context
list | gen_kwargs
dict | repeat_idx
int64 | request_idx
int64 | task_name
string | metadata
dict | model_outputs
string |
|---|---|---|---|---|---|---|
[
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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 a string s and an integer k, return the total number of substrings of s where at least one character appears at least k times.\n \nExample 1:\n\nInput: s = \"abacb\", k = 2\nOutput: 4\nExplanation:\nThe valid substrings are:\n\n\"aba\" (character 'a' appears 2 times).\n\"abac\" (character 'a' appears 2 times).\n\"abacb\" (character 'a' appears 2 times).\n\"bacb\" (character 'b' appears 2 times).\n\n\nExample 2:\n\nInput: s = \"abcde\", k = 1\nOutput: 15\nExplanation:\nAll substrings are valid because every character appears at least once.\n\n \nConstraints:\n\n1 <= s.length <= 3000\n1 <= k <= s.length\ns consists only of lowercase English letters.",
"role": "user"
}
] |
{
"do_sample": false,
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"seed": 1,
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| 1 | 310 |
LiveCodeBenchV5
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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.\nA subsequence sub of nums with length x is called valid if it satisfies:\n\n(sub[0] + sub[1]) % 2 == (sub[1] + sub[2]) % 2 == ... == (sub[x - 2] + sub[x - 1]) % 2.\n\nReturn the length of the longest valid subsequence of nums.\nA subsequence is an array that can be derived from another array by deleting some or no elements without changing the order of the remaining elements.\n \nExample 1:\n\nInput: nums = [1,2,3,4]\nOutput: 4\nExplanation:\nThe longest valid subsequence is [1, 2, 3, 4].\n\nExample 2:\n\nInput: nums = [1,2,1,1,2,1,2]\nOutput: 6\nExplanation:\nThe longest valid subsequence is [1, 2, 1, 2, 1, 2].\n\nExample 3:\n\nInput: nums = [1,3]\nOutput: 2\nExplanation:\nThe longest valid subsequence is [1, 3].\n\n \nConstraints:\n\n2 <= nums.length <= 2 * 10^5\n1 <= nums[i] <= 10^7",
"role": "user"
}
] |
{
"do_sample": false,
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"seed": 2,
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| 2 | 66 |
LiveCodeBenchV5
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{
"expected_answer": "",
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!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[
{
"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given a simple connected undirected graph with N vertices and M edges. Each vertex i\\,(1\\leq i \\leq N) has a weight A_i. Each edge j\\,(1\\leq j \\leq M) connects vertices U_j and V_j bidirectionally and has a weight B_j.\nThe weight of a path in this graph is defined as the sum of the weights of the vertices and edges that appear on the path.\nFor each i=2,3,\\dots,N, solve the following problem:\n\n- Find the minimum weight of a path from vertex 1 to vertex i.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN M\r\nA_1 A_2 \\dots A_N\r\nU_1 V_1 B_1\r\nU_2 V_2 B_2\r\n\\vdots\r\nU_M V_M B_M\n\nOutput\n\nPrint the answers for i=2,3,\\dots,N in a single line, separated by spaces.\n\nConstraints\n\n\n- 2 \\leq N \\leq 2 \\times 10^5\n- N-1 \\leq M \\leq 2 \\times 10^5\n- 1 \\leq U_j < V_j \\leq N\n- (U_i, V_i) \\neq (U_j, V_j) if i \\neq j.\n- The graph is connected.\n- 0 \\leq A_i \\leq 10^9\n- 0 \\leq B_j \\leq 10^9\n- All input values are integers.\n\nSample Input 1\n\n3 3\r\n1 2 3\r\n1 2 1\r\n1 3 6\r\n2 3 2\n\nSample Output 1\n\n4 9\r\n\nConsider the paths from vertex 1 to vertex 2.\r\nThe weight of the path 1 \\to 2 is A_1 + B_1 + A_2 = 1 + 1 + 2 = 4, and the weight of the path 1 \\to 3 \\to 2 is A_1 + B_2 + A_3 + B_3 + A_2 = 1 + 6 + 3 + 2 + 2 = 14. The minimum weight is 4.\nConsider the paths from vertex 1 to vertex 3.\r\nThe weight of the path 1 \\to 3 is A_1 + B_2 + A_3 = 1 + 6 + 3 = 10, and the weight of the path 1 \\to 2 \\to 3 is A_1 + B_1 + A_2 + B_3 + A_3 = 1 + 1 + 2 + 2 + 3 = 9. The minimum weight is 9.\n\nSample Input 2\n\n2 1\r\n0 1\r\n1 2 3\n\nSample Output 2\n\n4\n\nSample Input 3\n\n5 8\r\n928448202 994752369 906965437 942744902 907560126\r\n2 5 975090662\r\n1 2 908843627\r\n1 5 969061140\r\n3 4 964249326\r\n2 3 957690728\r\n2 4 942986477\r\n4 5 948404113\r\n1 3 988716403\n\nSample Output 3\n\n2832044198 2824130042 4696218483 2805069468\r\n\nNote that the answers may not fit in a 32-bit integer.",
"role": "user"
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"do_sample": false,
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"seed": 1,
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"expected_answer": "",
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|
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!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|
[
{
"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given an integer array nums.\nYou replace each element in nums with the sum of its digits.\nReturn the minimum element in nums after all replacements.\n \nExample 1:\n\nInput: nums = [10,12,13,14]\nOutput: 1\nExplanation:\nnums becomes [1, 3, 4, 5] after all replacements, with minimum element 1.\n\nExample 2:\n\nInput: nums = [1,2,3,4]\nOutput: 1\nExplanation:\nnums becomes [1, 2, 3, 4] after all replacements, with minimum element 1.\n\nExample 3:\n\nInput: nums = [999,19,199]\nOutput: 10\nExplanation:\nnums becomes [27, 10, 19] after all replacements, with minimum element 10.\n\n \nConstraints:\n\n1 <= nums.length <= 100\n1 <= nums[i] <= 10^4",
"role": "user"
}
] |
{
"do_sample": false,
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"seed": 2,
"temperature": 0.7
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| 2 | 198 |
LiveCodeBenchV5
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{
"expected_answer": "",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.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",
