Score : $700$ points

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

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

Input

Input is given from Standard Input in the following format:

$S$

Output

Print the number of strings that can be possibly obtained by repeatedly performing the operation, modulo $998244353$.

abc

3

abc, aaa and ccc can be obtained.

abbac

65

babacabac

6310

ababacbcacbacacbcbbcbbacbaccacbacbacba

148010497