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 $i = 1, \ldots, N$ in this order, do the following: insert the $i$\-th character in the decimal notation of $X$ at the beginning or end of $S$. - Let $Y$ be the positive integer represented by the string $S$. Let $f(X)$ denote the minimum positive integer that can be obtained from $X$ in this way. * * * You 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 $f(X) = Y$.

The input is given from Standard Input in the following format: > $Y$ #### Constraints - $Y$ is a positive integer none of whose digits is $0$. - $1 \leq Y < 10^{200000}$

Print the number, modulo $998244353$, of positive integers $X$ none of whose digits is $0$ such that $f(X) = Y$.