrm{case}_T\r\n\nEach case is given in the following format:\nN\r\nP_1 P_2 \\dots P_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 10^5\n- 3 \\leq N \\leq 2 \\times 10^5\n- P is a permutation of (1,2,\\dots,N).\n- All input values are integers.\n- The sum of N across the test cases in a single input is at most 2 \\times 10^5.\n\nSample Input 1\n\n3\r\n5\r\n2 1 3 5 4\r\n3\r\n1 2 3\r\n7\r\n3 2 1 7 5 6 4\n\nSample Output 1\n\n1\r\n0\r\n2\r\n\nFor the first test case,\n\n- \r\nPerforming the operation with k=1 results in P becoming (2,1,3,4,5).\n\n- \r\nPerforming the operation with k=2 results in P becoming (2,1,3,4,5).\n\n- \r\nPerforming the operation with k=3 results in P becoming (1,2,3,4,5).\n\n- \r\nPerforming the operation with k=4 results in P becoming (1,2,3,5,4).\n\n- \r\nPerforming the operation with k=5 results in P becoming (1,2,3,5,4).\n\n\nSpecifically, performing the operation with k=3 results in P satisfying P_i=i for all i=1,2,\\dots,5. Therefore, the minimum number of operations required is 1.\nFor the third test case, performing the operation with k=4 followed by k=3 results in P changing as (3,2,1,7,5,6,4) \\rightarrow (1,2,3,7,4,5,6) \\rightarrow (1,2,3,4,5,6,7).",
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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 printing machine that prints line segments on the xy-plane by emitting a laser.\n\n- At the start of printing, the laser position is at coordinate (0, 0).\n- \nWhen printing a line segment, the procedure below is followed.\n\n- First, move the laser position to one of the endpoints of the line segment.\n- One may start drawing from either endpoint.\n\n\n- Then, move the laser position in a straight line from the current endpoint to the other endpoint while emitting the laser.\n- It is not allowed to stop printing in the middle of a line segment.\n\n\n\n\n- \nWhen not emitting the laser, the laser position can move in any direction at a speed of S units per second.\n\n- When emitting the laser, the laser position can move along the line segment being printed at a speed of T units per second.\n- The time required for operations other than moving the laser position can be ignored.\n\nTakahashi wants to print N line segments using this printing machine.\nThe i-th line segment connects coordinates (A_i, B_i) and (C_i, D_i).\nSome line segments may overlap, in which case he needs to print the overlapping parts for each line segment separately.\nWhat is the minimum number of seconds required to complete printing all the line segments when he operates the printing machine optimally?\n\nInput\n\nThe input is given from Standard Input in the following format:\nN S T\nA_1 B_1 C_1 D_1\n\\vdots\nA_N B_N C_N D_N\n\nOutput\n\nPrint the answer.\nYour output will be considered correct if the absolute or relative error from the true value does not exceed 10^{-6}.\n\nConstraints\n\n\n- All input values are integers.\n- 1 \\le N \\le 6\n- 1 \\le T \\le S \\le 1000\n- -1000 \\le A_i,B_i,C_i,D_i \\le 1000\n- (A_i,B_i) \\neq (C_i,D_i) ( 1 \\le i \\le N )\n\nSample Input 1\n\n3 2 1\n1 3 2 1\n0 2 0 0\n3 0 2 0\n\nSample Output 1\n\n6.44317475868633722080\n\n\n- Emit the laser while moving the laser position from (0,0) to (0,2), printing the second line segment.\n- This takes 2 seconds.\n\n\n- Move the laser position from (0,2) to (1,3) without emitting the laser.\n- This takes \\sqrt{2}/2 seconds.\n\n\n- Emit the laser while moving the laser position from (1,3) to (2,1), printing the first line segment.\n- This takes \\sqrt{5} seconds.\n\n\n- Move the laser position from (2,1) to (2,0) without emitting the laser.\n- This takes 1/2 second.\n\n\n- Emit the laser while moving the laser position from (2,0) to (3,0), printing the third line segment.\n- This takes 1 second.\n\n\n- The total time taken is 2 + (\\sqrt{2}/2) + \\sqrt{5} + (1/2) + 1 \\approx 6.443175 seconds.\n\nSample Input 2\n\n2 1 1\n0 0 10 10\n0 2 2 0\n\nSample Output 2\n\n20.97056274847714058517\n\nSample Input 3\n\n6 3 2\n-1000 -1000 1000 1000\n1000 -1000 -1000 1000\n-1000 -1000 1000 1000\n1000 -1000 -1000 1000\n1000 1000 -1000 -1000\n-1000 1000 1000 -1000\n\nSample Output 3\n\n9623.35256169626864153344\n\nMultiple line segments overlap here, and you need to print the overlapping parts for each line segment separately.\n\nSample Input 4\n\n6 10 8\n1000 1000 -1000 -1000\n1000 -1000 -1000 -1000\n-1000 1000 1000 1000\n-1000 1000 -1000 -1000\n1000 1000 1000 -1000\n1000 -1000 -1000 1000\n\nSample Output 4\n\n2048.52813742385702910909",
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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.Alice and Bob are playing a game where they take turns removing stones from a pile, with Alice going first.\n\nAlice starts by removing exactly 10 stones on her first turn.\nFor each subsequent turn, each player removes exactly 1 fewer stone than the previous opponent.\n\nThe player who cannot make a move loses the game.\nGiven a positive integer n, return true if Alice wins the game and false otherwise.\n \nExample 1:\n\nInput: n = 12\nOutput: true\nExplanation:\n\nAlice removes 10 stones on her first turn, leaving 2 stones for Bob.\nBob cannot remove 9 stones, so Alice wins.\n\n\nExample 2:\n\nInput: n = 1\nOutput: false\nExplanation:\n\nAlice cannot remove 10 stones, so Alice loses.\n\n\n \nConstraints:\n\n1 <= n <= 50",
