{"raw_statement":[{"iden":"problem statement","content":"For a string $S$ consisting of digits from `1` through `9`, let $f(S)$ be the string $T$ obtained by the following procedure. ($S_i$ denotes the $i$\\-th character of $S$.)\n\n*   Let $T$ be an initially empty string.\n*   For $i=1, 2, \\dots, |S| - 1$, perform the following operation:\n    *   Append $n$ copies of $S_i$ to the tail of $T$, where $n$ is the value when $S_{i+1}$ is interpreted as an integer.\n\nFor example, $S =$ `313` yields $f(S) =$ `3111` by the following steps.\n\n*   $T$ is initially empty.\n*   For $i=1$, we have $n = 1$. Append one copy of `3` to $T$, which becomes `3`.\n*   For $i=2$, we have $n = 3$. Append three copies of `1` to $T$, which becomes `3111`.\n*   Terminate the procedure. We obtain $T =$ `3111`.\n\nYou are given a length-$N$ string $S$ consisting of digits from `1` through `9`.  \nYou repeat the following operation until the length of $S$ becomes $1$: replace $S$ with $f(S)$.  \nFind how many times, modulo $998244353$, you perform the operation until you complete it. If you will repeat the operation indefinitely, print `-1` instead."},{"iden":"constraints","content":"*   $2 \\leq N \\leq 10^6$\n*   $S$ is a length-$N$ string consisting of `1`, `2`, `3`, `4`, `5`, `6`, `7`, `8`, and `9`."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$\n$S$"},{"iden":"sample input 1","content":"3\n313"},{"iden":"sample output 1","content":"4\n\nIf $S =$ `313`, the length of $S$ be comes $1$ after four operations.\n\n*   We have $f(S) =$ `3111`. Replace $S$ with `3111`.\n*   We have $f(S) =$ `311`. Replace $S$ with `311`.\n*   We have $f(S) =$ `31`. Replace $S$ with `31`.\n*   We have $f(S) =$ `3`. Replace $S$ with `3`.\n*   Now that the length of $S$ is $1$, terminate the repetition."},{"iden":"sample input 2","content":"9\n123456789"},{"iden":"sample output 2","content":"\\-1\n\nIf $S =$ `123456789`, you indefinitely repeat the operation. In this case, `-1` should be printed."},{"iden":"sample input 3","content":"2\n11"},{"iden":"sample output 3","content":"1"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}