#include <bits/stdc++.h>
#define chk(c,v) (c?v:0)
using u32 = uint32_t;
const u32 mod = 998244353;
const u32 N = 1000 + 3;
char s[N], t[N];
template <typename T, T mod> class Zmod {
private:
  T v;

public:
  Zmod(T value = 0) : v((value % mod + mod) % mod) {}
  const T value() const { return this->v; }
  Zmod operator+(const Zmod &rhs) const { return Zmod(v + rhs.v); }
  Zmod operator-(const Zmod &rhs) const { return Zmod(v - rhs.v); }
  Zmod operator*(const Zmod &rhs) const { return Zmod(v * rhs.v); }
};
using Zp = Zmod<u32, mod>;
Zp f[N][N][2][4];

int main() {
  scanf("%s", s + 1);
  scanf("%s", t + 1);
  int n = strlen(s + 1), m = strlen(t + 1);

  Zp ans = 0;
  for (int i = 1; i <= n; i++) {
    f[i][0][0][0b01] = Zp(1) + chk(s[i - 1] != s[i], f[i - 1][0][0][0b01]);
  }
  for (int j = 1; j <= m; j++) {
    f[0][j][1][0b10] = Zp(1) + chk(t[j - 1] != t[j], f[0][j - 1][1][0b10]);
  }
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= m; j++) {
      // 0b01
      f[i][j][0][0b01] = Zp(1) + chk(s[i-1]!=s[i],f[i - 1][j][0][0b01]);
      // 0b10
      f[i][j][1][0b10] = Zp(1) + chk(t[j-1]!=t[j],f[i][j-1][1][0b10]);
      // 0b11
      f[i][j][0][0b11] = chk(s[i-1]!=s[i],f[i-1][j][0][0b11])+chk(t[j]!=s[i],f[i-1][j][1][0b10]+f[i-1][j][1][0b11]);
      f[i][j][1][0b11] = chk(t[j-1]!=t[j],f[i][j-1][1][0b11])+chk(s[i]!=t[j],f[i][j-1][0][0b01]+f[i][j-1][0][0b11]);

      ans = ans + f[i][j][0][0b11] + f[i][j][1][0b11];
    }
  }
  std::cout << ans.value() << std::endl;
  return 0;
}

### Prompt

Develop a solution in CPP to the problem described below:

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 chk(c,v) (c?v:0)
using u32 = uint32_t;
const u32 mod = 998244353;
const u32 N = 1000 + 3;
char s[N], t[N];
template <typename T, T mod> class Zmod {
private:
  T v;

public:
  Zmod(T value = 0) : v((value % mod + mod) % mod) {}
  const T value() const { return this->v; }
  Zmod operator+(const Zmod &rhs) const { return Zmod(v + rhs.v); }
  Zmod operator-(const Zmod &rhs) const { return Zmod(v - rhs.v); }
  Zmod operator*(const Zmod &rhs) const { return Zmod(v * rhs.v); }
};
using Zp = Zmod<u32, mod>;
Zp f[N][N][2][4];

int main() {
  scanf("%s", s + 1);
  scanf("%s", t + 1);
  int n = strlen(s + 1), m = strlen(t + 1);

  Zp ans = 0;
  for (int i = 1; i <= n; i++) {
    f[i][0][0][0b01] = Zp(1) + chk(s[i - 1] != s[i], f[i - 1][0][0][0b01]);
  }
  for (int j = 1; j <= m; j++) {
    f[0][j][1][0b10] = Zp(1) + chk(t[j - 1] != t[j], f[0][j - 1][1][0b10]);
  }
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= m; j++) {
      // 0b01
      f[i][j][0][0b01] = Zp(1) + chk(s[i-1]!=s[i],f[i - 1][j][0][0b01]);
      // 0b10
      f[i][j][1][0b10] = Zp(1) + chk(t[j-1]!=t[j],f[i][j-1][1][0b10]);
      // 0b11
      f[i][j][0][0b11] = chk(s[i-1]!=s[i],f[i-1][j][0][0b11])+chk(t[j]!=s[i],f[i-1][j][1][0b10]+f[i-1][j][1][0b11]);
      f[i][j][1][0b11] = chk(t[j-1]!=t[j],f[i][j-1][1][0b11])+chk(s[i]!=t[j],f[i][j-1][0][0b01]+f[i][j-1][0][0b11]);

      ans = ans + f[i][j][0][0b11] + f[i][j][1][0b11];
    }
  }
  std::cout << ans.value() << std::endl;
  return 0;
}

```