#include <bits/stdc++.h>
#pragma GCC optimize("Ofast")  
#pragma GCC target("avx,avx2,fma")
 
#define f(i,a,b) for(ll  i = a; i < (ll) b ; i++ ) 
#define af(i,a,b) for(ll i = a; i >= (ll) b ; i--)
#define rep(i,a,b,k) for(ll  i = a; i < (ll) b ; i+= k )
#define arep(i,a,b,k) for(ll i = a; i >= (ll) b ; i-= k)
#define ff first
#define ss second
#define pb push_back
#define mp make_pair
#define all(a) a.begin(), a.end()
#define sz(a) (ll) a.size()
#define sor(a) sort( a.begin(), a.end() )
#define fastio ios_base::sync_with_stdio(false);cin.tie(NULL)
#define ller   ios::sync_with_stdio(false);cin.tie(0)
 
// policy-based
 
 
 
 
using namespace std;
 
typedef long long ll; // ll or ll
typedef long double ld;
typedef pair<ll,ll> ii ;
typedef vector<ll>  vi ;
typedef vector<ii> vii ;

const ll MAX = 1e3 + 20;
const ll MAXI = 2e7 + 1;
const ll mod = 998244353;
const ll inf = 1e9;


ll dp[MAX][MAX][2],ans = 0;


int main(){ 
	fastio;
	ll n,m;
	string x,y;
	cin >> x >> y;
	n = x.size(),m = y.size();
	x = '%' + x, y = '*' + y;

	f(i,0,n+1){
		f(j,0,m+1){
			if(i == 0 && j ==  0){
				dp[i][j][0] = dp[i][j][1] = 0;
				continue;
			}
			if(i == 0){
				dp[i][j][1] = 1;
				if(y[j] != y[j-1])
					dp[i][j][1] += dp[i][j-1][1];
				continue;
			}
			if(j == 0){
				dp[i][j][0] = 1;
				if(x[i] != x[i-1])
					dp[i][j][0] += dp[i-1][j][0];
				continue;
			}
			
			if(i > 1 && x[i] != x[i-1] ){
				dp[i][j][0] += dp[i-1][j][0];
			}
			if(x[i] != y[j] ){
				dp[i][j][0] += dp[i-1][j][1];
				if(i > 1) dp[i][j][0] += dp[0][j][1];
			}
			if(j > 1 && y[j] != y[j-1] ){
				dp[i][j][1] += dp[i][j-1][1];
			}
			if(y[j] != x[i] ){
				dp[i][j][1] += dp[i][j-1][0];
				if(j > 1) dp[i][j][1] += dp[i][0][0];
			}
			f(k,0,2) dp[i][j][k] %= mod;
			
			if(i > 0 && j > 0) ans +=  (dp[i][j][0] + dp[i][j][1])  ;
			ans %= mod;
			
		}
	}
	
	cout << ans << endl;
	return 0;
}
### 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>
#pragma GCC optimize("Ofast")  
#pragma GCC target("avx,avx2,fma")
 
#define f(i,a,b) for(ll  i = a; i < (ll) b ; i++ ) 
#define af(i,a,b) for(ll i = a; i >= (ll) b ; i--)
#define rep(i,a,b,k) for(ll  i = a; i < (ll) b ; i+= k )
#define arep(i,a,b,k) for(ll i = a; i >= (ll) b ; i-= k)
#define ff first
#define ss second
#define pb push_back
#define mp make_pair
#define all(a) a.begin(), a.end()
#define sz(a) (ll) a.size()
#define sor(a) sort( a.begin(), a.end() )
#define fastio ios_base::sync_with_stdio(false);cin.tie(NULL)
#define ller   ios::sync_with_stdio(false);cin.tie(0)
 
// policy-based
 
 
 
 
using namespace std;
 
typedef long long ll; // ll or ll
typedef long double ld;
typedef pair<ll,ll> ii ;
typedef vector<ll>  vi ;
typedef vector<ii> vii ;

const ll MAX = 1e3 + 20;
const ll MAXI = 2e7 + 1;
const ll mod = 998244353;
const ll inf = 1e9;


ll dp[MAX][MAX][2],ans = 0;


int main(){ 
	fastio;
	ll n,m;
	string x,y;
	cin >> x >> y;
	n = x.size(),m = y.size();
	x = '%' + x, y = '*' + y;

	f(i,0,n+1){
		f(j,0,m+1){
			if(i == 0 && j ==  0){
				dp[i][j][0] = dp[i][j][1] = 0;
				continue;
			}
			if(i == 0){
				dp[i][j][1] = 1;
				if(y[j] != y[j-1])
					dp[i][j][1] += dp[i][j-1][1];
				continue;
			}
			if(j == 0){
				dp[i][j][0] = 1;
				if(x[i] != x[i-1])
					dp[i][j][0] += dp[i-1][j][0];
				continue;
			}
			
			if(i > 1 && x[i] != x[i-1] ){
				dp[i][j][0] += dp[i-1][j][0];
			}
			if(x[i] != y[j] ){
				dp[i][j][0] += dp[i-1][j][1];
				if(i > 1) dp[i][j][0] += dp[0][j][1];
			}
			if(j > 1 && y[j] != y[j-1] ){
				dp[i][j][1] += dp[i][j-1][1];
			}
			if(y[j] != x[i] ){
				dp[i][j][1] += dp[i][j-1][0];
				if(j > 1) dp[i][j][1] += dp[i][0][0];
			}
			f(k,0,2) dp[i][j][k] %= mod;
			
			if(i > 0 && j > 0) ans +=  (dp[i][j][0] + dp[i][j][1])  ;
			ans %= mod;
			
		}
	}
	
	cout << ans << endl;
	return 0;
}
```