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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 binary string s.\nYou can perform the following operation on the string any number of times:\n\nChoose any index i from the string where i + 1 < s.length such that s[i] == '1' and s[i + 1] == '0'.\nMove the character s[i] to the right until it reaches the end of the string or another '1'. For example, for s = \"010010\", if we choose i = 1, the resulting string will be s = \"000110\".\n\nReturn the maximum number of operations that you can perform.\n \nExample 1:\n\nInput: s = \"1001101\"\nOutput: 4\nExplanation:\nWe can perform the following operations:\n\nChoose index i = 0. The resulting string is s = \"0011101\".\nChoose index i = 4. The resulting string is s = \"0011011\".\nChoose index i = 3. The resulting string is s = \"0010111\".\nChoose index i = 2. The resulting string is s = \"0001111\".\n\n\nExample 2:\n\nInput: s = \"00111\"\nOutput: 0\n\n \nConstraints:\n\n1 <= s.length <= 10^5\ns[i] is either '0' or '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 are three brothers named A, B, and C. The age relationships among them are given by three characters S_{\\mathrm{AB}}, S_{\\mathrm{AC}}, S_{\\mathrm{BC}}, which mean the following:\n\n- If S_{\\mathrm{AB}} is <, then A is younger than B; if it is >, then A is older than B.\n- If S_{\\mathrm{AC}} is <, then A is younger than C; if it is >, then A is older than C.\n- If S_{\\mathrm{BC}} is <, then B is younger than C; if it is >, then B is older than C.\n\nWho is the middle brother, that is, the second oldest among the three?\n\nInput\n\nThe input is given from Standard Input in the following format:\nS_{\\mathrm{AB}} S_{\\mathrm{AC}} S_{\\mathrm{BC}}\n\nOutput\n\nPrint the name of the middle brother, that is, the second oldest among the three.\n\nConstraints\n\n\n- Each of S_{\\mathrm{AB}}, S_{\\mathrm{AC}}, S_{\\mathrm{BC}} is < or >.\n- The input contains no contradictions; that is, there always exists an age relationship that satisfies all given inequalities.\n\nSample Input 1\n\n< < <\n\nSample Output 1\n\nB\n\nSince A is younger than B, and B is younger than C, we can determine that C is the oldest, B is the middle, and A is the youngest. Hence, the answer is B.\n\nSample Input 2\n\n< < >\n\nSample Output 2\n\nC",
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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.As KEYENCE headquarters have more and more workers, they decided to divide the departments in the headquarters into two groups and stagger their lunch breaks.\nKEYENCE headquarters have N departments, and the number of people in the i-th department (1\\leq i\\leq N) is K_i.\nWhen assigning each department to Group A or Group B, having each group take lunch breaks at the same time, and ensuring that the lunch break times of Group A and Group B do not overlap, find the minimum possible value of the maximum number of people taking a lunch break at the same time.\r\nIn other words, find the minimum possible value of the larger of the following: the total number of people in departments assigned to Group A, and the total number of people in departments assigned to Group B.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\r\nK_1 K_2 \\ldots K_N\n\nOutput\n\nPrint the minimum possible value of the maximum number of people taking a lunch break at the same time.\n\nConstraints\n\n\n- 2 \\leq N \\leq 20\n- 1 \\leq K_i \\leq 10^8\n- All input values are integers.\n\nSample Input 1\n\n5\r\n2 3 5 10 12\n\nSample Output 1\n\n17\r\n\nWhen assigning departments 1, 2, and 5 to Group A, and departments 3 and 4 to Group B, Group A has a total of 2+3+12=17 people, and Group B has a total of 5+10=15 people. Thus, the maximum number of people taking a lunch break at the same time is 17.\nIt is impossible to assign the departments so that both groups have 16 or fewer people, so print 17.\n\nSample Input 2\n\n2\r\n1 1\n\nSample Output 2\n\n1\r\n\nMultiple departments may have the same number of people.\n\nSample Input 3\n\n6\r\n22 25 26 45 22 31\n\nSample Output 3\n\n89\r\n\nFor example, when assigning departments 1, 4, and 5 to Group A, and departments 2, 3, and 6 to Group B, the maximum number of people taking a lunch break at the same time is 89.",
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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.Given an array of integers nums and an integer k, return the number of subarrays of nums where the bitwise AND of the elements of the subarray equals k.\n \nExample 1:\n\nInput: nums = [1,1,1], k = 1\nOutput: 6\nExplanation:\nAll subarrays contain only 1's.\n\nExample 2:\n\nInput: nums = [1,1,2], k = 1\nOutput: 3\nExplanation:\nSubarrays having an AND value of 1 are: [1,1,2], [1,1,2], [1,1,2].\n\nExample 3:\n\nInput: nums = [1,2,3], k = 2\nOutput: 2\nExplanation:\nSubarrays having an AND value of 2 are: [1,2,3], [1,2,3].\n\n \nConstraints:\n\n1 <= nums.length <= 10^5\n0 <= nums[i], k <= 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 a grid with H horizontal rows and W vertical columns.\r\nLet (i, j) denote the cell at the i-th row (1\\leq i\\leq H) from the top and j-th column (1\\leq j\\leq W) from the left.