Problem where +s Separate Digits

AtCoder

IDabc224_f

Time2000ms

Memory256MB

Difficulty—

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) set $A$ of different integers where each element is between $1$ and $|S|-1$ (inclusive). * For each element $x$ in descending order, do the following. * Insert a `+` between the $x$\-th and $(x+1)$\-th characters of $T$. For example, when $S=$ `1234` and $A= \lbrace 2,3 \rbrace$, we will have $T$\= `12+3+4`. Consider evaluating all possible formulae $T$ obtained by these operations. Find the sum, modulo $998244353$, of the evaluations. ## Constraints * $1 \le |S| \le 2 \times 10^5$ * $S$ consists of `1`, `2`, `3`, `4`, `5`, `6`, `7`, `8`, and `9`. ## Input Input is given from Standard Input in the following format: $S$ [samples]

Samples

Input #1

Output #1

1736

There 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`.  
The sum of the evaluations of these formulae is $1736$.

Input #2

Output #2

1

$S$ may have a length of $1$, in which case the only possible choice for $A$ is the empty set.

Input #3

31415926535897932384626433832795

Output #3

85607943

Be sure to find the sum modulo $998244353$.

API Response (JSON)

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      "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)",
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      "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)...",
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