#include<bits/stdc++.h>
using namespace std;
#define lln long long int
#define pb push_back 
lln dp[1005][1005][2];
const lln mo=998244353;
int main(){ 
    string x,y;
    cin>>x>>y;
    
    int n1=x.size(),n2=y.size();
   
    int suf1[n1],suf2[n2];
    suf1[n1-1]=1;suf2[n2-1]=1;
   for(int i=n1-2;i>=0;i--){
       if(x[i]==x[i+1])suf1[i]=1;
       else suf1[i]=suf1[i+1]+1;
   }    
    int n=n1;
   for(int i=n2-2;i>=0;i--){
       if(y[i]==y[i+1])suf2[i]=1;
       else suf2[i]=suf2[i+1]+1;
       
   }int m=n2;/*
       vector<lln> suf1(n+1);
    suf1[n-1] = 1;
    for(int i=n-2;i>=0;i--){
    	int j;
    	for(j=i;j<n-1;j++){
    		if(x[j]==x[j+1]) break;
    	}
    	suf1[i] = j-i+1;
    }
 
    vector<lln> suf2(m+1);
    suf2[m-1] = 1;
    for(int i=m-2;i>=0;i--){
    	int j;
    	for(j=i;j<m-1;j++){
    		if(y[j]==y[j+1]) break;
    	}
    	suf2[i] = j-i+1;
    }*/
   lln ans=0;
 //for(int i=0;i<1005;i++)for(int j=0;j<1005;j++) dp[i][j][0]=dp[i][j][1]=0;
   for(int i=n-1;i>=0;i--){
       for(int j=m-1;j>=0;j--){
              		dp[i][j][0] = (x[i]!=x[i+1]?dp[i+1][j][0]:0) + (x[i]!=y[j]?(dp[i+1][j][1]+suf2[j]):0);
    		dp[i][j][0] %= mo;
    		dp[i][j][1] = (y[j]!=y[j+1]?dp[i][j+1][1]:0) + (x[i]!=y[j]?(dp[i][j+1][0]+suf1[i]):0) ;
    		dp[i][j][1] %= mo;
       }
   }
       for(int i=0;i<n;i++){
    	for(int j=0;j<m;j++){
    		ans = (ans+dp[i][j][0] + dp[i][j][1])%mo;
    	}
    }
   cout<<ans;
   
}
### Prompt

Your challenge is to write 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 lln long long int
#define pb push_back 
lln dp[1005][1005][2];
const lln mo=998244353;
int main(){ 
    string x,y;
    cin>>x>>y;
    
    int n1=x.size(),n2=y.size();
   
    int suf1[n1],suf2[n2];
    suf1[n1-1]=1;suf2[n2-1]=1;
   for(int i=n1-2;i>=0;i--){
       if(x[i]==x[i+1])suf1[i]=1;
       else suf1[i]=suf1[i+1]+1;
   }    
    int n=n1;
   for(int i=n2-2;i>=0;i--){
       if(y[i]==y[i+1])suf2[i]=1;
       else suf2[i]=suf2[i+1]+1;
       
   }int m=n2;/*
       vector<lln> suf1(n+1);
    suf1[n-1] = 1;
    for(int i=n-2;i>=0;i--){
    	int j;
    	for(j=i;j<n-1;j++){
    		if(x[j]==x[j+1]) break;
    	}
    	suf1[i] = j-i+1;
    }
 
    vector<lln> suf2(m+1);
    suf2[m-1] = 1;
    for(int i=m-2;i>=0;i--){
    	int j;
    	for(j=i;j<m-1;j++){
    		if(y[j]==y[j+1]) break;
    	}
    	suf2[i] = j-i+1;
    }*/
   lln ans=0;
 //for(int i=0;i<1005;i++)for(int j=0;j<1005;j++) dp[i][j][0]=dp[i][j][1]=0;
   for(int i=n-1;i>=0;i--){
       for(int j=m-1;j>=0;j--){
              		dp[i][j][0] = (x[i]!=x[i+1]?dp[i+1][j][0]:0) + (x[i]!=y[j]?(dp[i+1][j][1]+suf2[j]):0);
    		dp[i][j][0] %= mo;
    		dp[i][j][1] = (y[j]!=y[j+1]?dp[i][j+1][1]:0) + (x[i]!=y[j]?(dp[i][j+1][0]+suf1[i]):0) ;
    		dp[i][j][1] %= mo;
       }
   }
       for(int i=0;i<n;i++){
    	for(int j=0;j<m;j++){
    		ans = (ans+dp[i][j][0] + dp[i][j][1])%mo;
    	}
    }
   cout<<ans;
   
}
```