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>

const int N = 3005, djq = 998244353;

int A, B, C, D, f[N][N], g[N][N];

int main()
{
	std::cin >> 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] = (1ll * f[i - 1][j] * j + g[i - 1][j]) % djq;
			g[i][j] = 1ll * (f[i][j - 1] + g[i][j - 1]) * i % djq;
		}
	return std::cout << (f[C][D] + g[C][D]) % djq << std::endl, 0;
}