{"problem":{"name":"Chmax","description":{"content":"For a permutation $P = (P_1, P_2, \\dots, P_N)$ of $(1, 2, \\dots, N)$, we define $F(P)$ by the following procedure: *   There is a sequence $B = (1, 2, \\dots, N)$.       As long as there is an integer","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc171_b"},"statements":[{"statement_type":"Markdown","content":"For a permutation $P = (P_1, P_2, \\dots, P_N)$ of $(1, 2, \\dots, N)$, we define $F(P)$ by the following procedure:\n\n*   There is a sequence $B = (1, 2, \\dots, N)$.  \n    As long as there is an integer $i$ such that $B_i \\lt P_{B_i}$, perform the following operation:\n    \n    *   Let $j$ be the smallest integer $i$ that satisfies $B_i \\lt P_{B_i}$. Then, replace $B_j$ with $P_{B_j}$.\n    \n    Define $F(P)$ as the $B$ at the end of this process. (It can be proved that the process terminates after a finite number of steps.)\n\nYou are given a sequence $A = (A_1, A_2, \\dots, A_N)$ of length $N$. How many permutations $P$ of $(1,2,\\dots,N)$ satisfy $F(P) = A$? Find the count modulo $998244353$.\n\n## Constraints\n\n*   $1 \\leq N \\leq 2 \\times 10^5$\n*   $1 \\leq A_i \\leq N$\n*   All input values are integers.\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$N$\n$A_1$ $A_2$ $\\dots$ $A_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc171_b","tags":[],"sample_group":[["4\n3 3 3 4","1\n\nFor example, if $P = (2, 3, 1, 4)$, then $F(P)$ is determined to be $(3, 3, 3, 4)$ by the following steps:\n\n*   Initially, $B = (1, 2, 3, 4)$.\n*   The smallest integer $i$ such that $B_i \\lt P_{B_i}$ is $1$. Replace $B_1$ with $P_{B_1} = 2$, making $B = (2, 2, 3, 4)$.\n*   The smallest integer $i$ such that $B_i \\lt P_{B_i}$ is $1$. Replace $B_1$ with $P_{B_1} = 3$, making $B = (3, 2, 3, 4)$.\n*   The smallest integer $i$ such that $B_i \\lt P_{B_i}$ is $2$. Replace $B_2$ with $P_{B_2} = 3$, making $B = (3, 3, 3, 4)$.\n*   There are no more $i$ that satisfy $B_i \\lt P_{B_i}$, so the process ends. The current $B = (3, 3, 3, 4)$ is defined as $F(P)$.\n\nThere is only one permutation $P$ such that $F(P) = A$, which is $(2, 3, 1, 4)$."],["4\n2 2 4 3","0"],["8\n6 6 8 4 5 6 8 8","18"]],"created_at":"2026-03-03 11:01:13"}}