#include<bits/stdc++.h>
using namespace std;

typedef long long LL;
const int maxn = 2e3 + 1;
const LL mod = 998244353;

char x[maxn], y[maxn];
LL dp[maxn][maxn][2][2][2]; // 0 x, 1 y,

int main(){
    LL ans = 0;
    cin >> (x + 1) >> (y + 1);
    x[0] = y[0] = '?';
    for(int i = 0; x[i]; i++){
        for(int j = 0; y[j]; j++){
            if(i) dp[i][j][0][1][0]++;
            if(j) dp[i][j][1][0][1]++;
            if(i && x[i] != x[i - 1]){
                for(int k = 0; k < 2; k++){
                    dp[i][j][0][1][k] += dp[i - 1][j][0][1][k];
                }
            }
            if(j && y[j] != y[j - 1]){
                for(int k = 0; k < 2; k++){
                    dp[i][j][1][k][1] += dp[i][j - 1][1][k][1];
                }
            }

            if(i && j && x[i] != y[j]){
                dp[i][j][0][1][1] += dp[i - 1][j][1][1][1] + dp[i - 1][j][1][0][1];
                dp[i][j][1][1][1] += dp[i][j - 1][0][1][1] + dp[i][j - 1][0][1][0];
            }
            for(int a = 0; a < 2; a++)
                for(int b = 0; b < 2; b++)
                    for(int c = 0; c < 2; c++)
                        dp[i][j][a][b][c] %= mod;
            ans = (ans + dp[i][j][0][1][1] + dp[i][j][1][1][1]) % mod;
            ans %= mod;
        }
    }
    cout << ans << endl;
}
/*
 2
5 2
1000 2
 */
### Prompt

In cpp, your task is to solve the following problem:

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>
using namespace std;

typedef long long LL;
const int maxn = 2e3 + 1;
const LL mod = 998244353;

char x[maxn], y[maxn];
LL dp[maxn][maxn][2][2][2]; // 0 x, 1 y,

int main(){
    LL ans = 0;
    cin >> (x + 1) >> (y + 1);
    x[0] = y[0] = '?';
    for(int i = 0; x[i]; i++){
        for(int j = 0; y[j]; j++){
            if(i) dp[i][j][0][1][0]++;
            if(j) dp[i][j][1][0][1]++;
            if(i && x[i] != x[i - 1]){
                for(int k = 0; k < 2; k++){
                    dp[i][j][0][1][k] += dp[i - 1][j][0][1][k];
                }
            }
            if(j && y[j] != y[j - 1]){
                for(int k = 0; k < 2; k++){
                    dp[i][j][1][k][1] += dp[i][j - 1][1][k][1];
                }
            }

            if(i && j && x[i] != y[j]){
                dp[i][j][0][1][1] += dp[i - 1][j][1][1][1] + dp[i - 1][j][1][0][1];
                dp[i][j][1][1][1] += dp[i][j - 1][0][1][1] + dp[i][j - 1][0][1][0];
            }
            for(int a = 0; a < 2; a++)
                for(int b = 0; b < 2; b++)
                    for(int c = 0; c < 2; c++)
                        dp[i][j][a][b][c] %= mod;
            ans = (ans + dp[i][j][0][1][1] + dp[i][j][1][1][1]) % mod;
            ans %= mod;
        }
    }
    cout << ans << endl;
}
/*
 2
5 2
1000 2
 */
```