{"problem":{"name":"Construct Sequences","description":{"content":"#nck { width: 30px; height: auto; }You are given a permutation $p$ of the set {$1, 2, ..., N$}. Please construct two sequences of positive integers $a_1$, $a_2$, ..., $a_N$ and $b_1$, $b_2$, ..., $b_N","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"agc007_b"},"statements":[{"statement_type":"Markdown","content":"#nck { width: 30px; height: auto; }You are given a permutation $p$ of the set {$1, 2, ..., N$}. Please construct two sequences of positive integers $a_1$, $a_2$, ..., $a_N$ and $b_1$, $b_2$, ..., $b_N$ satisfying the following conditions:\n\n*   $1 \\leq a_i, b_i \\leq 10^9$ for all $i$\n*   $a_1 < a_2 < ... < a_N$\n*   $b_1 > b_2 > ... > b_N$\n*   $a_{p_1}+b_{p_1} < a_{p_2}+b_{p_2} < ... < a_{p_N}+b_{p_N}$\n\n## Constraints\n\n*   $2 \\leq N \\leq 20,000$\n*   $p$ is a permutation of the set {$1, 2, ..., N$}\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$N$\n$p_1$ $p_2$ $...$ $p_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"agc007_b","tags":[],"sample_group":[["2\n1 2","1 4\n5 4\n\n$a_1 + b_1 = 6$ and $a_2 + b_2 = 8$. So this output satisfies all conditions."],["3\n3 2 1","1 2 3\n5 3 1"],["3\n2 3 1","5 10 100\n100 10 1"]],"created_at":"2026-03-03 11:01:14"}}