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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 N keys numbered 1, 2, \\dots, N.\r\nSome of these are real keys, while the others are dummies.\nThere is a door, Door X, into which you can insert any number of keys. Door X will open if and only if at least K real keys are inserted.\nYou have conducted M tests on these keys. The i-th test went as follows:\n\n- You inserted C_i keys A_{i,1}, A_{i,2}, \\dots, A_{i,C_i} into Door X.\n- The test result is represented by a single English letter R_i.\n- R_i = o means that Door X opened in the i-th test.\n- R_i = x means that Door X did not open in the i-th test.\n\n\n\nThere are 2^N possible combinations of which keys are real and which are dummies. Among these, find the number of combinations that do not contradict any of the test results.\r\nIt is possible that the given test results are incorrect and no combination satisfies the conditions. In such a case, report 0.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN M K\r\nC_1 A_{1,1} A_{1,2} \\dots A_{1,C_1} R_1\r\nC_2 A_{2,1} A_{2,2} \\dots A_{2,C_2} R_2\r\n\\vdots\r\nC_M A_{M,1} A_{M,2} \\dots A_{M,C_M} R_M\n\nOutput\n\nPrint the answer as an integer.\n\nConstraints\n\n\n- N, M, K, C_i, and A_{i,j} are integers.\n- 1 \\le K \\le N \\le 15\n- 1 \\le M \\le 100\n- 1 \\le C_i \\le N\n- 1 \\le A_{i,j} \\le N\n- A_{i,j} \\neq A_{i,k} if j \\neq k.\n- R_i is o or x.\n\nSample Input 1\n\n3 2 2\r\n3 1 2 3 o\r\n2 2 3 x\n\nSample Output 1\n\n2\r\n\nIn this input, there are three keys and two tests were conducted.\r\nTwo correct keys are required to open Door X.\n\n- In the first test, keys 1, 2, 3 were used, and Door X opened.\n- In the second test, keys 2, 3 were used, and Door X did not open.\n\nThere are two combinations of which keys are real and which are dummies that do not contradict any of the test results:\n\n- Key 1 is real, key 2 is a dummy, and key 3 is real.\n- Key 1 is real, key 2 is real, and key 3 is a dummy.\n\nSample Input 2\n\n4 5 3\r\n3 1 2 3 o\r\n3 2 3 4 o\r\n3 3 4 1 o\r\n3 4 1 2 o\r\n4 1 2 3 4 x\n\nSample Output 2\n\n0\r\n\nAs mentioned in the problem statement, the answer may be 0.\n\nSample Input 3\n\n11 4 9\r\n10 1 2 3 4 5 6 7 8 9 10 o\r\n11 1 2 3 4 5 6 7 8 9 10 11 o\r\n10 11 10 9 8 7 6 5 4 3 2 x\r\n10 11 9 1 4 3 7 5 6 2 10 x\n\nSample Output 3\n\n8",
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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. Return the function body without invoking it at the final solution.You are given three integers n, m, k. A good array arr of size n is defined as follows:\n\nEach element in arr is in the inclusive range [1, m].\nExactly k indices i (where 1 <= i < n) satisfy the condition arr[i - 1] == arr[i].\n\nReturn the number of good arrays that can be formed.\nSince the answer may be very large, return it modulo 10^9 + 7.\n \nExample 1:\n\nInput: n = 3, m = 2, k = 1\nOutput: 4\nExplanation:\n\nThere are 4 good arrays. They are [1, 1, 2], [1, 2, 2], [2, 1, 1] and [2, 2, 1].\nHence, the answer is 4.\n\n\nExample 2:\n\nInput: n = 4, m = 2, k = 2\nOutput: 6\nExplanation:\n\nThe good arrays are [1, 1, 1, 2], [1, 1, 2, 2], [1, 2, 2, 2], [2, 1, 1, 1], [2, 2, 1, 1] and [2, 2, 2, 1].\nHence, the answer is 6.\n\n\nExample 3:\n\nInput: n = 5, m = 2, k = 0\nOutput: 2\nExplanation:\n\nThe good arrays are [1, 2, 1, 2, 1] and [2, 1, 2, 1, 2]. Hence, the answer is 2.\n\n\n \nConstraints:\n\n1 <= n <= 10^5\n1 <= m <= 10^5\n0 <= k <= n - 1",
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"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.There is a dungeon with n x m rooms arranged as a grid.\nYou are given a 2D array moveTime of size n x m, where moveTime[i][j] represents the minimum time in seconds when you can start moving to that room. You start from the room (0, 0) at time t = 0 and can move to an adjacent room. Moving between adjacent rooms takes exactly one second.\nReturn the minimum time to reach the room (n - 1, m - 1).\nTwo rooms are adjacent if they share a common wall, either horizontally or vertically.\n \nExample 1:\n\nInput: moveTime = [[0,4],[4,4]]\nOutput: 6\nExplanation:\nThe minimum time required is 6 seconds.\n\nAt time t == 4, move from room (0, 0) to room (1, 0) in one second.\nAt time t == 5, move from room (1, 0) to room (1, 1) in one second.\n\n\nExample 2:\n\nInput: moveTime = [[0,0,0],[0,0,0]]\nOutput: 3\nExplanation:\nThe minimum time required is 3 seconds.\n\nAt time t == 0, move from room (0, 0) to room (1, 0) in one second.\nAt time t == 1, move from room (1, 0) to room (1, 1) in one second.\nAt time t == 2, move from room (1, 1) to room (1, 2) in one second.\n\n\nExample 3:\n\nInput: moveTime = [[0,1],[1,2]]\nOutput: 3\n\n \nConstraints:\n\n2 <= n == moveTime.length <= 50\n2 <= m == moveTime[i].length <= 50\n0 <= moveTime[i][j] <= 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.You are given three length-N sequences of positive integers: A=(A_1,A_2,\\ldots,A_N), B=(B_1,B_2,\\ldots,B_N), and C=(C_1,C_2,\\ldots,C_N). \nFind the number of pairs of positive integers (x, y) that satisfy the following condition: \n\n- A_i \\times x + B_i \\times y < C_i for all 1 \\leq i \\leq N. \n\nIt can be proved that the number of such pairs of positive integers satisfying the condition is finite. \nYou are given T test cases, each of which should be solved.\n\nInput\n\nThe input is given from Standard Input in the following format. Here, \\mathrm{case}_i refers to the i-th test case.\nT \r\n\\mathrm{case}_1 \r\n\\mathrm{case}_2 \r\n\\vdots \r\n\\mathrm{case}_T \r\n\nEach test case is given in the following format:\nN \r\nA_1 B_1 C_1 \r\nA_2 B_2 C_2 \r\n\\vdots \r\nA_N B_N C_N\n\nOutput\n\nPrint T lines. The i-th line (1 \\leq i \\leq T) should contain the answer for \\mathrm{case}_i.\n\nConstraints\n\n\n- 1 \\leq T \\leq 2 \\times 10^5 \n- 1 \\leq N \\leq 2 \\times 10^5 \n- 1 \\leq A_i, B_i, C_i \\leq 10^9 \n- The sum of N over all test cases is at most 2 \\times 10^5. \n- All input values are integers.\n\nSample Input 1\n\n2\r\n2\r\n1 1 4\r\n1 2 5\r\n1\r\n1 1 2\n\nSample Output 1\n\n2\r\n0\r\n\nIn the first test case, there are two valid pairs of integers: (x, y) = (1, 1), (2,1). Thus, the first line should contain 2. \nIn the second test case, there are no valid pairs of integers. Thus, the second line should contain 0.\n\nSample Input 2\n\n3\r\n7\r\n138 16011 918976\r\n5478 7748 499926\r\n5234 17727 748589\r\n1157 10511 643136\r\n31200 3005 721285\r\n28839 14469 798851\r\n1933 5378 864127\r\n9\r\n17775 1665 386430\r\n37001 863 922418\r\n9756 4182 746671\r\n12379 9106 807578\r\n3984 4049 640539\r\n25333 9869 780810\r\n20372 7000 688738\r\n16107 11974 827227\r\n10779 10531 770510\r\n5\r\n4916 14132 460944\r\n11856 45422 610561\r\n56014 18216 825793\r\n10363 6220 945356\r\n37418 33866 851593\n\nSample Output 2\n\n660\r\n995\r\n140",
