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 dp[3005][3005];
const long long mod = 998244353;

int main()
{
	int a, b, c, d;
	cin >> a >> b >> c >> d;
	dp[a][b] = 1;
	for(int i = a; i <= c; i++){
		for(int j = b; j <= d; j++){
			if(a < i) dp[i][j] = (dp[i][j] + dp[i - 1][j] * j) % mod;
			if(b < j) dp[i][j] = (dp[i][j] + dp[i][j - 1] * i) % mod;
			if(a < i && b < j){
				dp[i][j] -= dp[i - 1][j - 1] * (i - 1) * (j - 1);
				dp[i][j] = ((dp[i][j] % mod) + mod) % mod;
			}
		}
	}
	cout << dp[c][d] << endl;
	return 0;
}