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You are given a positive integer N and a length-N string s_0s_1\ldots s_{N-1} consisting only of 0 and 1. Consider a simple undirected graph G with (N+1) vertices numbered 0, 1, 2, \ldots, N, and the following edges: - For each i = 0, 1, \ldots, N-1, there is an undirected edge between vertices i and (i+1)\bmod N. - F...
[{"role": "system", "content": "You are a helpful coding assistant.\n\nYou have access to a Python interpreter.\nTo execute code, wrap it inside <interact></interact>. I will run it and return stdout/stderr in a subsequent turn.\n\nIMPORTANT CONTEXT:\n- This is a multi-turn conversation.\n- The Python interpreter is a ...
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[{"code": "N = 3\ns = \"010\"\nk = sum(1 for c in s if c == '1') # k = 1\n\n# The cycle: 0-1, 1-2, 2-0\n# The spoke: 1-3 (since s[1] = '1')\n\n# For the cycle, we need to orient 3 edges\n# For the spoke, we have 2 choices: 1\u21923 or 3\u21921\n\n# Let's enumerate all possibilities\nfrom itertools import product\n\n# ...
{"inputs": ["3\n010", "20\n00001100111010100101", "8\n01000101", "18\n101000001001101101", "8\n00111011", "43\n0110110101011001010110101100100111101110000", "12\n001101110111", "14\n01100000000001", "3\n000", "18\n110000001110010111", "7\n0101010", "199\n01001010001000111001011111101001111010000110111010000001110100100...
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================================================================================ Question: You are given a positive integer N and a length-N ... Reward: 0.13 | Turns: 2 | Terminated: True | Truncated: False ================================================================================ [SYSTEM] You are a helpful codi...
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You are given a positive integer N and a length-N string s_0s_1\ldots s_{N-1} consisting only of 0 and 1. Consider a simple undirected graph G with (N+1) vertices numbered 0, 1, 2, \ldots, N, and the following edges: - For each i = 0, 1, \ldots, N-1, there is an undirected edge between vertices i and (i+1)\bmod N. - F...
[{"role": "system", "content": "You are a helpful coding assistant.\n\nYou have access to a Python interpreter.\nTo execute code, wrap it inside <interact></interact>. I will run it and return stdout/stderr in a subsequent turn.\n\nIMPORTANT CONTEXT:\n- This is a multi-turn conversation.\n- The Python interpreter is a ...
3
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[{"code": "N = 3\ns = \"010\"\n\n# Build list of edges\nedges = []\n# Cycle edges\nfor i in range(N):\n edges.append((i, (i+1) % N))\n# Spoke edges\nfor i in range(N):\n if s[i] == '1':\n edges.append((i, N))\n\n# Count distinct in-degree sequences\nfrom itertools import product\n\ndistinct_sequences = set...
{"inputs": ["3\n010", "20\n00001100111010100101", "8\n01000101", "18\n101000001001101101", "8\n00111011", "43\n0110110101011001010110101100100111101110000", "12\n001101110111", "14\n01100000000001", "3\n000", "18\n110000001110010111", "7\n0101010", "199\n01001010001000111001011111101001111010000110111010000001110100100...
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================================================================================ Question: You are given a positive integer N and a length-N ... Reward: 0.07 | Turns: 3 | Terminated: True | Truncated: False ================================================================================ [SYSTEM] You are a helpful codi...
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You are given a positive integer N and a length-N string s_0s_1\ldots s_{N-1} consisting only of 0 and 1. Consider a simple undirected graph G with (N+1) vertices numbered 0, 1, 2, \ldots, N, and the following edges: - For each i = 0, 1, \ldots, N-1, there is an undirected edge between vertices i and (i+1)\bmod N. - F...
[{"role": "system", "content": "You are a helpful coding assistant.\n\nYou have access to a Python interpreter.\nTo execute code, wrap it inside <interact></interact>. I will run it and return stdout/stderr in a subsequent turn.\n\nIMPORTANT CONTEXT:\n- This is a multi-turn conversation.\n- The Python interpreter is a ...
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[{"code": "def solve(N, s):\n MOD = 998244353\n from itertools import product\n \n # Count edges\n cycle_edges = N # edges (i, i+1 mod N) for i in range(N)\n star_edges = sum(1 for c in s if c == '1')\n total_edges = cycle_edges + star_edges\n \n # We'll generate all possible direction assig...
{"inputs": ["3\n010", "20\n00001100111010100101", "8\n01000101", "18\n101000001001101101", "8\n00111011", "43\n0110110101011001010110101100100111101110000", "12\n001101110111", "14\n01100000000001", "3\n000", "18\n110000001110010111", "7\n0101010", "199\n01001010001000111001011111101001111010000110111010000001110100100...
