{"problem":{"name":"Problem where +s Separate Digits","description":{"content":"Given is a string $S$ consisting of digits from $1$ through $9$.   From this string $S$, let us make a formula $T$ by the following operations. *   Initially, let $T=S$. *   Choose a (possibly empty)","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc224_f"},"statements":[{"statement_type":"Markdown","content":"Given is a string $S$ consisting of digits from $1$ through $9$.  \nFrom this string $S$, let us make a formula $T$ by the following operations.\n\n*   Initially, let $T=S$.\n*   Choose a (possibly empty) set $A$ of different integers where each element is between $1$ and $|S|-1$ (inclusive).\n*   For each element $x$ in descending order, do the following.\n    *   Insert a `+` between the $x$\\-th and $(x+1)$\\-th characters of $T$.\n\nFor example, when $S=$ `1234` and $A= \\lbrace 2,3 \\rbrace$, we will have $T$\\= `12+3+4`.\nConsider evaluating all possible formulae $T$ obtained by these operations. Find the sum, modulo $998244353$, of the evaluations.\n\n## Constraints\n\n*   $1 \\le |S| \\le 2 \\times 10^5$\n*   $S$ consists of `1`, `2`, `3`, `4`, `5`, `6`, `7`, `8`, and `9`.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$S$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc224_f","tags":[],"sample_group":[["1234","1736\n\nThere are eight formulae that can be obtained as $T$: `1234`, `123+4`, `12+34`, `12+3+4`, `1+234`, `1+23+4`, `1+2+34`, and `1+2+3+4`.  \nThe sum of the evaluations of these formulae is $1736$."],["1","1\n\n$S$ may have a length of $1$, in which case the only possible choice for $A$ is the empty set."],["31415926535897932384626433832795","85607943\n\nBe sure to find the sum modulo $998244353$."]],"created_at":"2026-03-03 11:01:13"}}