#include <bits/stdc++.h>
#define X first
#define Y second

using namespace std;
typedef long long llint;

const int maxn = 1005;
const int base = 31337;
const int mod = 998244353;
const int inf = 0x3f3f3f3f;
const int logo = 20;
const int off = 1 << logo;
const int treesiz = off << 1;

int n, m;
char a[maxn], b[maxn];
int dp[maxn][maxn][2][2][2];

int f(int x, int y, int wh, bool flag1, bool flag2) {
	int &ret = dp[x][y][wh][flag1][flag2];
	if (ret != -1) return ret;
	
	ret = (flag1 && flag2);
	char las;
	if (wh == 0) las = a[x - 1];
	else las = b[y - 1];
	
	if (x < n && a[x] != las) ret += f(x + 1, y, 0, true, flag2), ret %= mod;
	if (y < m && b[y] != las) ret += f(x, y + 1, 1, flag1, true), ret %= mod;
	return ret;
}

int main() {
	scanf("%s%s", a, b);
	n = strlen(a);
	m = strlen(b);
	
	memset(dp, -1, sizeof dp);
	int sol = 0;
	for (int i = 0; i < n; i++) {
		for (int j = 0; j < m; j++) {
			sol += f(i + 1, j, 0, true, false);
			sol %= mod;
		}
	}
	for (int i = 0; i < n; i++) {
		for (int j = 0; j < m; j++) {
			sol += f(i, j + 1, 1, false, true);
			sol %= mod;
		}
	}
	printf("%d\n", sol);
	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 X first
#define Y second

using namespace std;
typedef long long llint;

const int maxn = 1005;
const int base = 31337;
const int mod = 998244353;
const int inf = 0x3f3f3f3f;
const int logo = 20;
const int off = 1 << logo;
const int treesiz = off << 1;

int n, m;
char a[maxn], b[maxn];
int dp[maxn][maxn][2][2][2];

int f(int x, int y, int wh, bool flag1, bool flag2) {
	int &ret = dp[x][y][wh][flag1][flag2];
	if (ret != -1) return ret;
	
	ret = (flag1 && flag2);
	char las;
	if (wh == 0) las = a[x - 1];
	else las = b[y - 1];
	
	if (x < n && a[x] != las) ret += f(x + 1, y, 0, true, flag2), ret %= mod;
	if (y < m && b[y] != las) ret += f(x, y + 1, 1, flag1, true), ret %= mod;
	return ret;
}

int main() {
	scanf("%s%s", a, b);
	n = strlen(a);
	m = strlen(b);
	
	memset(dp, -1, sizeof dp);
	int sol = 0;
	for (int i = 0; i < n; i++) {
		for (int j = 0; j < m; j++) {
			sol += f(i + 1, j, 0, true, false);
			sol %= mod;
		}
	}
	for (int i = 0; i < n; i++) {
		for (int j = 0; j < m; j++) {
			sol += f(i, j + 1, 1, false, true);
			sol %= mod;
		}
	}
	printf("%d\n", sol);
	return 0;
}

```