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

#define vt vector

const int mod = 998244353;

void add(int &a, int b) {
    a += b;
    if (a >= mod) a -= mod;
}

void sub(int &a, int b) {
    a -= b;
    if (a < 0) a += mod;
}

void foo() {
    string s, t;
    cin >> s >> t;
    int n = s.length();
    int m = t.length();
    
    vt<vt<vt<vt<int>>>> dp(n + 1, vt<vt<vt<int>>>(m + 1, vt<vt<int>>(2, vt<int>(4))));
    int ans = 0;
    for (int i = 0; i <= n; i++) {
        for (int j = 0; j <= m; j++) {
            if (i) add(dp[i][j][0][1], 1);
            if (j) add(dp[i][j][1][2], 1);
            add(ans, dp[i][j][0][3]);
            add(ans, dp[i][j][1][3]);
            for (int mask = 0; mask < 4; mask++) {
                if (i < n && (i && s[i - 1] != s[i])) add(dp[i + 1][j][0][mask | 1], dp[i][j][0][mask]);
                if (i < n && (j && t[j - 1] != s[i])) add(dp[i + 1][j][0][mask | 1], dp[i][j][1][mask]);
                if (j < m && (i && s[i - 1] != t[j])) add(dp[i][j + 1][1][mask | 2], dp[i][j][0][mask]);
                if (j < m && (j && t[j - 1] != t[j])) add(dp[i][j + 1][1][mask | 2], dp[i][j][1][mask]);
            }
        }
    }
    
    cout << ans << endl;
}

int main() {
    ios::sync_with_stdio(0);
    cin.tie(0);
    foo();
}

### Prompt

Your task is to create a cpp solution to 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;

#define vt vector

const int mod = 998244353;

void add(int &a, int b) {
    a += b;
    if (a >= mod) a -= mod;
}

void sub(int &a, int b) {
    a -= b;
    if (a < 0) a += mod;
}

void foo() {
    string s, t;
    cin >> s >> t;
    int n = s.length();
    int m = t.length();
    
    vt<vt<vt<vt<int>>>> dp(n + 1, vt<vt<vt<int>>>(m + 1, vt<vt<int>>(2, vt<int>(4))));
    int ans = 0;
    for (int i = 0; i <= n; i++) {
        for (int j = 0; j <= m; j++) {
            if (i) add(dp[i][j][0][1], 1);
            if (j) add(dp[i][j][1][2], 1);
            add(ans, dp[i][j][0][3]);
            add(ans, dp[i][j][1][3]);
            for (int mask = 0; mask < 4; mask++) {
                if (i < n && (i && s[i - 1] != s[i])) add(dp[i + 1][j][0][mask | 1], dp[i][j][0][mask]);
                if (i < n && (j && t[j - 1] != s[i])) add(dp[i + 1][j][0][mask | 1], dp[i][j][1][mask]);
                if (j < m && (i && s[i - 1] != t[j])) add(dp[i][j + 1][1][mask | 2], dp[i][j][0][mask]);
                if (j < m && (j && t[j - 1] != t[j])) add(dp[i][j + 1][1][mask | 2], dp[i][j][1][mask]);
            }
        }
    }
    
    cout << ans << endl;
}

int main() {
    ios::sync_with_stdio(0);
    cin.tie(0);
    foo();
}

```