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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 three-digit integer N where each digit is an integer between 1 and 9, inclusive.\nLet a, b, c be the hundreds, tens, ones digits of N, respectively. Print an integer formed by arranging b, c, a in this order, and an integer formed by arranging c, a, b in this order.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\n\nOutput\n\nPrint two integers separated by a space in the following order: an integer formed by arranging b, c, a in this order, and an integer formed by arranging c, a, b in this order.\n\nConstraints\n\n\n- N is a three-digit integer where each digit is an integer between 1 and 9, inclusive.\n\nSample Input 1\n\n379\n\nSample Output 1\n\n793 937\r\n\nThe hundreds, tens, ones digits of 379 are 3, 7, 9, respectively, so print 793 and 937.\n\nSample Input 2\n\n919\n\nSample Output 2\n\n199 991\r\n\nThe hundreds, tens, ones digits of 919 are 9, 1, 9, respectively, so print 199 and 991.",
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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 array nums.\nYou can do the following operation on the array any number of times (possibly zero):\n\nChoose any 3 consecutive elements from the array and flip all of them.\n\nFlipping an element means changing its value from 0 to 1, and from 1 to 0.\nReturn the minimum number of operations required to make all elements in nums equal to 1. If it is impossible, return -1.\n \nExample 1:\n\nInput: nums = [0,1,1,1,0,0]\nOutput: 3\nExplanation:\nWe can do the following operations:\n\nChoose the elements at indices 0, 1 and 2. The resulting array is nums = [1,0,0,1,0,0].\nChoose the elements at indices 1, 2 and 3. The resulting array is nums = [1,1,1,0,0,0].\nChoose the elements at indices 3, 4 and 5. The resulting array is nums = [1,1,1,1,1,1].\n\n\nExample 2:\n\nInput: nums = [0,1,1,1]\nOutput: -1\nExplanation:\nIt is impossible to make all elements equal to 1.\n\n \nConstraints:\n\n3 <= nums.length <= 10^5\n0 <= nums[i] <= 1",
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"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.There exists an undirected tree with n nodes numbered 0 to n - 1. You are given a 2D integer array edges of length n - 1, where edges[i] = [u_i, v_i] indicates that there is an edge between nodes u_i and v_i in the tree.\nInitially, all nodes are unmarked. For each node i:\n\nIf i is odd, the node will get marked at time x if there is at least one node adjacent to it which was marked at time x - 1.\nIf i is even, the node will get marked at time x if there is at least one node adjacent to it which was marked at time x - 2.\n\nReturn an array times where times[i] is the time when all nodes get marked in the tree, if you mark node i at time t = 0.\nNote that the answer for each times[i] is independent, i.e. when you mark node i all other nodes are unmarked.\n \nExample 1:\n\nInput: edges = [[0,1],[0,2]]\nOutput: [2,4,3]\nExplanation:\n\n\nFor i = 0:\n\n\t\nNode 1 is marked at t = 1, and Node 2 at t = 2.\n\n\nFor i = 1:\n\t\nNode 0 is marked at t = 2, and Node 2 at t = 4.\n\n\nFor i = 2:\n\t\nNode 0 is marked at t = 2, and Node 1 at t = 3.\n\n\n\n\nExample 2:\n\nInput: edges = [[0,1]]\nOutput: [1,2]\nExplanation:\n\n\nFor i = 0:\n\n\t\nNode 1 is marked at t = 1.\n\n\nFor i = 1:\n\t\nNode 0 is marked at t = 2.\n\n\n\n\nExample 3:\n\nInput: edges = [[2,4],[0,1],[2,3],[0,2]]\nOutput: [4,6,3,5,5]\nExplanation:\n\n\n \nConstraints:\n\n2 <= n <= 10^5\nedges.length == n - 1\nedges[i].length == 2\n0 <= edges[i][0], edges[i][1] <= n - 1\nThe input is generated such that edges represents a valid tree.",
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LiveCodeBenchV5
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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 slimes lined up in a row from left to right.\r\nFor i = 1, 2, \\ldots, N, the i-th slime from the left has size A_i.\r\nFor each K = 1, 2, \\ldots, N, solve the following problem.\n\nTakahashi is the K-th slime from the left in the initial state.\r\nFind the maximum size that he can have after performing the following action any number of times, possibly zero:\n\n- Choose a slime adjacent to him that is strictly smaller than him, and absorb it.\r\nAs a result, the absorbed slime disappears, and Takahashi's size increases by the size of the absorbed slime.\n\nWhen a slime disappears due to absorption, the gap is immediately closed, and the slimes that were adjacent to the disappearing slime (if they exist) become adjacent (see the explanation in Sample Input 1).\n\nInput\n\nThe input is given from Standard Input in the following format:\nN\r\nA_1 A_2 \\ldots A_N\n\nOutput\n\nPrint the answers B_K for each K = 1, 2, \\ldots, N, separated by spaces, in the following format:\nB_1 B_2 \\ldots B_N\n\nConstraints\n\n\n- 2 \\leq N \\leq 5 \\times 10^5\n- 1 \\leq A_i \\leq 10^9\n- All input values are integers.\n\nSample Input 1\n\n6\r\n4 13 2 3 2 6\n\nSample Output 1\n\n4 30 2 13 2 13\r\n\nAs an example, consider the problem for K = 4.\r\nWe will refer to the sizes of the remaining slimes, listed from left to right, with Takahashi's size enclosed in square brackets [ ], as the state of the row.\r\nThat is, the initial state is (4, 13, 2, [3], 2, 6). Consider the following sequence of actions by Takahashi.\n\n- He absorbs the slime to his right. As a result, the absorbed slime disappears, and his size becomes 3 + 2 = 5. The state becomes (4, 13, 2, [5], 6).\n- He absorbs the slime to his left. As a result, the absorbed slime disappears, and his size becomes 5 + 2 = 7. The state becomes (4, 13, [7], 6).\n- He absorbs the slime to his right. As a result, the absorbed slime disappears, and his size becomes 7 + 6 = 13. The state becomes (4, 13, [13]).\n\nThere are no slimes adjacent to him that are strictly smaller than him, so he cannot perform any more actions. His final size is 13, which is the maximum possible.\n\nSample Input 2\n\n12\r\n22 25 61 10 21 37 2 14 5 8 6 24\n\nSample Output 2\n\n22 47 235 10 31 235 2 235 5 235 6 235",
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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 a string s containing only digits, return the lexicographically smallest string that can be obtained after swapping adjacent digits in s with the same parity at most once.\nDigits have the same parity if both are odd or both are even. For example, 5 and 9, as well as 2 and 4, have the same parity, while 6 and 9 do not.\n \nExample 1:\n\nInput: s = \"45320\"\nOutput: \"43520\"\nExplanation: \ns[1] == '5' and s[2] == '3' both have the same parity, and swapping them results in the lexicographically smallest string.\n\nExample 2:\n\nInput: s = \"001\"\nOutput: \"001\"\nExplanation:\nThere is no need to perform a swap because s is already the lexicographically smallest.\n\n \nConstraints:\n\n2 <= s.length <= 100\ns consists only of digits.",
