{"raw_statement":[{"iden":"problem statement","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 $\\max(p_1, p_2, \\dots, p_i) \\neq i$."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 2.5 \\times 10^5$\n*   $N$ is an integer"},{"iden":"input","content":"The input is given from standard input in the following format:\n\n$N$"},{"iden":"sample input 1","content":"3"},{"iden":"sample output 1","content":"3\n\nThe following $3$ permutations $p$ satisfy the condition:\n\n*   $(2,3,1)$\n*   $(3,1,2)$\n*   $(3,2,1)$"},{"iden":"sample input 2","content":"123456"},{"iden":"sample output 2","content":"923416117"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}