\nInitially, there is a slime with strength S _ {i,j} in cell (i,j), and Takahashi is the slime in the cell (P,Q).\nFind the maximum possible strength of Takahashi after performing the following action any number of times (possibly zero):\n\n- Among the slimes adjacent to him, choose one whose strength is strictly less than \\dfrac{1}{X} times his strength and absorb it.\r\n As a result, the absorbed slime disappears, and Takahashi's strength increases by the strength of the absorbed slime.\n\nWhen performing the above action, the gap left by the disappeared slime is immediately filled by Takahashi, and the slimes that were adjacent to the disappeared one (if any) become newly adjacent to Takahashi (refer to the explanation in sample 1).\n\nInput\n\nThe input is given in the following format from Standard Input:\nH W X \r\nP Q\r\nS _ {1,1} S _ {1,2} \\ldots S _ {1,W}\r\nS _ {2,1} S _ {2,2} \\ldots S _ {2,W}\r\n\\vdots\r\nS _ {H,1} S _ {H,2} \\ldots S _ {H,W}\n\nOutput\n\nPrint the maximum possible strength of Takahashi after performing the action.\n\nConstraints\n\n\n- 1\\leq H,W\\leq500\n- 1\\leq P\\leq H\n- 1\\leq Q\\leq W\n- 1\\leq X\\leq10^9\n- 1\\leq S _ {i,j}\\leq10^{12}\n- All input values are integers.\n\nSample Input 1\n\n3 3 2\r\n2 2\r\n14 6 9\r\n4 9 20\r\n17 15 7\n\nSample Output 1\n\n28\r\n\nInitially, the strength of the slime in each cell is as follows:\n\nFor example, Takahashi can act as follows:\n\n\n- Absorb the slime in cell (2,1). His strength becomes 9+4=13, and the slimes in cells (1,1) and (3,1) become newly adjacent to him.\n- Absorb the slime in cell (1,2). His strength becomes 13+6=19, and the slime in cell (1,3) becomes newly adjacent to him.\n- Absorb the slime in cell (1,3). His strength becomes 19+9=28.\n\nAfter these actions, his strength is 28.\nNo matter how he acts, it is impossible to get a strength greater than 28, so print 28.\nNote that Takahashi can only absorb slimes whose strength is strictly less than half of his strength. For example, in the figure on the right above, he cannot absorb the slime in cell (1,1).\n\nSample Input 2\n\n3 4 1\r\n1 1\r\n5 10 1 1\r\n10 1 1 1\r\n1 1 1 1\n\nSample Output 2\n\n5\r\n\nHe cannot absorb any slimes.\n\nSample Input 3\n\n8 10 2\r\n1 5\r\n388 130 971 202 487 924 247 286 237 316\r\n117 166 918 106 336 928 493 391 235 398\r\n124 280 425 955 212 988 227 222 307 226\r\n336 302 478 246 950 368 291 236 170 101\r\n370 200 204 141 287 410 388 314 205 460\r\n291 104 348 337 404 399 416 263 415 339\r\n105 420 302 334 231 481 466 366 401 452\r\n119 432 292 403 371 417 351 231 482 184\n\nSample Output 3\n\n1343",
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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=(P_1,P_2,\\dots,P_N) of (1,2,\\dots,N).\nConsider the following operations k\\ (k=2,3,\\dots,N) on this permutation.\n\n- Operation k: For i=1,2,\\dots,k-1 in this order, if P_i > P_{i+1}, swap the values of the i-th and (i+1)-th elements of P.\n\nYou are also given a non-decreasing sequence A=(A_1,A_2,\\dots,A_M)\\ (2 \\leq A_i \\leq N) of length M.\nFor each i=1,2,\\dots,M, find the inversion number of P after applying the operations A_1, A_2, \\dots, A_i in this order.\n\n What is the inversion number of a sequence?\r\n\r\nThe inversion number of a sequence x=(x_1,x_2,\\dots,x_n) of length n is the number of pairs of integers (i,j)\\ (1\\leq i < j \\leq n) such that x_i > x_j.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\r\nP_1 P_2 \\dots P_N\r\nM\r\nA_1 A_2 \\dots A_M\n\nOutput\n\nPrint M lines. The k-th line should contain the answer to the problem for i=k.\n\nConstraints\n\n\n- 2 \\leq N \\leq 2 \\times 10^5\n- 1 \\leq M \\leq 2 \\times 10^5\n- 2 \\leq A_i \\leq N\n- P is a permutation of (1,2,\\dots,N).\n- A_i \\leq A_{i+1} for i=1,2,\\dots,M-1.\n- All input values are integers.\n\nSample Input 1\n\n6\r\n3 2 4 1 6 5\r\n2\r\n4 6\n\nSample Output 1\n\n3\r\n1\r\n\nFirst, operation 4 is performed. During this, P changes as follows: (3,2,4,1,6,5) \\rightarrow (2,3,4,1,6,5) \\rightarrow (2,3,4,1,6,5) \\rightarrow (2,3,1,4,6,5). The inversion number of P afterward is 3.\nNext, operation 6 is performed, where P eventually becomes (2,1,3,4,5,6), whose inversion number is 1.\n\nSample Input 2\n\n20\r\n12 14 16 8 7 15 19 6 18 5 13 9 10 17 4 1 11 20 2 3\r\n15\r\n3 4 6 8 8 9 10 12 13 15 18 18 19 19 20\n\nSample Output 2\n\n117\r\n116\r\n113\r\n110\r\n108\r\n105\r\n103\r\n99\r\n94\r\n87\r\n79\r\n72\r\n65\r\n58\r\n51",
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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+2 cells arranged in a row. Let cell i denote the i-th cell from the left.\nThere is one stone placed in each of the cells from cell 1 to cell N.\r\nFor each 1 \\leq i \\leq N, the stone in cell i is white if S_i is W, and black if S_i is B.\r\nCells N+1 and N+2 are empty.\nYou can perform the following operation any number of times (possibly zero):\n\n- Choose a pair of adjacent cells that both contain stones, and move these two stones to the empty two cells while preserving their order.\r\n More precisely, choose an integer x such that 1 \\leq x \\leq N+1 and both cells x and x+1 contain stones. Let k and k+1 be the empty two cells. Move the stones from cells x and x+1 to cells k and k+1, respectively.