#include<iostream>
#include<algorithm>
#include<cstdio>
#include<cstdlib>
#include<cstring>
using namespace std;

const int maxn=2e5+10,mod=998244353;
int n,mod3,dp[maxn][3][3][2],ans=1;
char s[maxn];

inline bool allthesame(){
	for(int i=2;i<=n;++i)
		if(s[i]!=s[1])
			return false;
	return true;
}

int main(){
	cin>>(s+1);
	n=strlen(s+1);
	for(int i=1;i<=n;++i)
		s[i]-='0';
	if(allthesame()){
		puts("1");
		return 0;
	}
	if(n<=3){
		if(n==2)
			puts("2");
		else if(s[1]==s[3])
			puts("7");
		else if(s[1]==s[2]||s[2]==s[3])
			puts("6");
		else
			puts("3");
		return 0;
	}
	for(int i=1;i<=n;++i)
		(mod3+=s[i])%=3;
	dp[1][0][0][0]=dp[1][1][1][0]=dp[1][2][2][0]=1;
	for(int i=1;i<n;++i)
		for(int j=0;j<3;++j)
			for(int k=0;k<3;++k)
				for(int l=0;l<2;++l)
					for(int x=0;x<3;++x)
						(dp[i+1][x][(x+k)%3][l||x==j]+=dp[i][j][k][l])%=mod;
	for(int i=0;i<3;++i)
		(ans+=dp[n][i][mod3][1])%=mod;
	for(int i=1;i<n;++i)
		if(s[i]==s[i+1]){
			ans=(ans+mod-1)%mod;
			break;
		}
	printf("%d\n",ans);
	return 0;
}
### Prompt

Create a solution in cpp for the following problem:

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`.

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.

Examples

Input

abc


Output

3


Input

abbac


Output

65


Input

babacabac


Output

6310


Input

ababacbcacbacacbcbbcbbacbaccacbacbacba


Output

148010497

### Response

```cpp
#include<iostream>
#include<algorithm>
#include<cstdio>
#include<cstdlib>
#include<cstring>
using namespace std;

const int maxn=2e5+10,mod=998244353;
int n,mod3,dp[maxn][3][3][2],ans=1;
char s[maxn];

inline bool allthesame(){
	for(int i=2;i<=n;++i)
		if(s[i]!=s[1])
			return false;
	return true;
}

int main(){
	cin>>(s+1);
	n=strlen(s+1);
	for(int i=1;i<=n;++i)
		s[i]-='0';
	if(allthesame()){
		puts("1");
		return 0;
	}
	if(n<=3){
		if(n==2)
			puts("2");
		else if(s[1]==s[3])
			puts("7");
		else if(s[1]==s[2]||s[2]==s[3])
			puts("6");
		else
			puts("3");
		return 0;
	}
	for(int i=1;i<=n;++i)
		(mod3+=s[i])%=3;
	dp[1][0][0][0]=dp[1][1][1][0]=dp[1][2][2][0]=1;
	for(int i=1;i<n;++i)
		for(int j=0;j<3;++j)
			for(int k=0;k<3;++k)
				for(int l=0;l<2;++l)
					for(int x=0;x<3;++x)
						(dp[i+1][x][(x+k)%3][l||x==j]+=dp[i][j][k][l])%=mod;
	for(int i=0;i<3;++i)
		(ans+=dp[n][i][mod3][1])%=mod;
	for(int i=1;i<n;++i)
		if(s[i]==s[i+1]){
			ans=(ans+mod-1)%mod;
			break;
		}
	printf("%d\n",ans);
	return 0;
}
```