Problem Statement

You are given a string $T$ of length $N$ consisting of lowercase English letters.

Output, modulo $998244353$, the number of sequences of strings $s=(s_0,s_1,\ldots,s_N)$ that satisfy all of the following conditions.

• $s_0$ is an empty string.
• For $i=1,2,\ldots,N$, the string $s_{i}$ is obtained by inserting one arbitrary character at an arbitrary position (possibly beginning or end) in $s_{i-1}$.
• $s_N=T$

Constraints

• $1\leq N\leq 22$
• $N$ is an integer.
• $T$ is a string of length $N$ consisting of lowercase English letters.

Input

The input is given from Standard Input in the following format:

N
T

Output

Output the answer.