{"problem":{"name":"Deque Minimization","description":{"content":"For a positive integer $X$ none of whose digits is $0$, consider obtaining a positive integer $Y$ as follows. *   Initialize $S$ as an empty string. *   Let $N$ be the number of digits in $X$. For $i","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":5000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc153_e"},"statements":[{"statement_type":"Markdown","content":"For a positive integer $X$ none of whose digits is $0$, consider obtaining a positive integer $Y$ as follows.\n\n*   Initialize $S$ as an empty string.\n*   Let $N$ be the number of digits in $X$. For $i = 1, \\ldots, N$ in this order, do the following: insert the $i$\\-th character in the decimal notation of $X$ at the beginning or end of $S$.\n*   Let $Y$ be the positive integer represented by the string $S$.\n\nLet $f(X)$ denote the minimum positive integer that can be obtained from $X$ in this way.\n\n* * *\n\nYou are given a positive integer $Y$ none of whose digits is $0$. Print the number, modulo $998244353$, of positive integers $X$ none of whose digits is $0$ such that $f(X) = Y$.\n\n## Constraints\n\n*   $Y$ is a positive integer none of whose digits is $0$.\n*   $1\\leq Y < 10^{200000}$\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$Y$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc153_e","tags":[],"sample_group":[["1332","3\n\nThree integers, $1332$, $3132$, and $3312$, satisfy the conditions."],["3312","0"],["12234433442","153"]],"created_at":"2026-03-03 11:01:13"}}