#include<bits/stdc++.h>
#define ll long long
#define pii pair<int, int>
#define st first
#define nd second
#define turbo ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define pb push_back
#define vi vector<int>
#define vvi vector<vi>
#define qi queue<int>
#define ld long double

using namespace std;

/*---------------------------------------------------------///CODE///---------------------------------------------------------*/

const int N = 1e3;
const int MOD = 998244353;
ll dp[N + 10][N + 10][2][2][2];

int add(int a, int b)
{
    int res = (a + b) % MOD;
    res = (res + MOD) % MOD;
    return res;
}
int main()
{
    turbo

    string a, b; cin >> a >> b;

    ll res = 0;

    for(int i = 0; i <= a.size(); i++)
        for(int j = 0; j <= b.size(); j++)
        {
            if(i == 0 && j > 0) dp[0][j][1][0][1] = (j == 1 ? 1 : b[j - 2] != b[j - 1] ? add(dp[0][j - 1][1][0][1], 1) : 1);
            if(j == 0 && i > 0) dp[i][0][0][1][0] = (i == 1 ? 1 : a[i - 2] != a[i - 1] ? add(dp[i - 1][0][0][1][0], 1) : 1);
            if(i > 0 && j > 0)
            {
                if(i > 1 && a[i - 2] != a[i - 1]) dp[i][j][0][1][1] = dp[i - 1][j][0][1][1];
                if(b[j - 1] != a[i - 1]) dp[i][j][0][1][1] = add(add(dp[i - 1][j][1][1][1], dp[0][j][1][0][1]), dp[i][j][0][1][1]);
                if(j > 1 && b[j - 2] != b[j - 1]) dp[i][j][1][1][1] = dp[i][j - 1][1][1][1];
                if(a[i - 1] != b[j - 1]) dp[i][j][1][1][1] = add(add(dp[i][j - 1][0][1][1], dp[i][0][0][1][0]), dp[i][j][1][1][1]);
                res = add(add(dp[i][j][0][1][1], dp[i][j][1][1][1]), res);
            }
        }

    cout << res;

    return 0;
}
### Prompt

Create a solution in cpp for 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>
#define ll long long
#define pii pair<int, int>
#define st first
#define nd second
#define turbo ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define pb push_back
#define vi vector<int>
#define vvi vector<vi>
#define qi queue<int>
#define ld long double

using namespace std;

/*---------------------------------------------------------///CODE///---------------------------------------------------------*/

const int N = 1e3;
const int MOD = 998244353;
ll dp[N + 10][N + 10][2][2][2];

int add(int a, int b)
{
    int res = (a + b) % MOD;
    res = (res + MOD) % MOD;
    return res;
}
int main()
{
    turbo

    string a, b; cin >> a >> b;

    ll res = 0;

    for(int i = 0; i <= a.size(); i++)
        for(int j = 0; j <= b.size(); j++)
        {
            if(i == 0 && j > 0) dp[0][j][1][0][1] = (j == 1 ? 1 : b[j - 2] != b[j - 1] ? add(dp[0][j - 1][1][0][1], 1) : 1);
            if(j == 0 && i > 0) dp[i][0][0][1][0] = (i == 1 ? 1 : a[i - 2] != a[i - 1] ? add(dp[i - 1][0][0][1][0], 1) : 1);
            if(i > 0 && j > 0)
            {
                if(i > 1 && a[i - 2] != a[i - 1]) dp[i][j][0][1][1] = dp[i - 1][j][0][1][1];
                if(b[j - 1] != a[i - 1]) dp[i][j][0][1][1] = add(add(dp[i - 1][j][1][1][1], dp[0][j][1][0][1]), dp[i][j][0][1][1]);
                if(j > 1 && b[j - 2] != b[j - 1]) dp[i][j][1][1][1] = dp[i][j - 1][1][1][1];
                if(a[i - 1] != b[j - 1]) dp[i][j][1][1][1] = add(add(dp[i][j - 1][0][1][1], dp[i][0][0][1][0]), dp[i][j][1][1][1]);
                res = add(add(dp[i][j][0][1][1], dp[i][j][1][1][1]), res);
            }
        }

    cout << res;

    return 0;
}
```