#include <cstdio>
#include <cstring>
#include <algorithm>
#include <queue>
#include <vector>
using namespace std;
typedef long long ll;
const int maxn = 1e3 + 7;
const int mod = 998244353;
char s[maxn], t[maxn];
int dp[maxn][maxn][2];
int add(int a, int b) { return a + b >= mod ? a + b - mod : a + b; }
int sub(int a, int b) { return a >= b ? a - b : a - b + mod; }
int main()
{
    scanf("%s%s", s, t);
    int n = strlen(s), m = strlen(t);
    int ans = 0;
    for (int i = 0; i <= n; ++i) {
        for (int j = 0; j <= m; ++j) {
            if (i < n) dp[i + 1][j][0] = add(dp[i + 1][j][0], 1);
            if (j < m) dp[i][j + 1][1] = add(dp[i][j + 1][1], 1);
            if (i && i < n && s[i - 1] != s[i]) dp[i + 1][j][0] = add(dp[i + 1][j][0], dp[i][j][0]);
            if (j && i < n && t[j - 1] != s[i]) dp[i + 1][j][0] = add(dp[i + 1][j][0], dp[i][j][1]);
            if (i && j < m && s[i - 1] != t[j]) dp[i][j + 1][1] = add(dp[i][j + 1][1], dp[i][j][0]);
            if (j && j < m && t[j - 1] != t[j]) dp[i][j + 1][1] = add(dp[i][j + 1][1], dp[i][j][1]);
            ans = add(ans, dp[i][j][0]);
            ans = add(ans, dp[i][j][1]);
        }
    }
//    printf("%d\n", ans);
    for (int i = 0; i < n; ++i) {
        int j = i;
        while (j + 1 < n && s[j] != s[j + 1]) j++;
        int len = j - i + 1;
        ans = sub(ans, len * (len + 1) / 2 * (m + 1) % mod);
        i = j;
    }
    for (int i = 0; i < m; ++i) {
        int j = i;
        while (j + 1 < m && t[j] != t[j + 1]) j++;
        int len = j - i + 1;
        ans  = sub(ans, len * (len + 1) / 2 * (n + 1) % mod);
        i = j;
    }
    printf("%d\n", ans);
}

### 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 <cstdio>
#include <cstring>
#include <algorithm>
#include <queue>
#include <vector>
using namespace std;
typedef long long ll;
const int maxn = 1e3 + 7;
const int mod = 998244353;
char s[maxn], t[maxn];
int dp[maxn][maxn][2];
int add(int a, int b) { return a + b >= mod ? a + b - mod : a + b; }
int sub(int a, int b) { return a >= b ? a - b : a - b + mod; }
int main()
{
    scanf("%s%s", s, t);
    int n = strlen(s), m = strlen(t);
    int ans = 0;
    for (int i = 0; i <= n; ++i) {
        for (int j = 0; j <= m; ++j) {
            if (i < n) dp[i + 1][j][0] = add(dp[i + 1][j][0], 1);
            if (j < m) dp[i][j + 1][1] = add(dp[i][j + 1][1], 1);
            if (i && i < n && s[i - 1] != s[i]) dp[i + 1][j][0] = add(dp[i + 1][j][0], dp[i][j][0]);
            if (j && i < n && t[j - 1] != s[i]) dp[i + 1][j][0] = add(dp[i + 1][j][0], dp[i][j][1]);
            if (i && j < m && s[i - 1] != t[j]) dp[i][j + 1][1] = add(dp[i][j + 1][1], dp[i][j][0]);
            if (j && j < m && t[j - 1] != t[j]) dp[i][j + 1][1] = add(dp[i][j + 1][1], dp[i][j][1]);
            ans = add(ans, dp[i][j][0]);
            ans = add(ans, dp[i][j][1]);
        }
    }
//    printf("%d\n", ans);
    for (int i = 0; i < n; ++i) {
        int j = i;
        while (j + 1 < n && s[j] != s[j + 1]) j++;
        int len = j - i + 1;
        ans = sub(ans, len * (len + 1) / 2 * (m + 1) % mod);
        i = j;
    }
    for (int i = 0; i < m; ++i) {
        int j = i;
        while (j + 1 < m && t[j] != t[j + 1]) j++;
        int len = j - i + 1;
        ans  = sub(ans, len * (len + 1) / 2 * (n + 1) % mod);
        i = j;
    }
    printf("%d\n", ans);
}

```