#include <bits/stdc++.h>
#define ll long long
#define pb push_back
#define mem(x, y) memset(& x, y, sizeof(x))
#define all(x) begin(x), end(x)
#define SZ(x) (int)(x).size()
using namespace std;

const int n0=1003,mod=998244353;
int bp(int x,int y) {
	int res=1;
	while(y) {
		if(y&1) res=(ll)res*x%mod;
		x=(ll)x*x%mod;
		y/=2;
	}
	return res;
}
struct mint {
	int x;
	mint(int _x=0) {
		x=_x;
	}
	void operator += (mint a) {
		x+=a.x;
		if(x>=mod) x-=mod;
	}
	void operator -= (mint a) {
		x-=a.x;
		if(x<0) x+=mod;
	}
	void operator *= (mint a) {
		x=(ll)x*a.x%mod;
	}
	void operator /= (mint a) {
		x=(ll)x*bp(a.x,mod-2)%mod;
	}
	mint operator + (mint a) {
		mint res=*this;
		res+=a;
		return res;
	}
	mint operator - (mint a) {
		mint res=*this;
		res-=a;
		return res;
	}
	mint operator * (mint a) {
		mint res=*this;
		res*=a;
		return res;
	}
	mint operator / (mint a) {
		mint res=*this;
		res/=a;
		return res;
	}
};
int n,m;
mint dp[n0][n0][2];
string a,b;

int main() {
	ios_base::sync_with_stdio(0), cin.tie(0);
	cin >> a >> b;
	n=SZ(a),m=SZ(b);
	mint ans=0;
	for(int i=0; i<=n; i++) {
		for(int j=0; j<=m; j++) {
			if(i) {
				dp[i][j][0]=1;
				if(i-2<0 || a[i-1]!=a[i-2]) {
					dp[i][j][0]+=dp[i-1][j][0];
				}
				if(j-1<0 || a[i-1]!=b[j-1]) {
					dp[i][j][0]+=dp[i-1][j][1];
				}
			}
			if(j) {
				dp[i][j][1]=1;
				if(j-2<0 || b[j-1]!=b[j-2]) {
					dp[i][j][1]+=dp[i][j-1][1];
				}
				if(i-1<0 || b[j-1]!=a[i-1]) {
					dp[i][j][1]+=dp[i][j-1][0];
				}
			}
			ans+=dp[i][j][0]+dp[i][j][1];
		}
	}
	for(int i=1; i<=n; i++) {
		for(int j=i; j<=n; j++) {
			if(j>i && a[j-1]==a[j-2]) break;
			ans-=m+1;
		}
	}
	for(int i=1; i<=m; i++) {
		for(int j=i; j<=m; j++) {
			if(j>i && b[j-1]==b[j-2]) break;
			ans-=n+1;
		}
	}
	cout << ans.x;
}

### Prompt

Please formulate 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
#define pb push_back
#define mem(x, y) memset(& x, y, sizeof(x))
#define all(x) begin(x), end(x)
#define SZ(x) (int)(x).size()
using namespace std;

const int n0=1003,mod=998244353;
int bp(int x,int y) {
	int res=1;
	while(y) {
		if(y&1) res=(ll)res*x%mod;
		x=(ll)x*x%mod;
		y/=2;
	}
	return res;
}
struct mint {
	int x;
	mint(int _x=0) {
		x=_x;
	}
	void operator += (mint a) {
		x+=a.x;
		if(x>=mod) x-=mod;
	}
	void operator -= (mint a) {
		x-=a.x;
		if(x<0) x+=mod;
	}
	void operator *= (mint a) {
		x=(ll)x*a.x%mod;
	}
	void operator /= (mint a) {
		x=(ll)x*bp(a.x,mod-2)%mod;
	}
	mint operator + (mint a) {
		mint res=*this;
		res+=a;
		return res;
	}
	mint operator - (mint a) {
		mint res=*this;
		res-=a;
		return res;
	}
	mint operator * (mint a) {
		mint res=*this;
		res*=a;
		return res;
	}
	mint operator / (mint a) {
		mint res=*this;
		res/=a;
		return res;
	}
};
int n,m;
mint dp[n0][n0][2];
string a,b;

int main() {
	ios_base::sync_with_stdio(0), cin.tie(0);
	cin >> a >> b;
	n=SZ(a),m=SZ(b);
	mint ans=0;
	for(int i=0; i<=n; i++) {
		for(int j=0; j<=m; j++) {
			if(i) {
				dp[i][j][0]=1;
				if(i-2<0 || a[i-1]!=a[i-2]) {
					dp[i][j][0]+=dp[i-1][j][0];
				}
				if(j-1<0 || a[i-1]!=b[j-1]) {
					dp[i][j][0]+=dp[i-1][j][1];
				}
			}
			if(j) {
				dp[i][j][1]=1;
				if(j-2<0 || b[j-1]!=b[j-2]) {
					dp[i][j][1]+=dp[i][j-1][1];
				}
				if(i-1<0 || b[j-1]!=a[i-1]) {
					dp[i][j][1]+=dp[i][j-1][0];
				}
			}
			ans+=dp[i][j][0]+dp[i][j][1];
		}
	}
	for(int i=1; i<=n; i++) {
		for(int j=i; j<=n; j++) {
			if(j>i && a[j-1]==a[j-2]) break;
			ans-=m+1;
		}
	}
	for(int i=1; i<=m; i++) {
		for(int j=i; j<=m; j++) {
			if(j>i && b[j-1]==b[j-2]) break;
			ans-=n+1;
		}
	}
	cout << ans.x;
}

```