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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 nation of AtCoder, there are N cities numbered 1 to N, and M roads numbered 1 to M.\r\nRoad i connects cities A_i and B_i bidirectionally and has a length of C_i.\nYou are given Q queries to process in order. The queries are of the following two types.\n\n- 1 i: Road i becomes closed.\n- 2 x y: Print the shortest distance from city x to city y, using only roads that are not closed. If city y cannot be reached from city x, print -1 instead.\n\nIt is guaranteed that each test case contains at most 300 queries of the first type.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN M Q\r\nA_1 B_1 C_1\r\n\\vdots\r\nA_M B_M C_M\r\n\\mathrm{query}_1\r\n\\vdots\r\n\\mathrm{query}_Q\r\n\nEach query is in one of the following two formats:\n1 i\r\n\n2 x y\n\nOutput\n\nProcess the queries in order.\n\nConstraints\n\n\n- 2 \\leq N \\leq 300\n- 0 \\leq M \\leq \\frac{N(N-1)}{2}\n- 1 \\leq A_i < B_i \\leq N\n- All pairs (A_i, B_i) are distinct.\n- 1 \\leq C_i \\leq 10^9\n- 1 \\leq Q \\leq 2 \\times 10^5\n- In the queries of the first type, 1 \\leq i \\leq M.\n- The road given in a query of the first type is not already closed at that time.\n- The number of queries of the first type is at most 300.\n- In the queries of the second type, 1 \\leq x < y \\leq N.\n- All input values are integers.\n\nSample Input 1\n\n3 3 5\r\n1 2 5\r\n1 3 10\r\n2 3 6\r\n2 1 3\r\n1 2\r\n2 1 3\r\n1 1\r\n2 1 3\n\nSample Output 1\n\n10\r\n11\r\n-1\r\n\n\n- In the first query, print the shortest distance from city 1 to city 3, which is 10.\n- In the second query, road 2 becomes closed.\n- In the third query, print the shortest distance from city 1 to city 3, which is 11.\n- In the fourth query, road 1 becomes closed.\n- In the fifth query, city 3 cannot be reached from city 1, so print -1.\n\nSample Input 2\n\n4 6 6\r\n2 3 1\r\n2 4 1\r\n3 4 1\r\n1 2 1\r\n1 3 1\r\n1 4 1\r\n1 4\r\n1 5\r\n1 6\r\n2 1 2\r\n2 1 3\r\n2 1 4\n\nSample Output 2\n\n-1\r\n-1\r\n-1",
"role": "user"
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"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.There is a game dungeon comprised of n x n rooms arranged in a grid.\nYou are given a 2D array fruits of size n x n, where fruits[i][j] represents the number of fruits in the room (i, j). Three children will play in the game dungeon, with initial positions at the corner rooms (0, 0), (0, n - 1), and (n - 1, 0).\nThe children will make exactly n - 1 moves according to the following rules to reach the room (n - 1, n - 1):\n\nThe child starting from (0, 0) must move from their current room (i, j) to one of the rooms (i + 1, j + 1), (i + 1, j), and (i, j + 1) if the target room exists.\nThe child starting from (0, n - 1) must move from their current room (i, j) to one of the rooms (i + 1, j - 1), (i + 1, j), and (i + 1, j + 1) if the target room exists.\nThe child starting from (n - 1, 0) must move from their current room (i, j) to one of the rooms (i - 1, j + 1), (i, j + 1), and (i + 1, j + 1) if the target room exists.\n\nWhen a child enters a room, they will collect all the fruits there. If two or more children enter the same room, only one child will collect the fruits, and the room will be emptied after they leave.\nReturn the maximum number of fruits the children can collect from the dungeon.\n \nExample 1:\n\nInput: fruits = [[1,2,3,4],[5,6,8,7],[9,10,11,12],[13,14,15,16]]\nOutput: 100\nExplanation:\n\nIn this example:\n\nThe 1^st child (green) moves on the path (0,0) -> (1,1) -> (2,2) -> (3, 3).\nThe 2^nd child (red) moves on the path (0,3) -> (1,2) -> (2,3) -> (3, 3).\nThe 3^rd child (blue) moves on the path (3,0) -> (3,1) -> (3,2) -> (3, 3).\n\nIn total they collect 1 + 6 + 11 + 16 + 4 + 8 + 12 + 13 + 14 + 15 = 100 fruits.\n\nExample 2:\n\nInput: fruits = [[1,1],[1,1]]\nOutput: 4\nExplanation:\nIn this example:\n\nThe 1^st child moves on the path (0,0) -> (1,1).\nThe 2^nd child moves on the path (0,1) -> (1,1).\nThe 3^rd child moves on the path (1,0) -> (1,1).\n\nIn total they collect 1 + 1 + 1 + 1 = 4 fruits.\n\n \nConstraints:\n\n2 <= n == fruits.length == fruits[i].length <= 1000\n0 <= fruits[i][j] <= 1000",
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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. Return the function body without invoking it at the final solution.Given an integer array nums, return the number of subarrays of length 3 such that the sum of the first and third numbers equals exactly half of the second number.\n \nExample 1:\n\nInput: nums = [1,2,1,4,1]\nOutput: 1\nExplanation:\nOnly the subarray [1,4,1] contains exactly 3 elements where the sum of the first and third numbers equals half the middle number.\n\nExample 2:\n\nInput: nums = [1,1,1]\nOutput: 0\nExplanation:\n[1,1,1] is the only subarray of length 3. However, its first and third numbers do not add to half the middle number.\n\n \nConstraints:\n\n3 <= nums.length <= 100\n-100 <= nums[i] <= 100",
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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 buildings, building 1, building 2, \\ldots, building N, arranged in this order in a straight line from west to east. Building 1 is the westernmost, and building N is the easternmost. The height of building i\\ (1\\leq i\\leq N) is H_i.\nFor a pair of integers (i,j)\\ (1\\leq i\\lt j\\leq N), building j can be seen from building i if the following condition is satisfied.\n\n- There is no building taller than building j between buildings i and j. In other words, there is no integer k\\ (i\\lt k\\lt j) such that H_k > H_j.\n\nYou are given Q queries. In the i-th query, given a pair of integers (l_i,r_i)\\ (l_i\\lt r_i), find the number of buildings to the east of building r_i (that is, buildings r_i + 1, r_i + 2, \\ldots, N) that can be seen from both buildings l_i and r_i.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN Q\nH_1 H_2 \\ldots H_N\nl_1 r_1\nl_2 r_2\n\\vdots\nl_Q r_Q\n\nOutput\n\nPrint Q lines. The i-th line (1 \\leq i \\leq Q) should contain the answer to the i-th query.\n\nConstraints\n\n\n- 2 \\leq N \\leq 2 \\times 10^5\n- 1 \\leq Q \\leq 2 \\times 10^5\n- 1 \\leq H_i \\leq N\n- H_i\\neq H_j\\ (i\\neq j)\n- 1 \\leq l_i < r_i \\leq N\n- All input values are integers.\n\nSample Input 1\n\n5 3\n2 1 4 3 5\n1 2\n3 5\n1 4\n\nSample Output 1\n\n2\n0\n1\n\n\n- For the first query, among the buildings to the east of building 2, buildings 3 and 5 can be seen from both buildings 1 and 2, so the answer is 2.\n- For the second query, there are no buildings to the east of building 5.\n- For the third query, among the buildings to the east of building 4, building 5 can be seen from both buildings 1 and 4, so the answer is 1.\n\nSample Input 2\n\n10 10\n2 1 5 3 4 6 9 8 7 10\n3 9\n2 5\n4 8\n5 6\n3 8\n2 10\n7 8\n6 7\n8 10\n4 10\n\nSample Output 2\n\n1\n3\n1\n2\n1\n0\n1\n1\n0\n0",