\n\nDetermine if it is possible to achieve the following state, and if so, find the minimum number of operations required:\n\n- Each of the cells from cell 1 to cell N contains one stone, and for each 1 \\leq i \\leq N, the stone in cell i is white if T_i is W, and black if T_i is B.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\r\nS\r\nT\n\nOutput\n\nIf it is possible to achieve the desired state, print the minimum number of operations required. If it is impossible, print -1.\n\nConstraints\n\n\n- 2 \\leq N \\leq 14\n- N is an integer.\n- Each of S and T is a string of length N consisting of B and W.\n\nSample Input 1\n\n6\r\nBWBWBW\r\nWWWBBB\n\nSample Output 1\n\n4\r\n\nUsing . to represent an empty cell, the desired state can be achieved in four operations as follows, which is the minimum:\n\n- BWBWBW..\n- BW..BWBW\n- BWWBB..W\n- ..WBBBWW\n- WWWBBB..\n\nSample Input 2\n\n6\r\nBBBBBB\r\nWWWWWW\n\nSample Output 2\n\n-1\n\nSample Input 3\n\n14\r\nBBBWBWWWBBWWBW\r\nWBWWBBWWWBWBBB\n\nSample Output 3\n\n7",
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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 boxes numbered 1 to N and N items numbered 1 to N. Item i (1 \\leq i \\leq N) is in box A_i and has a weight of W_i.\nYou can repeatedly perform the operation of choosing an item and moving it to another box zero or more times. If the weight of the item being moved is w, the cost of the operation is w.\nFind the minimum total cost required to make each box contain exactly one item.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\r\nA_1 A_2 \\ldots A_N\r\nW_1 W_2 \\ldots W_N\n\nOutput\n\nPrint the minimum total cost required to make each box contain exactly one item.\n\nConstraints\n\n\n- 1 \\leq N \\leq 10^{5}\n- 1 \\leq A_i \\leq N (1 \\leq i \\leq N)\n- 1 \\leq W_i \\leq 10^{4} (1 \\leq i \\leq N)\n- All input values are integers.\n\nSample Input 1\n\n5\r\n2 2 3 3 5\r\n33 40 2 12 16\n\nSample Output 1\n\n35\r\n\nWith the following two moves, you can make each box contain exactly one item:\n\n- Move item 1 from box 2 to box 1. The cost is 33.\n- Move item 3 from box 3 to box 4. The cost is 2.\n\nThe total cost of these two moves is 35. It is impossible to make each box contain exactly one item with a cost less than 35, so print 35.\n\nSample Input 2\n\n12\r\n3 6 7 4 12 4 8 11 11 1 8 11\r\n3925 9785 9752 3587 4013 1117 3937 7045 6437 6208 3391 6309\n\nSample Output 2\n\n17254",
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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 sequence A = (A_1, A_2, \\dots, A_N) of length N. For each k = 1, 2, \\dots, N, find the number, modulo 998244353, of (not necessarily contiguous) subsequences of A of length k that are arithmetic sequences. Two subsequences are distinguished if they are taken from different positions, even if they are equal as sequences.\n\nWhat is a subsequence?\nA subsequence of a sequence A is a sequence obtained by deleting zero or more elements from A and arranging the remaining elements without changing the order.\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 answers for k = 1, 2, \\dots, N in this order, in a single line, separated by spaces.\n\nConstraints\n\n\n- 1 \\leq N \\leq 80\n- 1 \\leq A_i \\leq 10^9\n- All input values are integers.\n\nSample Input 1\n\n5\n1 2 3 2 3\n\nSample Output 1\n\n5 10 3 0 0\n\n\n- There are 5 subsequences of length 1, all of which are arithmetic sequences.\n- There are 10 subsequences of length 2, all of which are arithmetic sequences.\n- There are 3 subsequences of length 3 that are arithmetic sequences: (A_1, A_2, A_3), (A_1, A_2, A_5), and (A_1, A_4, A_5).\n- There are no arithmetic subsequences of length 4 or more.\n\nSample Input 2\n\n4\n1 2 3 4\n\nSample Output 2\n\n4 6 2 1\n\nSample Input 3\n\n1\n100\n\nSample Output 3\n\n1",
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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.For a sequence A = (A_1, \\ldots, A_N) of length N, define f(A) as follows.\n\n- Prepare a graph with N vertices labeled 1 to N and zero edges. For every integer pair (i, j) satisfying 1 \\leq i < j \\leq N, if A_i \\leq A_j, draw a bidirectional edge connecting vertices i and j. Define f(A) as the number of connected components in the resulting graph.\n\nYou are given a sequence B = (B_1, \\ldots, B_N) of length N. Each element of B is -1 or an integer between 1 and M, inclusive.\nBy replacing every occurrence of -1 in B with an integer between 1 and M, one can obtain M^q sequences B', where q is the number of -1 in B.\nFind the sum, modulo 998244353, of f(B') over all possible B'.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN M\nB_1 \\ldots B_N\n\nOutput\n\nPrint the answer.\n\nConstraints\n\n\n- All input numbers are integers.\n- 2 \\leq N \\leq 2000\n- 1 \\leq M \\leq 2000\n- Each B_i is -1 or an integer between 1 and M, inclusive.\n\nSample Input 1\n\n3 3\n2 -1 1\n\nSample Output 1\n\n6\n\nThere are three possible sequences B': (2,1,1), (2,2,1), and (2,3,1).\nWhen B' = (2,1,1), an edge is drawn only between vertices 2 and 3, so the number of connected components is 2. Thus, f(B') = 2.\nSimilarly, f(B') = 2 for B' = (2,2,1) and f(B') = 2 for B' = (2,3,1), so the answer is 2 + 2 + 2 = 6.\n\nSample Input 2\n\n10 8\n-1 7 -1 -1 -1 2 -1 1 -1 2\n\nSample Output 2\n\n329785\n\nSample Input 3\n\n11 12\n-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1\n\nSample Output 3\n\n529513150\n\nRemember to find the sum modulo 998244353.",
