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No.1481 Rotation ABC

レベル : / AI推定難易度 : 1825 / 実行時間制限 : 1ケース 2.000秒 / メモリ制限 : 512 MB / 標準ジャッジ問題
タグ : （AC するまで非表示） / 解いたユーザー数 45
作問者 : nok0 / テスター : fairy_lettuce chineristAC ygussany PCTprobability
お気に入りにしたユーザー ProblemId : 5901 / 自分の提出
問題文最終更新日: 2021-03-21 18:11:05
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yukicoder contest 291 (順位表) の他の問題:

Problem Statement

There is a string $S$ of length $N$ consisting of A,B,C.

You may perform the following operation on $S$ $0$ or more times.

  • Choose a triple $\left(i,j,k\right)$ such that $S_i =$ A, $S_j = $B,$S_k =$ C. Replace $S_i,S_j,S_k$ with B,C,A, respectively. Here, the chosen triple $\left(i,j,k\right)$ must satisfy one of the following order relations.
    • $1 \le i < j < k \le N$
    • $1 \le j < k < i \le N$
    • $1 \le k < i < j \le N$

Output the number of distinct strings that $S$ can be after performing the operation $0$ or more times, modulo $998244353$.

Constraints

  • $1\le N \le 10^5$
  • $S$ is a string of length $N$ consisting of A,B,C.

Input

$N$
$S$

Output

Output the number of distinct strings that $S$ can be after performing the operation $0$ or more times, modulo $998244353$.

Sample

Sample 1
Input
3
ABC
Output
3

Performing the operation $0$ times gives ABC, performing it $1$ time gives BCA, and performing it $2$ times gives CAB.

Sample 2
Input
5
AAAAB
Output
1

The operation cannot be performed even $1$ time.

Sample 3
Input
4
AABC
Output
8

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