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;
const int mo = 998244353;
const int N = 3010;
long long f[N][N];
int main() {
    int a,b,c,d;
    scanf("%d%d%d%d", &a,&b,&c,&d);
    f[a][b] = 1;
    for(int i = a; i<=c; ++i) {
        for(int j = b; j<=d; ++j) {
            if(i==a&&j==b) continue;
            f[i][j] = (f[i-1][j]*j%mo+f[i][j-1]*i%mo)%mo;
            f[i][j] = (f[i][j]-(i-1)*(j-1)*f[i-1][j-1]%mo+mo)%mo;
        }
    }
    printf("%lld\n",f[c][d]);
    return 0;
}