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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 permutations P=(P_1,P_2,\\dots,P_N) and Q=(Q_1,Q_2,\\dots,Q_N) of (1,2,\\dots,N).\nWrite one of the characters 0 and 1 in each cell of an N-by-N grid so that all of the following conditions are satisfied:\n\n- Let S_i be the string obtained by concatenating the characters in the i-th row from the 1-st to the N-th column. Then, S_{P_1} < S_{P_2} < \\dots < S_{P_N} in lexicographical order.\n- Let T_i be the string obtained by concatenating the characters in the i-th column from the 1-st to the N-th row. Then, T_{Q_1} < T_{Q_2} < \\dots < T_{Q_N} in lexicographical order.\n\nIt can be proved that for any P and Q, there is at least one way to write the characters that satisfies all the conditions.\n What does \"X < Y in lexicographical order\" mean?\nFor strings X=X_1X_2\\dots X_{|X|} and Y = Y_1Y_2\\dots Y_{|Y|}, \"X < Y in lexicographical order\" means that 1. or 2. below holds.\r\nHere, |X| and |Y| denote the lengths of X and Y, respectively.\n\n- |X| \\lt |Y| and X_1X_2\\ldots X_{|X|} = Y_1Y_2\\ldots Y_{|X|}. \n- There exists an integer 1 \\leq i \\leq \\min\\lbrace |X|, |Y| \\rbrace such that both of the following are true:\r\n\n- X_1X_2\\ldots X_{i-1} = Y_1Y_2\\ldots Y_{i-1}\n- X_i is less than Y_i.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\r\nP_1 P_2 \\dots P_N\r\nQ_1 Q_2 \\dots Q_N\n\nOutput\n\nPrint a way to fill the grid that satisfies the conditions in the following format, where A_{ij} is the character written at the i-th row and j-th column:\nA_{11}A_{12}\\dots A_{1N}\r\n\\vdots\r\nA_{N1}A_{N2}\\dots A_{NN}\r\n\nIf there are multiple ways to satisfy the conditions, any of them will be accepted.\n\nConstraints\n\n\n- 2 \\leq N \\leq 500\n- P and Q are permutations of (1,2,\\dots,N).\n- All input values are integers.\n\nSample Input 1\n\n3\r\n1 2 3\r\n2 1 3\n\nSample Output 1\n\n001\r\n101\r\n110\r\n\nIn this sample, S_1=001, S_2=101, S_3=110, and T_1=011, T_2=001, T_3=110. Therefore, S_1 < S_2 < S_3 and T_2 < T_1 < T_3 hold, satisfying the conditions.\n\nSample Input 2\n\n15\r\n8 15 10 2 4 3 1 13 5 12 9 6 14 11 7\r\n4 1 5 14 3 12 13 7 11 8 6 2 9 15 10\n\nSample Output 2\n\n010001111110101\r\n001000000101001\r\n010001001100010\r\n010000011110010\r\n010011101101101\r\n100101110100000\r\n111100011001000\r\n000001001100000\r\n100011011000101\r\n000111101011110\r\n101010101010101\r\n011010101011110\r\n010011000010011\r\n100110010110101\r\n000101101100100",
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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 horizontal rows and W vertical columns.\r\nLet (i, j) denote the cell at the i-th row (1\\leq i\\leq H) from the top and j-th column (1\\leq j\\leq W) from the left.\nInitially, there is a slime with strength S _ {i,j} in cell (i,j), and Takahashi is the slime in the cell (P,Q).\nFind the maximum possible strength of Takahashi after performing the following action any number of times (possibly zero):\n\n- Among the slimes adjacent to him, choose one whose strength is strictly less than \\dfrac{1}{X} times his strength and absorb it.\r\n As a result, the absorbed slime disappears, and Takahashi's strength increases by the strength of the absorbed slime.\n\nWhen performing the above action, the gap left by the disappeared slime is immediately filled by Takahashi, and the slimes that were adjacent to the disappeared one (if any) become newly adjacent to Takahashi (refer to the explanation in sample 1).\n\nInput\n\nThe input is given in the following format from Standard Input:\nH W X \r\nP Q\r\nS _ {1,1} S _ {1,2} \\ldots S _ {1,W}\r\nS _ {2,1} S _ {2,2} \\ldots S _ {2,W}\r\n\\vdots\r\nS _ {H,1} S _ {H,2} \\ldots S _ {H,W}\n\nOutput\n\nPrint the maximum possible strength of Takahashi after performing the action.\n\nConstraints\n\n\n- 1\\leq H,W\\leq500\n- 1\\leq P\\leq H\n- 1\\leq Q\\leq W\n- 1\\leq X\\leq10^9\n- 1\\leq S _ {i,j}\\leq10^{12}\n- All input values are integers.\n\nSample Input 1\n\n3 3 2\r\n2 2\r\n14 6 9\r\n4 9 20\r\n17 15 7\n\nSample Output 1\n\n28\r\n\nInitially, the strength of the slime in each cell is as follows:\n\nFor example, Takahashi can act as follows:\n\n\n- Absorb the slime in cell (2,1). His strength becomes 9+4=13, and the slimes in cells (1,1) and (3,1) become newly adjacent to him.\n- Absorb the slime in cell (1,2). His strength becomes 13+6=19, and the slime in cell (1,3) becomes newly adjacent to him.\n- Absorb the slime in cell (1,3). His strength becomes 19+9=28.\n\nAfter these actions, his strength is 28.\nNo matter how he acts, it is impossible to get a strength greater than 28, so print 28.\nNote that Takahashi can only absorb slimes whose strength is strictly less than half of his strength. For example, in the figure on the right above, he cannot absorb the slime in cell (1,1).\n\nSample Input 2\n\n3 4 1\r\n1 1\r\n5 10 1 1\r\n10 1 1 1\r\n1 1 1 1\n\nSample Output 2\n\n5\r\n\nHe cannot absorb any slimes.\n\nSample Input 3\n\n8 10 2\r\n1 5\r\n388 130 971 202 487 924 247 286 237 316\r\n117 166 918 106 336 928 493 391 235 398\r\n124 280 425 955 212 988 227 222 307 226\r\n336 302 478 246 950 368 291 236 170 101\r\n370 200 204 141 287 410 388 314 205 460\r\n291 104 348 337 404 399 416 263 415 339\r\n105 420 302 334 231 481 466 366 401 452\r\n119 432 292 403 371 417 351 231 482 184\n\nSample Output 3\n\n1343",
