#include<iostream>
#include<string>
using namespace std;
#define For(i,l,r) for(int i=l;i<=r;i++)
#define P 998244353
#define MAXN 1001
int N,M,f[MAXN][MAXN][2],x[MAXN],y[MAXN],ans;string a,b;void upd(int &x,int y){x=(x+y)%P;}
int main()
{
	cin>>a>>b,N=a.length(),M=b.length(),a=" "+a,b=" "+b;For(i,1,N)x[i]=(a[i]!=a[i-1])*x[i-1]+1;For(i,1,M)y[i]=(b[i]!=b[i-1])*y[i-1]+1;
	For(i,1,N)For(j,1,M){if(a[i]!=a[i-1])upd(f[i][j][0],f[i-1][j][0]);if(b[j]!=b[j-1])upd(f[i][j][1],f[i][j-1][1]);if(a[i]!=b[j])upd(f[i][j][0],f[i-1][j][1]+y[j]),upd(f[i][j][1],f[i][j-1][0]+x[i]);}
	For(i,1,N)For(j,1,M)upd(ans,f[i][j][0]),upd(ans,f[i][j][1]);cout<<ans<<endl;return 0;
}
### Prompt

Construct a cpp code solution to the problem outlined:

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<iostream>
#include<string>
using namespace std;
#define For(i,l,r) for(int i=l;i<=r;i++)
#define P 998244353
#define MAXN 1001
int N,M,f[MAXN][MAXN][2],x[MAXN],y[MAXN],ans;string a,b;void upd(int &x,int y){x=(x+y)%P;}
int main()
{
	cin>>a>>b,N=a.length(),M=b.length(),a=" "+a,b=" "+b;For(i,1,N)x[i]=(a[i]!=a[i-1])*x[i-1]+1;For(i,1,M)y[i]=(b[i]!=b[i-1])*y[i-1]+1;
	For(i,1,N)For(j,1,M){if(a[i]!=a[i-1])upd(f[i][j][0],f[i-1][j][0]);if(b[j]!=b[j-1])upd(f[i][j][1],f[i][j-1][1]);if(a[i]!=b[j])upd(f[i][j][0],f[i-1][j][1]+y[j]),upd(f[i][j][1],f[i][j-1][0]+x[i]);}
	For(i,1,N)For(j,1,M)upd(ans,f[i][j][0]),upd(ans,f[i][j][1]);cout<<ans<<endl;return 0;
}
```