Encoding Subsets

AtCoder

IDagc020_e

Time5000ms

Memory256MB

Difficulty—

Consider the following set of rules for encoding strings consisting of `0` and `1`: * Strings `0` and `1` can be encoded as `0` and `1`, respectively. * If strings $A$ and $B$ can be encoded as $P$ and $Q$, respectively, then string $AB$ can be encoded as $PQ$. * If string $A$ can be encoded as $P$ and $K \geq 2$ is a positive integer, then string $AA...A$ ($A$ repeated $K$ times) can be encoded as `(`$P$`x`$K$`)`. For example, string `001001001`, among other possibilities, can be encoded as `001001001`, `00(1(0x2)x2)1` and `(001x3)`. Let's call string $A$ a subset of string $B$ if: * $A$ and $B$ are equal in length and consist of `0` and `1`; * for all indices $i$ such that $A_i$ = `1`, it's also true that $B_i$ = `1`. You are given string $S$ consisting of `0` and `1`. Find the total number of distinct encodings of all subsets of $S$, modulo $998244353$. ## Constraints * $1 \leq |S| \leq 100$ * $S$ consists of `0` and `1`. ## Input Input is given from Standard Input in the following format: $S$ [samples]

Samples

Input #1

Output #1

9

There are four subsets of $S$:

*   `011` can be encoded as `011` and `0(1x2)`;
*   `010` can be encoded as `010`;
*   `001` can be encoded as `001` and `(0x2)1`;
*   `000` can be encoded as `000`, `0(0x2)`, `(0x2)0` and `(0x3)`.

Thus, the total number of encodings of all subsets of $S$ is $2 + 1 + 2 + 4 = 9$.

Input #2

Output #2

10

This time $S$ has only one subset, but it can be encoded in $10$ different ways.

Input #3

Output #3

Input #4

001110111010110001100000100111

Output #4

363383189

Don't forget to take the result modulo $998244353$.

API Response (JSON)

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