#include<bits/stdc++.h>
#define FOR(i,a,b) for(int i=(a),i##ss=(b);i<=i##ss;i++)
#define REP(i,a,b) for(int i=(a),i##ss=(b);i>=i##ss;i--)
#define deb(x) cerr<<(#x)<<":"<<(x)<<'\n'
#define pb push_back
#define fi first
#define se second
#define hvie '\n'
using namespace std;
typedef pair<int,int> pii;
typedef long long ll;
typedef unsigned long long ull;
typedef double db;
int yh(){
	int ret=0;bool f=0;char c=getchar();
	while(!isdigit(c)){if(c==EOF)return -1;if(c=='-')f=1;c=getchar();}
	while(isdigit(c))ret=(ret<<3)+(ret<<1)+(c^48),c=getchar();
	return f?-ret:ret;
}
const int maxn=1005,mod=998244353;
int dp[maxn][maxn][2][4];
void add(int &x,int y){x=(x+y)%mod;}
char s[maxn],t[maxn];
int main(){
	scanf("%s",s);
	scanf("%s",t);
	int n=strlen(s),m=strlen(t);
	int ans=0;
	FOR(i,0,n)FOR(j,0,m){
		if(i<n)add(dp[i+1][j][0][1],1);
		if(j<m)add(dp[i][j+1][1][2],1);
		FOR(mask,0,3){
			if(i&&i<n&&s[i]!=s[i-1]) add(dp[i+1][j][0][mask|1],dp[i][j][0][mask]);
			if(j&&i<n&&s[i]!=t[j-1]) add(dp[i+1][j][0][mask|1],dp[i][j][1][mask]);
			if(i&&j<m&&t[j]!=s[i-1]) add(dp[i][j+1][1][mask|2],dp[i][j][0][mask]);
			if(j&&j<m&&t[j]!=t[j-1]) add(dp[i][j+1][1][mask|2],dp[i][j][1][mask]);
		}
		add(ans,dp[i][j][0][3]);
		add(ans,dp[i][j][1][3]);
	}
	cout<<ans<<hvie;
	return 0;
}

### 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<bits/stdc++.h>
#define FOR(i,a,b) for(int i=(a),i##ss=(b);i<=i##ss;i++)
#define REP(i,a,b) for(int i=(a),i##ss=(b);i>=i##ss;i--)
#define deb(x) cerr<<(#x)<<":"<<(x)<<'\n'
#define pb push_back
#define fi first
#define se second
#define hvie '\n'
using namespace std;
typedef pair<int,int> pii;
typedef long long ll;
typedef unsigned long long ull;
typedef double db;
int yh(){
	int ret=0;bool f=0;char c=getchar();
	while(!isdigit(c)){if(c==EOF)return -1;if(c=='-')f=1;c=getchar();}
	while(isdigit(c))ret=(ret<<3)+(ret<<1)+(c^48),c=getchar();
	return f?-ret:ret;
}
const int maxn=1005,mod=998244353;
int dp[maxn][maxn][2][4];
void add(int &x,int y){x=(x+y)%mod;}
char s[maxn],t[maxn];
int main(){
	scanf("%s",s);
	scanf("%s",t);
	int n=strlen(s),m=strlen(t);
	int ans=0;
	FOR(i,0,n)FOR(j,0,m){
		if(i<n)add(dp[i+1][j][0][1],1);
		if(j<m)add(dp[i][j+1][1][2],1);
		FOR(mask,0,3){
			if(i&&i<n&&s[i]!=s[i-1]) add(dp[i+1][j][0][mask|1],dp[i][j][0][mask]);
			if(j&&i<n&&s[i]!=t[j-1]) add(dp[i+1][j][0][mask|1],dp[i][j][1][mask]);
			if(i&&j<m&&t[j]!=s[i-1]) add(dp[i][j+1][1][mask|2],dp[i][j][0][mask]);
			if(j&&j<m&&t[j]!=t[j-1]) add(dp[i][j+1][1][mask|2],dp[i][j][1][mask]);
		}
		add(ans,dp[i][j][0][3]);
		add(ans,dp[i][j][1][3]);
	}
	cout<<ans<<hvie;
	return 0;
}

```