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E - Chain Contestant

Score : $500$ points

Problem Statement

AtCoder in another world holds $10$ types of contests called AAC, ..., AJC. There will be $N$ contests from now on.
The types of these $N$ contests are given to you as a string $S$: if the $i$-th character of $S$ is $x$, the $i$-th contest will be A$x$C.
AtCoDeer will choose and participate in one or more contests from the $N$ so that the following condition is satisfied.

• In the sequence of contests he will participate in, the contests of the same type are consecutive.
  • Formally, when AtCoDeer participates in $x$ contests and the $i$-th of them is of type $T_i$, for every triple of integers $(i,j,k)$ such that $1 \le i < j < k \le x$, $T_i=T_j$ must hold if $T_i=T_k$.

Find the number of ways for AtCoDeer to choose contests to participate in, modulo $998244353$.
Two ways to choose contests are considered different when there is a contest $c$ such that AtCoDeer participates in $c$ in one way but not in the other.

Constraints

• $1 \le N \le 1000$
• $|S|=N$
• $S$ consists of uppercase English letters from A through J.

Input

Input is given from Standard Input in the following format:

$N$

$S$

Output

Print the answer as an integer.

4
BGBH

13

For example, participating in the $1$-st and $3$-rd contests is valid, and so is participating in the $2$-nd and $4$-th contests.
On the other hand, participating in the $1$-st, $2$-nd, $3$-rd, and $4$-th contests is invalid, since the participations in ABCs are not consecutive, violating the condition for the triple $(i,j,k)=(1,2,3)$.
Additionally, it is not allowed to participate in zero contests.
In total, there are $13$ valid ways to participate in some contests.

100
BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBIEIJEIJIJCGCCFGIEBIHFCGFBFAEJIEJAJJHHEBBBJJJGJJJCCCBAAADCEHIIFEHHBGF

330219020

Be sure to find the count modulo $998244353$.