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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.All KEYENCE product names consist of two uppercase English letters.\r\nThey have already used N product names, the i-th of which (1\\leq i\\leq N) is S_i.\r\nOnce a product name is used, it cannot be reused, so they decided to create an NG (Not Good) list to quickly identify previously used product names.\nThe NG list must satisfy the following conditions.\n\n- It consists of one or more strings, each consisting of uppercase English letters.\n- For each already used product name, there exists at least one string in the list that contains the name as a (contiguous) substring.\n- None of the strings in the list contain any length-2 (contiguous) substring that is not an already used product name.\n\nFind the minimum possible number of strings in the NG list.\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 minimum possible number of strings in the NG list.\n\nConstraints\n\n\n- 1\\leq N\\leq 26^2\n- N is an integer.\n- Each S_i is a string of length 2 consisting of uppercase English letters.\n- All S_1,S_2,\\ldots,S_N are distinct.\n\nSample Input 1\n\n7\r\nAB\r\nBC\r\nCA\r\nCD\r\nDE\r\nDF\r\nXX\n\nSample Output 1\n\n3\r\n\nOne NG list satisfying the conditions is the one consisting of the following three strings:\n\n- CABCDE\n- DF\n- XX\n\nThis has three strings, and there is no NG list satisfying the conditions with 2 or fewer strings, so print 3.\n\nSample Input 2\n\n5\r\nAC\r\nBC\r\nCD\r\nDE\r\nDF\n\nSample Output 2\n\n2\r\n\nOne NG list satisfying the conditions is the one consisting of the following two strings:\n\n- ACDE\n- BCDF\n\nNote that each used product name may appear in multiple strings in the NG list or multiple times within the same string.\n\nSample Input 3\n\n6\r\nAB\r\nAC\r\nCB\r\nAD\r\nDB\r\nBA\n\nSample Output 3\n\n1\r\n\nFor example, an NG list consisting only of ABACBADB satisfies the conditions.",
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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 array nums.\nYou can do the following operation on the array any number of times (possibly zero):\n\nChoose any 3 consecutive elements from the array and flip all of them.\n\nFlipping an element means changing its value from 0 to 1, and from 1 to 0.\nReturn the minimum number of operations required to make all elements in nums equal to 1. If it is impossible, return -1.\n \nExample 1:\n\nInput: nums = [0,1,1,1,0,0]\nOutput: 3\nExplanation:\nWe can do the following operations:\n\nChoose the elements at indices 0, 1 and 2. The resulting array is nums = [1,0,0,1,0,0].\nChoose the elements at indices 1, 2 and 3. The resulting array is nums = [1,1,1,0,0,0].\nChoose the elements at indices 3, 4 and 5. The resulting array is nums = [1,1,1,1,1,1].\n\n\nExample 2:\n\nInput: nums = [0,1,1,1]\nOutput: -1\nExplanation:\nIt is impossible to make all elements equal to 1.\n\n \nConstraints:\n\n3 <= nums.length <= 10^5\n0 <= nums[i] <= 1",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given the first N terms A _ 1,A _ 2,\\dotsc,A _ N of an infinite sequence A=(A _ 1,A _ 2,A _ 3,\\dotsc) that has period N.\nDetermine if there exists a non-empty contiguous subsequence of this infinite sequence whose sum is S.\nHere, an infinite sequence A has period N when A _ i=A _ {i-N} for every integer i>N.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN S\r\nA _ 1 A _ 2 \\dotsc A _ N\n\nOutput\n\nIf there exists a contiguous subsequence (A _ l,A _ {l+1},\\dotsc,A _ r) of A for which A _ l+A _ {l+1}+\\dotsb+A _ r=S, print Yes. Otherwise, print No.\n\nConstraints\n\n\n- 1\\leq N\\leq2\\times10 ^ 5\n- 1\\leq A _ i\\leq 10 ^ 9\n- 1\\leq S\\leq 10 ^ {18}\n- All input values are integers.\n\nSample Input 1\n\n3 42\r\n3 8 4\n\nSample Output 1\n\nYes\r\n\nThe sequence A is (3,8,4,3,8,4,3,8,4,\\dotsc).\nFor the subsequence (A _ 2,A _ 3,A _ 4,A _ 5,A _ 6,A _ 7,A _ 8,A _ 9)=(8,4,3,8,4,3,8,4), we have 8+4+3+8+4+3+8+4=42, so print Yes.\n\nSample Input 2\n\n3 1\r\n3 8 4\n\nSample Output 2\n\nNo\r\n\nAll elements of A are at least 3, so the sum of any non-empty contiguous subsequence is at least 3.\nThus, there is no subsequence with sum 1, so print No.\n\nSample Input 3\n\n20 83298426\r\n748 169 586 329 972 529 432 519 408 587 138 249 656 114 632 299 984 755 404 772\n\nSample Output 3\n\nYes\n\nSample Input 4\n\n20 85415869\r\n748 169 586 329 972 529 432 519 408 587 138 249 656 114 632 299 984 755 404 772\n\nSample Output 4\n\nNo",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There are four balls, and the color of the i-th ball is A_i.\nFind the maximum number of times you can perform this operation: choose two balls of the same color and discard both.\n\nInput\n\nThe input is given from Standard Input in the following format:\nA_1 A_2 A_3 A_4\n\nOutput\n\nPrint the maximum number of times the operation can be performed as an integer.\n\nConstraints\n\n\n- Each of A_1, A_2, A_3, A_4 is an integer between 1 and 4, inclusive.\n\nSample Input 1\n\n2 1 2 1\n\nSample Output 1\n\n2\r\n\nThe first and third balls both have color 2, so you can perform the operation to discard the first and third balls together.\nNext, the second and fourth balls both have color 1, so you can perform the operation to discard the second and fourth balls together.\nHence, you can perform a total of two operations.\n\nSample Input 2\n\n4 4 4 1\n\nSample Output 2\n\n1\n\nSample Input 3\n\n1 2 3 4\n\nSample Output 3\n\n0\r\n\nThere are cases where you cannot perform the operation even once.",
