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;
 
long long mod = 998244353;
long long A,B,C,D;
long long dp[3030][3030];
 
int main(){
  cin >> A >> B >> C >> D;
  dp[A][B] = 1;
  for (long long i = A; i <= C; i++){
    for (long long j = B; j <= D; j++){
      if ((i > A)||(j > B)){
        dp[i][j]=
          (i * dp[i][j-1] % mod
          + j * dp[i-1][j] % mod
          - (i - 1) * (j - 1) * dp[i-1][j-1] % mod + mod) % mod;
      }
    }
  }
  cout << dp[C][D];
}