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 $998244353$.