{"problem":{"name":"Choosing Up Sides","description":{"content":"Let $N$ be a positive integer. Consider a competition where two teams, each with $2^{N-1}$ players, play against each other. We have $2^N$ players numbered $1$ through $2^N$. Coach Snuke can do the fo","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"keyence2021_d"},"statements":[{"statement_type":"Markdown","content":"Let $N$ be a positive integer. Consider a competition where two teams, each with $2^{N-1}$ players, play against each other.\nWe have $2^N$ players numbered $1$ through $2^N$. Coach Snuke can do the following operation any number of times: separate the players into two teams A and B, each with $2^{N-1}$ players, and make them play against each other.\nHe wants to do this operation one or more times so that both of the following conditions are satisfied:\n\n1.  there exists an integer $n$ such that, for every $(i, j)$ such that $1 \\leq i < j \\leq 2^N$, Player $i$ and Player $j$ have belonged to the **same** team exactly $n$ times.\n2.  there exists an integer $m$ such that, for every $(i, j)$ such that $1 \\leq i < j \\leq 2^N$, Player $i$ and Player $j$ have belonged to **different** teams exactly $m$ times.\n\nWe can prove that there exist sequences of operations that achieve Snuke's objective. Among those sequences, present one sequence with the **minimum possible number of operations**.\n\n## Constraints\n\n*   All values in input are integers.\n*   $1 \\leq N \\leq 8$\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"keyence2021_d","tags":[],"sample_group":[["1","1\nAB\n\n*   We can satisfy the objective with one operation.\n*   Note that we must do at least one operation."]],"created_at":"2026-03-03 11:01:14"}}