#include <string>
#include <iostream>
using namespace std;
const int mod = 998244353;
int n, dp[200009][3][3]; string s;
int main() {
	cin >> s;
	n = s.size();
	dp[1][0][0] = dp[1][1][1] = dp[1][2][2] = 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 < 3; ++l) {
					if (j == l) continue;
					dp[i + 1][j][k] += dp[i][l][(k - j + 3) % 3];
					if (dp[i + 1][j][k] >= mod) dp[i + 1][j][k] -= mod;
				}
			}
		}
	}
	bool f = false, f2 = false;
	for (int i = 1; i < n; ++i) {
		if (s[i] != s[i - 1]) f = true;
		if (s[i] == s[i - 1]) f2 = true;
	}
	if (!f) cout << 1 << '\n';
	else if (s == "abc" || s == "acb" || s == "bac" || s == "bca" || s == "cab" || s == "cba") {
		cout << 3 << '\n';
	}
	else {
		int v = 0;
		for (int i = 0; i < n; ++i) {
			v = (v + (s[i] - 'a')) % 3;
		}
		int eli = 1;
		for (int i = 1; i < n; ++i) {
			eli = 3LL * eli % mod;
		}
		cout << (eli + mod - ((dp[n][0][v] + dp[n][1][v]) % mod + dp[n][2][v]) % mod + (f2 ? 0 : 1)) % mod << '\n';
	}
	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 <string>
#include <iostream>
using namespace std;
const int mod = 998244353;
int n, dp[200009][3][3]; string s;
int main() {
	cin >> s;
	n = s.size();
	dp[1][0][0] = dp[1][1][1] = dp[1][2][2] = 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 < 3; ++l) {
					if (j == l) continue;
					dp[i + 1][j][k] += dp[i][l][(k - j + 3) % 3];
					if (dp[i + 1][j][k] >= mod) dp[i + 1][j][k] -= mod;
				}
			}
		}
	}
	bool f = false, f2 = false;
	for (int i = 1; i < n; ++i) {
		if (s[i] != s[i - 1]) f = true;
		if (s[i] == s[i - 1]) f2 = true;
	}
	if (!f) cout << 1 << '\n';
	else if (s == "abc" || s == "acb" || s == "bac" || s == "bca" || s == "cab" || s == "cba") {
		cout << 3 << '\n';
	}
	else {
		int v = 0;
		for (int i = 0; i < n; ++i) {
			v = (v + (s[i] - 'a')) % 3;
		}
		int eli = 1;
		for (int i = 1; i < n; ++i) {
			eli = 3LL * eli % mod;
		}
		cout << (eli + mod - ((dp[n][0][v] + dp[n][1][v]) % mod + dp[n][2][v]) % mod + (f2 ? 0 : 1)) % mod << '\n';
	}
	return 0;
}
```