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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 of N^2 squares with N rows and N columns.\r\nLet (i,j) denote the square at the i-th row from the top (1\\leq i\\leq N) and j-th column from the left (1\\leq j\\leq N).\nEach square is either empty or has a piece placed on it.\r\nThere are M pieces placed on the grid, and the k-th (1\\leq k\\leq M) piece is placed on square (a_k,b_k).\nYou want to place your piece on an empty square in such a way that it cannot be captured by any of the existing pieces.\nA piece placed on square (i,j) can capture pieces that satisfy any of the following conditions:\n\n- Placed in row i\n- Placed in column j\n- Placed on any square (a,b)\\ (1\\leq a\\leq N,1\\leq b\\leq N) where i+j=a+b\n- Placed on any square (a,b)\\ (1\\leq a\\leq N,1\\leq b\\leq N) where i-j=a-b\n\nFor example, a piece placed on square (4,4) can capture pieces placed on the squares shown in blue in the following figure:\n\nHow many squares can you place your piece on?\n\nInput\n\nThe input is given from Standard Input in the following format:\nN M\r\na_1 b_1\r\na_2 b_2\r\n\\vdots\r\na_M b_M\n\nOutput\n\nPrint the number of empty squares where you can place your piece without it being captured by any existing pieces.\n\nConstraints\n\n\n- 1\\leq N\\leq10^9\n- 1\\leq M\\leq10^3\n- 1\\leq a_k\\leq N,1\\leq b_k\\leq N\\ (1\\leq k\\leq M)\n- (a_k,b_k)\\neq(a_l,b_l)\\ (1\\leq k\\lt l\\leq M)\n- All input values are integers.\n\nSample Input 1\n\n8 6\r\n1 4\r\n2 1\r\n3 8\r\n4 5\r\n5 2\r\n8 3\n\nSample Output 1\n\n2\r\n\nThe existing pieces can capture pieces placed on the squares shown in blue in the following figure:\n\nTherefore, you can place your piece on only two squares: squares (6,6) and (7,7).\n\nSample Input 2\n\n1000000000 1\r\n1 1\n\nSample Output 2\n\n999999997000000002\r\n\nOut of 10^{18} squares, the squares that cannot be used are: squares in row 1, squares in column 1, and squares (1,1), (2,2), \\ldots, (10^9,10^9), totaling 3\\times10^9-2 squares.\nNote that the answer may be 2^{32} or greater.\n\nSample Input 3\n\n20 10\r\n1 4\r\n7 11\r\n7 15\r\n8 10\r\n11 6\r\n12 5\r\n13 1\r\n15 2\r\n20 10\r\n20 15\n\nSample Output 3\n\n77",
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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 positive integers N, L, and R.\r\nFor a sequence A = (1, 2, \\dots, N) of length N, an operation of reversing the L-th through R-th elements was performed once.\r\nPrint the sequence after this operation.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN L R\n\nOutput\n\nLet A' = (A'_1, A'_2, \\dots, A'_N) be the sequence after the operation. Print it in the following format:\nA'_1 A'_2 \\dots A'_N\n\nConstraints\n\n\n- All input values are integers.\n- 1 \\leq L \\leq R \\leq N \\leq 100\n\nSample Input 1\n\n5 2 3\n\nSample Output 1\n\n1 3 2 4 5\r\n\nInitially, A = (1, 2, 3, 4, 5).\r\nAfter reversing the second through third elements, the sequence becomes (1, 3, 2, 4, 5), which should be printed.\n\nSample Input 2\n\n7 1 1\n\nSample Output 2\n\n1 2 3 4 5 6 7\r\n\nIt is possible that L = R.\n\nSample Input 3\n\n10 1 10\n\nSample Output 3\n\n10 9 8 7 6 5 4 3 2 1\r\n\nIt is possible that L = 1 or R = N.",
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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 decided to hold a programming contest.\nThe contest consists of five problems: A, B, C, D, E, with scores a, b, c, d, e, respectively.\nThere are 31 participants, and all of them solved at least one problem.\nMore specifically, for every non-empty subsequence (not necessarily contiguous) of the string ABCDE, there is a participant named after that subsequence who solved the problems corresponding to the letters in their name and did not solve the other problems.\nFor example, participant A solved only problem A, and participant BCE solved problems B, C, and E.\nPrint the names of the participants in order of their obtained scores, from the largest to the smallest.\r\nThe score obtained by a participant is the sum of the scores of the problems they solved.\nIf two participants obtained the same score, print the one whose name is lexicographically smaller first.\nWhat does \"lexicographically smaller\" mean?\nIn short, \"lexicographically smaller\" refers to the order in which words would appear in a dictionary.\nMore precisely, for distinct strings S,T consisting of uppercase English letters, S is lexicographically smaller than T if either of the following conditions holds:\n\n- The length |S| of S is less than the length of T, and the first |S| characters of T match S.\n- There exists an integer 1\\leq i\\leq\\min\\{ |S|,|T|\\} that satisfy both of the following two conditions:\n- For every integer j with 1\\leq j\\lt i, the j-th character of S equals the j-th character of T.\n- The i-th character of S is alphabetically smaller than the i-th character of T.\n\n\nFor example, if S= AB and T= ABC, the first condition holds, so S is lexicographically smaller than T.