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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 2D array events which represents a sequence of events where a child pushes a series of buttons on a keyboard.\nEach events[i] = [index_i, time_i] indicates that the button at index index_i was pressed at time time_i.\n\nThe array is sorted in increasing order of time.\nThe time taken to press a button is the difference in time between consecutive button presses. The time for the first button is simply the time at which it was pressed.\n\nReturn the index of the button that took the longest time to push. If multiple buttons have the same longest time, return the button with the smallest index.\n \nExample 1:\n\nInput: events = [[1,2],[2,5],[3,9],[1,15]]\nOutput: 1\nExplanation:\n\nButton with index 1 is pressed at time 2.\nButton with index 2 is pressed at time 5, so it took 5 - 2 = 3 units of time.\nButton with index 3 is pressed at time 9, so it took 9 - 5 = 4 units of time.\nButton with index 1 is pressed again at time 15, so it took 15 - 9 = 6 units of time.\n\n\nExample 2:\n\nInput: events = [[10,5],[1,7]]\nOutput: 10\nExplanation:\n\nButton with index 10 is pressed at time 5.\nButton with index 1 is pressed at time 7, so it took 7 - 5 = 2 units of time.\n\n\n \nConstraints:\n\n1 <= events.length <= 1000\nevents[i] == [index_i, time_i]\n1 <= index_i, time_i <= 10^5\nThe input is generated such that events is sorted in increasing order of time_i.",
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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.\nStart by selecting a starting position curr such that nums[curr] == 0, and choose a movement direction of either left or right.\nAfter that, you repeat the following process:\n\nIf curr is out of the range [0, n - 1], this process ends.\nIf nums[curr] == 0, move in the current direction by incrementing curr if you are moving right, or decrementing curr if you are moving left.\nElse if nums[curr] > 0:\n\t\nDecrement nums[curr] by 1.\nReverse your movement direction (left becomes right and vice versa).\nTake a step in your new direction.\n\n\n\nA selection of the initial position curr and movement direction is considered valid if every element in nums becomes 0 by the end of the process.\nReturn the number of possible valid selections.\n \nExample 1:\n\nInput: nums = [1,0,2,0,3]\nOutput: 2\nExplanation:\nThe only possible valid selections are the following:\n\nChoose curr = 3, and a movement direction to the left.\n\n\t\n[1,0,2,0,3] -> [1,0,2,0,3] -> [1,0,1,0,3] -> [1,0,1,0,3] -> [1,0,1,0,2] -> [1,0,1,0,2] -> [1,0,0,0,2] -> [1,0,0,0,2] -> [1,0,0,0,1] -> [1,0,0,0,1] -> [1,0,0,0,1] -> [1,0,0,0,1] -> [0,0,0,0,1] -> [0,0,0,0,1] -> [0,0,0,0,1] -> [0,0,0,0,1] -> [0,0,0,0,0].\n\n\nChoose curr = 3, and a movement direction to the right.\n\t\n[1,0,2,0,3] -> [1,0,2,0,3] -> [1,0,2,0,2] -> [1,0,2,0,2] -> [1,0,1,0,2] -> [1,0,1,0,2] -> [1,0,1,0,1] -> [1,0,1,0,1] -> [1,0,0,0,1] -> [1,0,0,0,1] -> [1,0,0,0,0] -> [1,0,0,0,0] -> [1,0,0,0,0] -> [1,0,0,0,0] -> [0,0,0,0,0].\n\n\n\n\nExample 2:\n\nInput: nums = [2,3,4,0,4,1,0]\nOutput: 0\nExplanation:\nThere are no possible valid selections.\n\n \nConstraints:\n\n1 <= nums.length <= 100\n0 <= nums[i] <= 100\nThere is at least one element i where nums[i] == 0.",
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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 n and k.\nAn integer x is called k-palindromic if:\n\nx is a palindrome.\nx is divisible by k.\n\nReturn the largest integer having n digits (as a string) that is k-palindromic.\nNote that the integer must not have leading zeros.\n \nExample 1:\n\nInput: n = 3, k = 5\nOutput: \"595\"\nExplanation:\n595 is the largest k-palindromic integer with 3 digits.\n\nExample 2:\n\nInput: n = 1, k = 4\nOutput: \"8\"\nExplanation:\n4 and 8 are the only k-palindromic integers with 1 digit.\n\nExample 3:\n\nInput: n = 5, k = 6\nOutput: \"89898\"\n\n \nConstraints:\n\n1 <= n <= 10^5\n1 <= k <= 9",
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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 and an integer k.\nYou are allowed to perform the following operation on each element of the array at most once:\n\nAdd an integer in the range [-k, k] to the element.\n\nReturn the maximum possible number of distinct elements in nums after performing the operations.\n \nExample 1:\n\nInput: nums = [1,2,2,3,3,4], k = 2\nOutput: 6\nExplanation:\nnums changes to [-1, 0, 1, 2, 3, 4] after performing operations on the first four elements.\n\nExample 2:\n\nInput: nums = [4,4,4,4], k = 1\nOutput: 3\nExplanation:\nBy adding -1 to nums[0] and 1 to nums[1], nums changes to [3, 5, 4, 4].\n\n \nConstraints:\n\n1 <= nums.length <= 10^5\n1 <= nums[i] <= 10^9\n0 <= k <= 10^9",
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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 n representing the dimensions of an n x n grid, with the origin at the bottom-left corner of the grid. You are also given a 2D array of coordinates rectangles, where rectangles[i] is in the form [start_x, start_y, end_x, end_y], representing a rectangle on the grid. Each rectangle is defined as follows:\n\n(start_x, start_y): The bottom-left corner of the rectangle.\n(end_x, end_y): The top-right corner of the rectangle.\n\nNote that the rectangles do not overlap. Your task is to determine if it is possible to make either two horizontal or two vertical cuts on the grid such that:\n\nEach of the three resulting sections formed by the cuts contains at least one rectangle.\nEvery rectangle belongs to exactly one section.\n\nReturn true if such cuts can be made; otherwise, return false.\n \nExample 1:\n\nInput: n = 5, rectangles = [[1,0,5,2],[0,2,2,4],[3,2,5,3],[0,4,4,5]]\nOutput: true\nExplanation:\n\nThe grid is shown in the diagram. We can make horizontal cuts at y = 2 and y = 4. Hence, output is true.\n\nExample 2:\n\nInput: n = 4, rectangles = [[0,0,1,1],[2,0,3,4],[0,2,2,3],[3,0,4,3]]\nOutput: true\nExplanation:\n\nWe can make vertical cuts at x = 2 and x = 3. Hence, output is true.\n\nExample 3:\n\nInput: n = 4, rectangles = [[0,2,2,4],[1,0,3,2],[2,2,3,4],[3,0,4,2],[3,2,4,4]]\nOutput: false\nExplanation:\nWe cannot make two horizontal or two vertical cuts that satisfy the conditions. Hence, output is false.\n\n \nConstraints:\n\n3 <= n <= 10^9\n3 <= rectangles.length <= 10^5\n0 <= rectangles[i][0] < rectangles[i][2] <= n\n0 <= rectangles[i][1] < rectangles[i][3] <= n\nNo two rectangles overlap.",
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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 2D array of integers coordinates of length n and an integer k, where 0 <= k < n.\ncoordinates[i] = [x_i, y_i] indicates the point (x_i, y_i) in a 2D plane.\nAn increasing path of length m is defined as a list of points (x_1, y_1), (x_2, y_2), (x_3, y_3), ..., (x_m, y_m) such that:\n\nx_i < x_i + 1 and y_i < y_i + 1 for all i where 1 <= i < m.\n(x_i, y_i) is in the given coordinates for all i where 1 <= i <= m.\n\nReturn the maximum length of an increasing path that contains coordinates[k].\n \nExample 1:\n\nInput: coordinates = [[3,1],[2,2],[4,1],[0,0],[5,3]], k = 1\nOutput: 3\nExplanation:\n(0, 0), (2, 2), (5, 3) is the longest increasing path that contains (2, 2).\n\nExample 2:\n\nInput: coordinates = [[2,1],[7,0],[5,6]], k = 2\nOutput: 2\nExplanation:\n(2, 1), (5, 6) is the longest increasing path that contains (5, 6).\n\n \nConstraints:\n\n1 <= n == coordinates.length <= 10^5\ncoordinates[i].length == 2\n0 <= coordinates[i][0], coordinates[i][1] <= 10^9\nAll elements in coordinates are distinct.\n0 <= k <= n - 1",
