Problem: We have a grid with A horizontal rows and B vertical columns, with the squares painted white. On this grid, we will repeatedly apply the following operation:

* Assume that the grid currently has a horizontal rows and b vertical columns. Choose "vertical" or "horizontal".
* If we choose "vertical", insert one row at the top of the grid, resulting in an (a+1) \times b grid.
* If we choose "horizontal", insert one column at the right end of the grid, resulting in an a \times (b+1) grid.
* Then, paint one of the added squares black, and the other squares white.



Assume the grid eventually has C horizontal rows and D vertical columns. Find the number of ways in which the squares can be painted in the end, modulo 998244353.

Constraints

* 1 \leq A \leq C \leq 3000
* 1 \leq B \leq D \leq 3000
* A, B, C, and D are integers.

Input

Input is given from Standard Input in the following format:


A B C D


Output

Print the number of ways in which the squares can be painted in the end, modulo 998244353.

Examples

Input

1 1 2 2


Output

3


Input

2 1 3 4


Output

65


Input

31 41 59 265


Output

387222020

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
#define ll long long

int main() {
    ll A, B, C, D;
    cin >> A >> B >> C >> D;
    ll mod = 998244353;
    
    vector<vector<ll>> dp(C+1, vector<ll>(D+1, 0));
    dp[A][B] = 1;
    for (ll i = A; i <= C; i++) {
        for (ll j = B; j <= D; j++) {
            if (i == A && j == B) continue;
            dp[i][j] = (dp[i][j-1]*i + dp[i-1][j]*j - dp[i-1][j-1]*(i-1)*(j-1)%mod + mod) % mod;
            //cout << i << " " << j << " " << dp[i][j] << endl;
        }
    }
    cout << dp[C][D] << endl;
    return 0;
}