\r\nIf S= ABD and T= ACD, the second condition holds for i=2, so S is lexicographically smaller than T.\n\nInput\n\nThe input is given from Standard Input in the following format:\na b c d e\n\nOutput\n\nPrint 31 lines.\r\nThe i-th line (1\\leq i\\leq 31) should contain the name of the participant who obtained the i-th highest score.\r\nIf multiple participants have the same score, print them in lexicographical order.\n\nConstraints\n\n\n- 100\\leq a\\leq b\\leq c\\leq d\\leq e\\leq 2718\n- All input values are integers.\n\nSample Input 1\n\n400 500 600 700 800\n\nSample Output 1\n\nABCDE\r\nBCDE\r\nACDE\r\nABDE\r\nABCE\r\nABCD\r\nCDE\r\nBDE\r\nADE\r\nBCE\r\nACE\r\nBCD\r\nABE\r\nACD\r\nABD\r\nABC\r\nDE\r\nCE\r\nBE\r\nCD\r\nAE\r\nBD\r\nAD\r\nBC\r\nAC\r\nAB\r\nE\r\nD\r\nC\r\nB\r\nA\r\n\nThe score of each participant is as follows:\n\nFor example, ADE and BCE obtained the same score, and ADE is lexicographically smaller, so print ADE before BCE.\n\nSample Input 2\n\n800 800 900 900 1000\n\nSample Output 2\n\nABCDE\r\nACDE\r\nBCDE\r\nABCE\r\nABDE\r\nABCD\r\nCDE\r\nACE\r\nADE\r\nBCE\r\nBDE\r\nABE\r\nACD\r\nBCD\r\nABC\r\nABD\r\nCE\r\nDE\r\nAE\r\nBE\r\nCD\r\nAC\r\nAD\r\nBC\r\nBD\r\nAB\r\nE\r\nC\r\nD\r\nA\r\nB\n\nSample Input 3\n\n128 256 512 1024 2048\n\nSample Output 3\n\nABCDE\r\nBCDE\r\nACDE\r\nCDE\r\nABDE\r\nBDE\r\nADE\r\nDE\r\nABCE\r\nBCE\r\nACE\r\nCE\r\nABE\r\nBE\r\nAE\r\nE\r\nABCD\r\nBCD\r\nACD\r\nCD\r\nABD\r\nBD\r\nAD\r\nD\r\nABC\r\nBC\r\nAC\r\nC\r\nAB\r\nB\r\nA",
"role": "user"
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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 road extending east and west, and N persons are on the road.\nThe road extends infinitely long to the east and west from a point called the origin.\nThe i-th person (1\\leq i\\leq N) is initially at a position X_i meters east from the origin.\nThe persons can move along the road to the east or west.\nSpecifically, they can perform the following movement any number of times.\n\n- Choose one person. If there is no other person at the destination, move the chosen person 1 meter east or west.\n\nThey have Q tasks in total, and the i-th task (1\\leq i\\leq Q) is as follows.\n\n- The T_i-th person arrives at coordinate G_i.\n\nFind the minimum total number of movements required to complete all Q tasks in order.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\nX_1 X_2 \\ldots X_N\nQ\nT_1 G_1\nT_2 G_2\n\\vdots\nT_Q G_Q\n\nOutput\n\nPrint the answer.\n\nConstraints\n\n\n- 1\\leq N\\leq2\\times10^5\n- 0\\leq X_1 < X_2 < \\dotsb < X_N \\leq10^8\n- 1\\leq Q\\leq2\\times10^5\n- 1\\leq T_i\\leq N\\ (1\\leq i\\leq Q)\n- 0\\leq G_i\\leq10^8\\ (1\\leq i\\leq Q)\n- All input values are integers.\n\nSample Input 1\n\n5\n10 20 30 40 50\n4\n3 45\n4 20\n1 35\n2 60\n\nSample Output 1\n\n239\n\nAn optimal sequence of movements for the persons is as follows (the positions of the persons are not necessarily drawn to scale):\n\nFor each task, the persons move as follows.\n\n- The 4th person moves 6 steps east, and the 3rd person moves 15 steps east.\n- The 2nd person moves 2 steps west, the 3rd person moves 26 steps west, and the 4th person moves 26 steps west.\n- The 4th person moves 18 steps east, the 3rd person moves 18 steps east, the 2nd person moves 18 steps east, and the 1st person moves 25 steps east.\n- The 5th person moves 13 steps east, the 4th person moves 24 steps east, the 3rd person moves 24 steps east, and the 2nd person moves 24 steps east.\n\nThe total number of movements is 21+54+79+85=239.\nYou cannot complete all tasks with a total movement count of 238 or less, so print 239.\n\nSample Input 2\n\n8\n0 1 2 3 4 5 6 100000000\n6\n1 100000000\n8 0\n1 100000000\n8 4\n1 100000000\n5 21006578\n\nSample Output 2\n\n4294967297\n\nNote that some persons may need to move to the west of the origin or more than 10^8 meters to the east of it.\nAlso, note that the answer may exceed 2^{32}.\n\nSample Input 3\n\n12\n1558 3536 3755 3881 4042 4657 5062 7558 7721 8330 8542 9845\n8\n9 1694\n7 3296\n12 5299\n5 5195\n5 5871\n1 2491\n8 1149\n8 2996\n\nSample Output 3\n\n89644",
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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 is planning to eat N dishes.\nThe i-th dish he plans to eat is sweet if S_i = sweet, and salty if S_i = salty.\nIf he eats two sweet dishes consecutively, he will feel sick and be unable to eat any more dishes.\nDetermine whether he can eat all the dishes.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\r\nS_1\r\nS_2\r\n\\vdots\r\nS_N\n\nOutput\n\nPrint Yes if Takahashi can eat all the dishes, and No otherwise.\n\nConstraints\n\n\n- N is an integer between 1 and 100, inclusive.\n- Each S_i is sweet or salty.\n\nSample Input 1\n\n5\r\nsalty\r\nsweet\r\nsalty\r\nsalty\r\nsweet\n\nSample Output 1\n\nYes\r\n\nHe will not eat two sweet dishes consecutively, so he can eat all the dishes without feeling sick.\n\nSample Input 2\n\n4\r\nsweet\r\nsalty\r\nsweet\r\nsweet\n\nSample Output 2\n\nYes\r\n\nHe will feel sick but can still eat all the dishes.\n\nSample Input 3\n\n6\r\nsalty\r\nsweet\r\nsweet\r\nsalty\r\nsweet\r\nsweet\n\nSample Output 3\n\nNo\r\n\nHe feels sick when eating the 3rd dish and cannot eat the 4th and subsequent dishes.",
