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Problem Statement

You are given a string $S$ consisting of a,b and c. Find the number of strings that can be possibly obtained by repeatedly performing the following operation zero or more times, modulo $998244353$:

• Choose an integer $i$ such that $1\leq i\leq |S|-1$ and the $i$-th and $(i+1)$-th characters in $S$ are different. Replace each of the $i$-th and $(i+1)$-th characters in $S$ with the character that differs from both of them (among a, b and c).

Constraints

• $2 \leq |S| \leq 2 × 10^5$
• $S$ consists of a, b and c.

Sample Input 1

abc

Sample Output 1

3

abc, aaa and ccc can be obtained.

Sample Input 2

abbac

Sample Output 2

65

Sample Input 3

babacabac

Sample Output 3

6310

Sample Input 4

ababacbcacbacacbcbbcbbacbaccacbacbacba

Sample Output 4

148010497