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"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.A competition consists of n players numbered from 0 to n - 1.\nYou are given an integer array skills of size n and a positive integer k, where skills[i] is the skill level of player i. All integers in skills are unique.\nAll players are standing in a queue in order from player 0 to player n - 1.\nThe competition process is as follows:\n\nThe first two players in the queue play a game, and the player with the higher skill level wins.\nAfter the game, the winner stays at the beginning of the queue, and the loser goes to the end of it.\n\nThe winner of the competition is the first player who wins k games in a row.\nReturn the initial index of the winning player.\n \nExample 1:\n\nInput: skills = [4,2,6,3,9], k = 2\nOutput: 2\nExplanation:\nInitially, the queue of players is [0,1,2,3,4]. The following process happens:\n\nPlayers 0 and 1 play a game, since the skill of player 0 is higher than that of player 1, player 0 wins. The resulting queue is [0,2,3,4,1].\nPlayers 0 and 2 play a game, since the skill of player 2 is higher than that of player 0, player 2 wins. The resulting queue is [2,3,4,1,0].\nPlayers 2 and 3 play a game, since the skill of player 2 is higher than that of player 3, player 2 wins. The resulting queue is [2,4,1,0,3].\n\nPlayer 2 won k = 2 games in a row, so the winner is player 2.\n\nExample 2:\n\nInput: skills = [2,5,4], k = 3\nOutput: 1\nExplanation:\nInitially, the queue of players is [0,1,2]. The following process happens:\n\nPlayers 0 and 1 play a game, since the skill of player 1 is higher than that of player 0, player 1 wins. The resulting queue is [1,2,0].\nPlayers 1 and 2 play a game, since the skill of player 1 is higher than that of player 2, player 1 wins. The resulting queue is [1,0,2].\nPlayers 1 and 0 play a game, since the skill of player 1 is higher than that of player 0, player 1 wins. The resulting queue is [1,2,0].\n\nPlayer 1 won k = 3 games in a row, so the winner is player 1.\n\n \nConstraints:\n\nn == skills.length\n2 <= n <= 10^5\n1 <= k <= 10^9\n1 <= skills[i] <= 10^6\nAll integers in skills are unique.",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.An election is being held with N candidates numbered 1, 2, \\ldots, N. There are K votes, some of which have been counted so far.\nUp until now, candidate i has received A_i votes.\nAfter all ballots are counted, candidate i (1 \\leq i \\leq N) will be elected if and only if the number of candidates who have received more votes than them is less than M. There may be multiple candidates elected.\nFor each candidate, find the minimum number of additional votes they need from the remaining ballots to guarantee their victory regardless of how the other candidates receive votes.\nFormally, solve the following problem for each i = 1,2,\\ldots,N.\nDetermine if there is a non-negative integer X not exceeding K - \\displaystyle{\\sum_{i=1}^{N}} A_i satisfying the following condition. If it exists, find the minimum possible such integer.\n\n- If candidate i receives X additional votes, then candidate i will always be elected.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN M K\nA_1 A_2 \\ldots A_N\n\nOutput\n\nLet C_i be the minimum number of additional votes candidate i needs from the remaining ballots to guarantee their victory regardless of how other candidates receive votes. Print C_1, C_2, \\ldots, C_N separated by spaces.\nIf candidate i has already secured their victory, then let C_i = 0. If candidate i cannot secure their victory under any circumstances, then let C_i = -1.\n\nConstraints\n\n\n- 1 \\leq M \\leq N \\leq 2 \\times 10^5\n- 1 \\leq K \\leq 10^{12}\n- 0 \\leq A_i \\leq 10^{12}\n- \\displaystyle{\\sum_{i=1}^{N} A_i} \\leq K\n- All input values are integers.\n\nSample Input 1\n\n5 2 16\n3 1 4 1 5\n\nSample Output 1\n\n2 -1 1 -1 0\n\n14 votes have been counted so far, and 2 votes are left.\nThe C to output is (2, -1, 1, -1, 0). For example:\n\n- Candidate 1 can secure their victory by obtaining 2 more votes, while not by obtaining 1 more vote. Thus, C_1 = 2.\n- Candidate 2 can never (even if they obtain 2 more votes) secure their victory, so C_2 = -1.\n\nSample Input 2\n\n12 1 570\n81 62 17 5 5 86 15 7 79 26 6 28\n\nSample Output 2\n\n79 89 111 117 117 74 112 116 80 107 117 106",
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"content": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.There is an integer sequence S of length N. Initially, all elements of S are 0.\nYou are also given two integer sequences of length Q: P=(P_1,P_2,\\dots,P_Q) and V=(V_1,V_2,\\dots,V_Q).\nSnuke wants to perform Q operations on the sequence S in order. The i-th operation is as follows:\n\n- Perform one of the following:\n- Replace each of the elements S_1, S_2, \\dots, S_{P_i} with V_i. However, before this operation, if there is an element among S_1, S_2, \\dots, S_{P_i} that is strictly greater than V_i, Snuke will start crying.\n- Replace each of the elements S_{P_i}, S_{P_i+1}, \\dots, S_N with V_i. However, before this operation, if there is an element among S_{P_i}, S_{P_i+1}, \\dots, S_N that is strictly greater than V_i, Snuke will start crying.\n\n\n\nFind the number of sequences of Q operations where Snuke can perform all operations without crying, modulo 998244353.\nTwo sequences of operations are distinguished if and only if there is 1 \\leq i \\leq Q such that the choice for the i-th operation is different.\n\nInput\n\nThe input is given from Standard Input in the following format:\nN Q\nP_1 V_1\nP_2 V_2\n\\vdots\nP_Q V_Q\n\nOutput\n\nPrint the answer as an integer.\n\nConstraints\n\n\n- 2 \\leq N \\leq 5000\n- 1 \\leq Q \\leq 5000\n- 1 \\leq P_i \\leq N\n- 1 \\leq V_i \\leq 10^9\n- All input values are integers.\n\nSample Input 1\n\n8 3\n1 8\n8 1\n2 1\n\nSample Output 1\n\n1\n\nSnuke can perform the three operations without crying as follows:\n\n- Replace S_1 with 8.\n- Replace S_8 with 1.