{"problem":{"name":"Permutation","description":{"content":"You are given an integer $N$.   Consider permutations $p = (p_1, p_2, \\dots, p_N)$ of $(1, 2, \\dots, N)$.   Count how many such permutations satisfy the following condition, and output the result modu","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"fps_24_k"},"statements":[{"statement_type":"Markdown","content":"You are given an integer $N$.  \nConsider permutations $p = (p_1, p_2, \\dots, p_N)$ of $(1, 2, \\dots, N)$.  \nCount how many such permutations satisfy the following condition, and output the result modulo $998244353$.\n\n*   For every integer $i$ such that $1 \\leq i \\leq N-1$, it must hold that $\\max(p_1, p_2, \\dots, p_i) \\neq i$.\n\n## Constraints\n\n*   $1 \\leq N \\leq 2.5 \\times 10^5$\n*   $N$ is an integer\n\n## Input\n\nThe input is given from standard input in the following format:\n\n$N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"fps_24_k","tags":[],"sample_group":[["3","3\n\nThe following $3$ permutations $p$ satisfy the condition:\n\n*   $(2,3,1)$\n*   $(3,1,2)$\n*   $(3,2,1)$"],["123456","923416117"]],"created_at":"2026-03-03 11:01:14"}}