#include<bits/stdc++.h>
#define LL long long
using namespace std;
const int M=998244353;
int n,m;
string s1,s2;
bool vis[1001][1001][3][2][2];
int mem[1001][1001][3][2][2],sum;
int dp(int i,int j,int lst,bool b1,bool b2){
    if (vis[i][j][lst][b1][b2])return mem[i][j][lst][b1][b2];
    vis[i][j][lst][b1][b2]=1;
    LL ret=0;
    if (b1&&b2)ret++;
    if (i<n&&(lst==0||(lst==2&&s1[i]!=s2[j-1])||(lst==1&&s1[i]!=s1[i-1])))ret=(ret+dp(i+1,j,1,1,b2))%M;
    if (j<m&&(lst==0||(lst==1&&s2[j]!=s1[i-1])||(lst==2&&s2[j]!=s2[j-1])))ret=(ret+dp(i,j+1,2,b1,1))%M;
    return mem[i][j][lst][b1][b2]=ret;
}

int main(){
    cin>>s1>>s2;
    n=s1.size();
    m=s2.size();
    for (int i=0;i<n;i++)
        for (int j=0;j<m;j++)
            sum=(sum+dp(i,j,0,0,0))%M;
    cout<<sum<<endl;
    return 0;
}

### Prompt

Generate 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>
#define LL long long
using namespace std;
const int M=998244353;
int n,m;
string s1,s2;
bool vis[1001][1001][3][2][2];
int mem[1001][1001][3][2][2],sum;
int dp(int i,int j,int lst,bool b1,bool b2){
    if (vis[i][j][lst][b1][b2])return mem[i][j][lst][b1][b2];
    vis[i][j][lst][b1][b2]=1;
    LL ret=0;
    if (b1&&b2)ret++;
    if (i<n&&(lst==0||(lst==2&&s1[i]!=s2[j-1])||(lst==1&&s1[i]!=s1[i-1])))ret=(ret+dp(i+1,j,1,1,b2))%M;
    if (j<m&&(lst==0||(lst==1&&s2[j]!=s1[i-1])||(lst==2&&s2[j]!=s2[j-1])))ret=(ret+dp(i,j+1,2,b1,1))%M;
    return mem[i][j][lst][b1][b2]=ret;
}

int main(){
    cin>>s1>>s2;
    n=s1.size();
    m=s2.size();
    for (int i=0;i<n;i++)
        for (int j=0;j<m;j++)
            sum=(sum+dp(i,j,0,0,0))%M;
    cout<<sum<<endl;
    return 0;
}

```