#include <bits/stdc++.h>
using namespace std;
const int MAXN=2e6+7;
#define mo 998244353
char s[MAXN];
int f[MAXN][3][3][2],n,ans;
inline bool check_all()
{
	for(int i=1;i<=n-1;i++)
		if(s[i]!=s[i+1]) return 0;
	return 1;
}
inline bool check_same()
{
	for(int i=1;i<=n-1;i++)
		if(s[i]==s[i+1]) return 0;
	return 1;
}
int main()
{
	scanf("%s",s+1);
	n=strlen(s+1);
	if(check_all()) {
		cout<<1;
		return 0;
	}
	if(n<=3){
		if(n==2) cout<<2;
		else if(s[1]!=s[2]&&s[2]!=s[3]&&s[1]!=s[3]) cout<<3;
		else if(s[1]==s[3]) cout<<7;
		else cout<<6;
		return 0;
	}
	int tot=0;
	for(int i=1;i<=n;i++)
		tot+=s[i]-'a';
	tot%=3;
	f[1][1][1][0]=f[1][2][2][0]=f[1][0][0][0]=1;
	for(int i=2;i<=n;i++)
		for(int j=0;j<=2;j++)
			for(int k=0;k<=2;k++)
				for(int p=0;p<=2;p++){
					int last=(j-k+3)%3;
					(f[i][j][k][1]+=f[i-1][last][p][1])%=mo;
					if(k==p) (f[i][j][k][1]+=f[i-1][last][p][0])%=mo;
					else (f[i][j][k][0]+=f[i-1][last][p][0])%=mo;
				}
	for(int i=0;i<=2;i++)
		(ans+=f[n][tot][i][1])%=mo;
	cout<<ans+check_same();
}
### Prompt

Develop a solution in cpp to the problem described below:

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 <bits/stdc++.h>
using namespace std;
const int MAXN=2e6+7;
#define mo 998244353
char s[MAXN];
int f[MAXN][3][3][2],n,ans;
inline bool check_all()
{
	for(int i=1;i<=n-1;i++)
		if(s[i]!=s[i+1]) return 0;
	return 1;
}
inline bool check_same()
{
	for(int i=1;i<=n-1;i++)
		if(s[i]==s[i+1]) return 0;
	return 1;
}
int main()
{
	scanf("%s",s+1);
	n=strlen(s+1);
	if(check_all()) {
		cout<<1;
		return 0;
	}
	if(n<=3){
		if(n==2) cout<<2;
		else if(s[1]!=s[2]&&s[2]!=s[3]&&s[1]!=s[3]) cout<<3;
		else if(s[1]==s[3]) cout<<7;
		else cout<<6;
		return 0;
	}
	int tot=0;
	for(int i=1;i<=n;i++)
		tot+=s[i]-'a';
	tot%=3;
	f[1][1][1][0]=f[1][2][2][0]=f[1][0][0][0]=1;
	for(int i=2;i<=n;i++)
		for(int j=0;j<=2;j++)
			for(int k=0;k<=2;k++)
				for(int p=0;p<=2;p++){
					int last=(j-k+3)%3;
					(f[i][j][k][1]+=f[i-1][last][p][1])%=mo;
					if(k==p) (f[i][j][k][1]+=f[i-1][last][p][0])%=mo;
					else (f[i][j][k][0]+=f[i-1][last][p][0])%=mo;
				}
	for(int i=0;i<=2;i++)
		(ans+=f[n][tot][i][1])%=mo;
	cout<<ans+check_same();
}
```