{"problem":{"name":"Simple Speed","description":{"content":"You are given a sequence of $N$ positive integers: $A=(A_1,A_2,\\dots,A_N)$. How many integer sequences $B$ consisting of integers between $1$ and $N$ (inclusive) satisfy all of the following condition","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc146_e"},"statements":[{"statement_type":"Markdown","content":"You are given a sequence of $N$ positive integers: $A=(A_1,A_2,\\dots,A_N)$.\nHow many integer sequences $B$ consisting of integers between $1$ and $N$ (inclusive) satisfy all of the following conditions? Print the count modulo $998244353$.\n\n*   For each integer $i$ such that $1 \\le i \\le N$, there are exactly $A_i$ occurrences of $i$ in $B$.\n*   For each integer $i$ such that $1 \\le i \\le |B|-1$, it holds that $|B_i - B_{i+1}|=1$.\n\n## Constraints\n\n*   $1 \\le N \\le 2 \\times 10^5$\n*   $1 \\le A_i \\le 2 \\times 10^5$\n*   All values in input are integers.\n\n## Input\n\nInput 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":"arc146_e","tags":[],"sample_group":[["3\n2 3 1","6\n\n$B$ can be the following six sequences.\n\n*   $(1,2,1,2,3,2)$\n*   $(1,2,3,2,1,2)$\n*   $(2,1,2,1,2,3)$\n*   $(2,1,2,3,2,1)$\n*   $(2,3,2,1,2,1)$\n*   $(3,2,1,2,1,2)$\n\nThus, the answer is $6$."],["1\n200000","0\n\nThere may be no sequence that satisfies the conditions."],["6\n12100 31602 41387 41498 31863 12250","750337372"]],"created_at":"2026-03-03 11:01:14"}}