#include <bits/stdc++.h>

#define forn(i, n) for (int i = 0; i < int(n); i++)

using namespace std;

const int MOD = 998244353;

int add(int a, int b){
	a += b;
	if (a >= MOD)
		a -= MOD;
	if (a < 0)
		a += MOD;
	return a;
}

int main() {
	string s, t;
	cin >> s >> t;
	int n = s.size(), m = t.size();
	vector<vector<vector<vector<int>>>> dp(n + 1, vector<vector<vector<int>>>(m + 1, vector<vector<int>>(2, vector<int>(4, 0))));
	int ans = 0;
	forn(i, n + 1) forn(j, m + 1){
		if (i < n) dp[i + 1][j][0][1] = add(dp[i + 1][j][0][1], 1);
		if (j < m) dp[i][j + 1][1][2] = add(dp[i][j + 1][1][2], 1);
		forn(mask, 4){
			if (0 < i && i < n && s[i - 1] != s[i]) dp[i + 1][j][0][mask | 1] = add(dp[i + 1][j][0][mask | 1], dp[i][j][0][mask]);
			if (0 < j && i < n && t[j - 1] != s[i]) dp[i + 1][j][0][mask | 1] = add(dp[i + 1][j][0][mask | 1], dp[i][j][1][mask]);
			if (0 < i && j < m && s[i - 1] != t[j]) dp[i][j + 1][1][mask | 2] = add(dp[i][j + 1][1][mask | 2], dp[i][j][0][mask]);
			if (0 < j && j < m && t[j - 1] != t[j]) dp[i][j + 1][1][mask | 2] = add(dp[i][j + 1][1][mask | 2], dp[i][j][1][mask]);
		}
		ans = add(ans, dp[i][j][0][3]);
		ans = add(ans, dp[i][j][1][3]);
	}
	printf("%d\n", ans);
	return 0;
}
### Prompt

Construct a cpp code solution to the problem outlined:

You are given two strings x and y, both consist only of lowercase Latin letters. Let |s| be the length of string s.

Let's call a sequence a a merging sequence if it consists of exactly |x| zeros and exactly |y| ones in some order.

A merge z is produced from a sequence a by the following rules: 

  * if a_i=0, then remove a letter from the beginning of x and append it to the end of z; 
  * if a_i=1, then remove a letter from the beginning of y and append it to the end of z. 



Two merging sequences a and b are different if there is some position i such that a_i ≠ b_i.

Let's call a string z chaotic if for all i from 2 to |z| z_{i-1} ≠ z_i.

Let s[l,r] for some 1 ≤ l ≤ r ≤ |s| be a substring of consecutive letters of s, starting from position l and ending at position r inclusive.

Let f(l_1, r_1, l_2, r_2) be the number of different merging sequences of x[l_1,r_1] and y[l_2,r_2] that produce chaotic merges. Note that only non-empty substrings of x and y are considered.

Calculate ∑ _{1 ≤ l_1 ≤ r_1 ≤ |x| \\\ 1 ≤ l_2 ≤ r_2 ≤ |y|} f(l_1, r_1, l_2, r_2). Output the answer modulo 998 244 353.

Input

The first line contains a string x (1 ≤ |x| ≤ 1000).

The second line contains a string y (1 ≤ |y| ≤ 1000).

Both strings consist only of lowercase Latin letters.

Output

Print a single integer — the sum of f(l_1, r_1, l_2, r_2) over 1 ≤ l_1 ≤ r_1 ≤ |x| and 1 ≤ l_2 ≤ r_2 ≤ |y| modulo 998 244 353.

Examples

Input


aaa
bb


Output


24


Input


code
forces


Output


1574


Input


aaaaa
aaa


Output


0


Input


justamassivetesttocheck
howwellyouhandlemodulooperations


Output


667387032

Note

In the first example there are: 

  * 6 pairs of substrings "a" and "b", each with valid merging sequences "01" and "10"; 
  * 3 pairs of substrings "a" and "bb", each with a valid merging sequence "101"; 
  * 4 pairs of substrings "aa" and "b", each with a valid merging sequence "010"; 
  * 2 pairs of substrings "aa" and "bb", each with valid merging sequences "0101" and "1010"; 
  * 2 pairs of substrings "aaa" and "b", each with no valid merging sequences; 
  * 1 pair of substrings "aaa" and "bb" with a valid merging sequence "01010"; 



Thus, the answer is 6 ⋅ 2 + 3 ⋅ 1 + 4 ⋅ 1 + 2 ⋅ 2 + 2 ⋅ 0 + 1 ⋅ 1 = 24.

### Response

```cpp
#include <bits/stdc++.h>

#define forn(i, n) for (int i = 0; i < int(n); i++)

using namespace std;

const int MOD = 998244353;

int add(int a, int b){
	a += b;
	if (a >= MOD)
		a -= MOD;
	if (a < 0)
		a += MOD;
	return a;
}

int main() {
	string s, t;
	cin >> s >> t;
	int n = s.size(), m = t.size();
	vector<vector<vector<vector<int>>>> dp(n + 1, vector<vector<vector<int>>>(m + 1, vector<vector<int>>(2, vector<int>(4, 0))));
	int ans = 0;
	forn(i, n + 1) forn(j, m + 1){
		if (i < n) dp[i + 1][j][0][1] = add(dp[i + 1][j][0][1], 1);
		if (j < m) dp[i][j + 1][1][2] = add(dp[i][j + 1][1][2], 1);
		forn(mask, 4){
			if (0 < i && i < n && s[i - 1] != s[i]) dp[i + 1][j][0][mask | 1] = add(dp[i + 1][j][0][mask | 1], dp[i][j][0][mask]);
			if (0 < j && i < n && t[j - 1] != s[i]) dp[i + 1][j][0][mask | 1] = add(dp[i + 1][j][0][mask | 1], dp[i][j][1][mask]);
			if (0 < i && j < m && s[i - 1] != t[j]) dp[i][j + 1][1][mask | 2] = add(dp[i][j + 1][1][mask | 2], dp[i][j][0][mask]);
			if (0 < j && j < m && t[j - 1] != t[j]) dp[i][j + 1][1][mask | 2] = add(dp[i][j + 1][1][mask | 2], dp[i][j][1][mask]);
		}
		ans = add(ans, dp[i][j][0][3]);
		ans = add(ans, dp[i][j][1][3]);
	}
	printf("%d\n", ans);
	return 0;
}
```