{"raw_statement":[{"iden":"problem statement","content":"You are given a positive integer $X$ with $N$ digits in decimal representation. None of the digits of $X$ is $0$.  \nFor a subset $S$ of $\\lbrace 1,2, \\ldots, N-1 \\rbrace $ , let $f(S)$ be defined as follows.\n\n> See the decimal representation of $X$ as a string of length $N$, and decompose it into $|S| + 1$ strings by splitting it between the $i$\\-th and $(i + 1)$\\-th characters if and only if $i \\in S$.  \n> Then, see these $|S| + 1$ strings as integers in decimal representation, and let $f(S)$ be the product of these $|S| + 1$ integers.\n\nThere are $2^{N-1}$ subsets of $\\lbrace 1,2, \\ldots, N-1 \\rbrace $ , including the empty set, which can be $S$. Find the sum of $f(S)$ over all these $S$, modulo $998244353$."},{"iden":"constraints","content":"*   $2 \\leq N \\leq 2 \\times 10^5$\n*   $X$ has $N$ digits in decimal representation, none of which is $0$.\n*   All values in the input are integers."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$\n$X$"},{"iden":"sample input 1","content":"3\n234"},{"iden":"sample output 1","content":"418\n\nFor $S = \\emptyset$, we have $f(S) = 234$.  \nFor $S = \\lbrace 1 \\rbrace$, we have $f(S) = 2 \\times 34 = 68$.  \nFor $S = \\lbrace 2 \\rbrace$, we have $f(S) = 23 \\times 4 = 92$.  \nFor $S = \\lbrace 1, 2 \\rbrace$, we have $f(S) = 2 \\times 3 \\times 4 = 24$.  \nThus, you should print $234 + 68 + 92 + 24 = 418$."},{"iden":"sample input 2","content":"4\n5915"},{"iden":"sample output 2","content":"17800"},{"iden":"sample input 3","content":"9\n998244353"},{"iden":"sample output 3","content":"258280134"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}