{"raw_statement":[{"iden":"problem statement","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**."},{"iden":"constraints","content":"*   All values in input are integers.\n*   $1 \\leq N \\leq 8$"},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$"},{"iden":"sample input 1","content":"1"},{"iden":"sample output 1","content":"1\nAB\n\n*   We can satisfy the objective with one operation.\n*   Note that we must do at least one operation."}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}