\n- Replace S_2, S_3, \\dots, S_8 with 1.\n\nNo other sequences of operations satisfy the conditions, so the answer is 1. For example, if he replaces S_1, S_2, \\dots, S_8 with 8 in the first operation, he will cry in the second operation regardless of the choice.\n\nSample Input 2\n\n8 3\n8 1\n1 8\n1 2\n\nSample Output 2\n\n0\n\nNo matter how he performs the first two operations, he will cry in the third operation.\n\nSample Input 3\n\n241 82\n190 3207371\n229 3639088\n61 4428925\n84 17258698\n34 42692503\n207 59753183\n180 67198566\n78 99285033\n60 102449991\n234 122146510\n111 126959145\n141 152331579\n78 159855439\n11 169658471\n22 189991287\n37 204602946\n73 209329065\n72 215363269\n152 236450854\n175 237822921\n22 261431608\n144 252550201\n54 268889550\n238 276997357\n69 313065279\n226 330144323\n6 335788783\n126 345410019\n220 348318997\n166 365778763\n142 382251905\n200 406191336\n234 392702679\n83 409660987\n183 410908761\n142 445707116\n205 470279207\n230 486436406\n156 494269002\n113 495687706\n200 500005738\n162 505246499\n201 548652987\n86 449551554\n62 459527873\n32 574001635\n230 601073337\n175 610244315\n174 613857555\n181 637452273\n158 637866397\n148 648101378\n172 646898076\n144 682578257\n239 703460335\n192 713255331\n28 727075136\n196 730768166\n111 751850547\n90 762445737\n204 762552166\n72 773170159\n240 803415865\n32 798873367\n195 814999380\n72 842641864\n125 851815348\n116 858041919\n200 869948671\n195 873324903\n5 877767414\n105 877710280\n150 877719360\n9 884707717\n230 880263190\n88 967344715\n49 977643789\n167 979463984\n70 981400941\n114 991068035\n94 991951735\n141 995762200\n\nSample Output 3\n\n682155965\n\nRemember to take the count modulo 998244353.",
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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 two positive integers n and k.\nYou can choose any bit in the binary representation of n that is equal to 1 and change it to 0.\nReturn the number of changes needed to make n equal to k. If it is impossible, return -1.\n \nExample 1:\n\nInput: n = 13, k = 4\nOutput: 2\nExplanation:\nInitially, the binary representations of n and k are n = (1101)_2 and k = (0100)_2.\nWe can change the first and fourth bits of n. The resulting integer is n = (0100)_2 = k.\n\nExample 2:\n\nInput: n = 21, k = 21\nOutput: 0\nExplanation:\nn and k are already equal, so no changes are needed.\n\nExample 3:\n\nInput: n = 14, k = 13\nOutput: -1\nExplanation:\nIt is not possible to make n equal to k.\n\n \nConstraints:\n\n1 <= n, k <= 10^6",
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"content": "Generate an executable Python function generated from the given prompt. Return the function body without invoking it at the final solution.You are given an array nums consisting of positive integers.\nWe call two integers x and y in this problem almost equal if both integers can become equal after performing the following operation at most once:\n\nChoose either x or y and swap any two digits within the chosen number.\n\nReturn the number of indices i and j in nums where i < j such that nums[i] and nums[j] are almost equal.\nNote that it is allowed for an integer to have leading zeros after performing an operation.\n \nExample 1:\n\nInput: nums = [3,12,30,17,21]\nOutput: 2\nExplanation:\nThe almost equal pairs of elements are:\n\n3 and 30. By swapping 3 and 0 in 30, you get 3.\n12 and 21. By swapping 1 and 2 in 12, you get 21.\n\n\nExample 2:\n\nInput: nums = [1,1,1,1,1]\nOutput: 10\nExplanation:\nEvery two elements in the array are almost equal.\n\nExample 3:\n\nInput: nums = [123,231]\nOutput: 0\nExplanation:\nWe cannot swap any two digits of 123 or 231 to reach the other.\n\n \nConstraints:\n\n2 <= nums.length <= 100\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.There are 12 strings S_1, S_2, \\ldots, S_{12} consisting of lowercase English letters.\nFind how many integers i (1 \\leq i \\leq 12) satisfy that the length of S_i is i.\n\nInput\n\nThe input is given from Standard Input in the following format:\nS_1\r\nS_2\r\n\\vdots\r\nS_{12}\n\nOutput\n\nPrint the number of integers i (1 \\leq i \\leq 12) such that the length of S_i is i.\n\nConstraints\n\n\n- Each S_i is a string of length between 1 and 100, inclusive, consisting of lowercase English letters. (1 \\leq i \\leq 12)\n\nSample Input 1\n\njanuary\r\nfebruary\r\nmarch\r\napril\r\nmay\r\njune\r\njuly\r\naugust\r\nseptember\r\noctober\r\nnovember\r\ndecember\n\nSample Output 1\n\n1\r\n\nThere is only one integer i such that the length of S_i is i: 9. Thus, print 1.\n\nSample Input 2\n\nve\r\ninrtfa\r\nnpccxva\r\ndjiq\r\nlmbkktngaovl\r\nmlfiv\r\nfmbvcmuxuwggfq\r\nqgmtwxmb\r\njii\r\nts\r\nbfxrvs\r\neqvy\n\nSample Output 2\n\n2\r\n\nThere are two integers i such that the length of S_i is i: 4 and 8. Thus, print 2.",
"role": "user"
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"do_sample": false,
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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 2D integer array grid with size m x n. You are also given an integer k.\nYour task is to calculate the number of paths you can take from the top-left cell (0, 0) to the bottom-right cell (m - 1, n - 1) satisfying the following constraints:\n\nYou can either move to the right or down. Formally, from the cell (i, j) you may move to the cell (i, j + 1) or to the cell (i + 1, j) if the target cell exists.\nThe XOR of all the numbers on the path must be equal to k.\n\nReturn the total number of such paths.\nSince the answer can be very large, return the result modulo 10^9 + 7.\n \nExample 1:\n\nInput: grid = [[2, 1, 5], [7, 10, 0], [12, 6, 4]], k = 11\nOutput: 3\nExplanation: \nThe 3 paths are:\n\n(0, 0) → (1, 0) → (2, 0) → (2, 1) → (2, 2)\n(0, 0) → (1, 0) → (1, 1) → (1, 2) → (2, 2)\n(0, 0) → (0, 1) → (1, 1) → (2, 1) → (2, 2)\n\n\nExample 2:\n\nInput: grid = [[1, 3, 3, 3], [0, 3, 3, 2], [3, 0, 1, 1]], k = 2\nOutput: 5\nExplanation:\nThe 5 paths are:\n\n(0, 0) → (1, 0) → (2, 0) → (2, 1) → (2, 2) → (2, 3)\n(0, 0) → (1, 0) → (1, 1) → (2, 1) → (2, 2) → (2, 3)\n(0, 0) → (1, 0) → (1, 1) → (1, 2) → (1, 3) → (2, 3)\n(0, 0) → (0, 1) → (1, 1) → (1, 2) → (2, 2) → (2, 3)\n(0, 0) → (0, 1) → (0, 2) → (1, 2) → (2, 2) → (2, 3)\n\n\nExample 3:\n\nInput: grid = [[1, 1, 1, 2], [3, 0, 3, 2], [3, 0, 2, 2]], k = 10\nOutput: 0\n\n \nConstraints:\n\n1 <= m == grid.length <= 300\n1 <= n == grid[r].length <= 300\n0 <= grid[r][c] < 16\n0 <= k < 16",
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Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.