102345: [AtCoder]ABC234 F - Reordering

Problem Statement

Given is a string $S$. How many different strings can be obtained as a permutation of a non-empty, not necessarily contiguous subsequence of $S$?

Since the count can be enormous, print it modulo $998244353$.

Constraints

• $S$ is a string of length $1$ and $5000$ (inclusive) consisting of lowercase English letters.

Input

Input is given from Standard Input in the following format:

$S$

Output

Print the number of different strings that can be obtained as a permutation of a subsequence of $S$, modulo $998244353$.

Sample Input 1

aab

Sample Output 1

8

There are $8$ different strings that can be obtained as a permutation of a subsequence of $S$: a, b, aa, ab, ba, aab, aba, baa.

Sample Input 2

aaa

Sample Output 2

3

Sample Input 3

abcdefghijklmnopqrstuvwxyz

Sample Output 3

149621752

Be sure to print the count modulo $998244353$.

问题描述

给定一个字符串$S$。可以得到多少个不同的字符串，作为$S$的一个非空的、不一定连续的子序列的排列？

由于计数可能非常大，因此请将其对$998244353$取模。

约束

• $S$是一个长度在$1$到$5000$（包括）之间，由小写英文字母组成的字符串。

输入

从标准输入按照以下格式获取输入：

$S$

输出

对$S$的子序列进行排列后可以得到的不同字符串的数量，对$998244353$取模。

样例输入1

aab

样例输出1

8

对于给定的字符串$S$，可以得到$8$个不同的字符串作为其子序列的排列：a，b，aa，ab，ba，aab，aba，baa。

样例输入2

aaa

样例输出2

3

样例输入3

abcdefghijklmnopqrstuvwxyz

样例输出3

149621752

请确保对计数取模$998244353$。