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================================================================================ Question: You are given a positive integer N and a length-N ... Reward: 0.13 | Turns: 3 | Terminated: True | Truncated: False ================================================================================ [SYSTEM] You are a helpful codi...
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"You are given a positive integer N and a length-N string s_0s_1\\ldots s_{N-1} consisting only of 0(...TRUNCATED)
"[{\"role\": \"system\", \"content\": \"You are a helpful coding assistant.\\n\\nYou have access to (...TRUNCATED)
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"[{\"code\": \"from itertools import product\\n\\ndef solve(N, s):\\n # Count the number of 1s in(...TRUNCATED)
"{\"inputs\": [\"3\\n010\", \"20\\n00001100111010100101\", \"8\\n01000101\", \"18\\n1010000010011011(...TRUNCATED)
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"================================================================================\nQuestion: You are(...TRUNCATED)
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"You are given a positive integer N and a length-N string s_0s_1\\ldots s_{N-1} consisting only of 0(...TRUNCATED)
"[{\"role\": \"system\", \"content\": \"You are a helpful coding assistant.\\n\\nYou have access to (...TRUNCATED)
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"[{\"code\": \"```python\\ndef solve(N, s):\\n MOD = 998244353\\n \\n # Count the number of(...TRUNCATED)
"{\"inputs\": [\"3\\n010\", \"20\\n00001100111010100101\", \"8\\n01000101\", \"18\\n1010000010011011(...TRUNCATED)
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"================================================================================\nQuestion: You are(...TRUNCATED)
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"You are given a positive integer N and a length-N string s_0s_1\\ldots s_{N-1} consisting only of 0(...TRUNCATED)
"[{\"role\": \"system\", \"content\": \"You are a helpful coding assistant.\\n\\nYou have access to (...TRUNCATED)
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"[{\"code\": \"# Let me compute T_20 using the recurrence\\nmod = 998244353\\n\\n# T_0 = 1, T_1 = 1\(...TRUNCATED)
"{\"inputs\": [\"3\\n010\", \"20\\n00001100111010100101\", \"8\\n01000101\", \"18\\n1010000010011011(...TRUNCATED)
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"================================================================================\nQuestion: You are(...TRUNCATED)
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"You are given a positive integer N and a length-N string s_0s_1\\ldots s_{N-1} consisting only of 0(...TRUNCATED)
"[{\"role\": \"system\", \"content\": \"You are a helpful coding assistant.\\n\\nYou have access to (...TRUNCATED)
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"[{\"code\": \"N = 3\\ns = \\\"010\\\"\\n\\n# Count total edges\\ncycle_edges = N # N edges in the (...TRUNCATED)
"{\"inputs\": [\"3\\n010\", \"20\\n00001100111010100101\", \"8\\n01000101\", \"18\\n1010000010011011(...TRUNCATED)
true
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"================================================================================\nQuestion: You are(...TRUNCATED)
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"You are given a positive integer N and a length-N string s_0s_1\\ldots s_{N-1} consisting only of 0(...TRUNCATED)
"[{\"role\": \"system\", \"content\": \"You are a helpful coding assistant.\\n\\nYou have access to (...TRUNCATED)
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"[{\"code\": \"# Read input\\nN = int(input())\\ns = input().strip()\\n\\n# Count the number of 1s i(...TRUNCATED)
"{\"inputs\": [\"3\\n010\", \"20\\n00001100111010100101\", \"8\\n01000101\", \"18\\n1010000010011011(...TRUNCATED)
true
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"================================================================================\nQuestion: You are(...TRUNCATED)
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"You are given a positive integer N and a length-N string s_0s_1\\ldots s_{N-1} consisting only of 0(...TRUNCATED)
"[{\"role\": \"system\", \"content\": \"You are a helpful coding assistant.\\n\\nYou have access to (...TRUNCATED)
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"[{\"code\": \"from itertools import product\\n\\ndef solve(N, s):\\n # Build the graph edges\\n (...TRUNCATED)
"{\"inputs\": [\"3\\n010\", \"20\\n00001100111010100101\", \"8\\n01000101\", \"18\\n1010000010011011(...TRUNCATED)
true
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"================================================================================\nQuestion: You are(...TRUNCATED)
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"You are given a positive integer N and a length-N string s_0s_1\\ldots s_{N-1} consisting only of 0(...TRUNCATED)
"[{\"role\": \"system\", \"content\": \"You are a helpful coding assistant.\\n\\nYou have access to (...TRUNCATED)
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"[{\"code\": \"import itertools\\n\\ndef solve(N, s):\\n MOD = 998244353\\n \\n # Build the(...TRUNCATED)
"{\"inputs\": [\"3\\n010\", \"20\\n00001100111010100101\", \"8\\n01000101\", \"18\\n1010000010011011(...TRUNCATED)
true
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"================================================================================\nQuestion: You are(...TRUNCATED)
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