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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 positive integers xCorner and yCorner, and a 2D array circles, where circles[i] = [x_i, y_i, r_i] denotes a circle with center at (x_i, y_i) and radius r_i.\nThere is a rectangle in the coordinate plane with its bottom left corner at the origin and top right corner at the coordinate (xCorner, yCorner). You need to check whether there is a path from the bottom left corner to the top right corner such that the entire path lies inside the rectangle, does not touch or lie inside any circle, and touches the rectangle only at the two corners.\nReturn true if such a path exists, and false otherwise.\n \nExample 1:\n\nInput: xCorner = 3, yCorner = 4, circles = [[2,1,1]]\nOutput: true\nExplanation:\n\nThe black curve shows a possible path between (0, 0) and (3, 4).\n\nExample 2:\n\nInput: xCorner = 3, yCorner = 3, circles = [[1,1,2]]\nOutput: false\nExplanation:\n\nNo path exists from (0, 0) to (3, 3).\n\nExample 3:\n\nInput: xCorner = 3, yCorner = 3, circles = [[2,1,1],[1,2,1]]\nOutput: false\nExplanation:\n\nNo path exists from (0, 0) to (3, 3).\n\nExample 4:\n\nInput: xCorner = 4, yCorner = 4, circles = [[5,5,1]]\nOutput: true\nExplanation:\n\n\n \nConstraints:\n\n3 <= xCorner, yCorner <= 10^9\n1 <= circles.length <= 1000\ncircles[i].length == 3\n1 <= x_i, y_i, r_i <= 10^9",
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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 an integer array nums. This array contains n elements, where exactly n - 2 elements are special numbers. One of the remaining two elements is the sum of these special numbers, and the other is an outlier.\nAn outlier is defined as a number that is neither one of the original special numbers nor the element representing the sum of those numbers.\nNote that special numbers, the sum element, and the outlier must have distinct indices, but may share the same value.\nReturn the largest potential outlier in nums.\n \nExample 1:\n\nInput: nums = [2,3,5,10]\nOutput: 10\nExplanation:\nThe special numbers could be 2 and 3, thus making their sum 5 and the outlier 10.\n\nExample 2:\n\nInput: nums = [-2,-1,-3,-6,4]\nOutput: 4\nExplanation:\nThe special numbers could be -2, -1, and -3, thus making their sum -6 and the outlier 4.\n\nExample 3:\n\nInput: nums = [1,1,1,1,1,5,5]\nOutput: 5\nExplanation:\nThe special numbers could be 1, 1, 1, 1, and 1, thus making their sum 5 and the other 5 as the outlier.\n\n \nConstraints:\n\n3 <= nums.length <= 10^5\n-1000 <= nums[i] <= 1000\nThe input is generated such that at least one potential outlier exists in nums.",
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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 integer array nums.\nAny positive divisor of a natural number x that is strictly less than x is called a proper divisor of x. For example, 2 is a proper divisor of 4, while 6 is not a proper divisor of 6.\nYou are allowed to perform an operation any number of times on nums, where in each operation you select any one element from nums and divide it by its greatest proper divisor.\nReturn the minimum number of operations required to make the array non-decreasing.\nIf it is not possible to make the array non-decreasing using any number of operations, return -1.\n \nExample 1:\n\nInput: nums = [25,7]\nOutput: 1\nExplanation:\nUsing a single operation, 25 gets divided by 5 and nums becomes [5, 7].\n\nExample 2:\n\nInput: nums = [7,7,6]\nOutput: -1\n\nExample 3:\n\nInput: nums = [1,1,1,1]\nOutput: 0\n\n \nConstraints:\n\n1 <= nums.length <= 10^5\n1 <= nums[i] <= 10^6",
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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.In the Kingdom of AtCoder, the eldest son is always given the name Taro. No one else is given the name Taro.\nThe eldest son is the earliest born male child in each family.\nThere are N families in the Kingdom, and M babies were born. Before the M babies were born, none of the N families had had any babies.\nInformation about the babies is given in chronological order of their birth.\nThe i-th baby born was born in family A_i, and the baby is male if B_i is M, and female if it is F.\nDetermine for each of the M babies whether the name given is Taro.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN M\nA_1 B_1\n\\vdots\nA_M B_M\n\nOutput\n\nPrint M lines.\nThe i-th line (1\\leq i \\leq M) should contain Yes if the name given to the i-th baby is Taro, and No otherwise.\n\nConstraints\n\n\n- 1\\leq N,M\\leq 100\n- 1\\leq A_i\\leq N\n- B_i is M or F.\n- All numbers in the input are integers.\n\nSample Input 1\n\n2 4\n1 M\n1 M\n2 F\n2 M\n\nSample Output 1\n\nYes\nNo\nNo\nYes\n\nThe first baby is the earliest born boy in family 1, so he is named Taro.\nThe second baby is not the earliest born boy in family 1, so he is not named Taro.\nThe third baby is a girl, so she is not named Taro.\nThe fourth baby is the earliest born boy in family 2, so he is named Taro. Note that the third baby is also born in family 2, but it is the earliest born boy who is named Taro.\n\nSample Input 2\n\n4 7\n2 M\n3 M\n1 F\n4 F\n4 F\n1 F\n2 M\n\nSample Output 2\n\nYes\nYes\nNo\nNo\nNo\nNo\nNo",
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|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.