Problem Statement

You are given a string $S$ consisting of lowercase English letters. Print the number of non-empty strings $T$ that satisfy the following condition, modulo $998244353$.

The concatenation $TT$ of two copies of $T$ is a subsequence of $S$ (not necessarily contiguous).

Constraints

• $S$ is a string consisting of lowercase English letters whose length is between $1$ and $100$, inclusive.

Sample Input 1Copy

ababbaba

Sample Output 1Copy

8

The eight strings satisfying the condition are a, aa, ab, aba, b, ba, bab, and bb.

Sample Input 2Copy

zzz

Sample Output 2Copy

1

The only string satisfying the condition is z. Note that this string contributes to the answer just once, although there are three ways to extract the subsequence zz from $S = S_1S_2S_3 =$ zzz: $S_1S_2 =$ zz, $S_1S_3 =$ zz, and $S_2S_3 =$ zz.

Sample Input 3Copy

ppppqqppqqqpqpqppqpqqqqpppqppq

Sample Output 3Copy

580