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 PYTHON3):

Solution:
def main():
	a,b,c,d=map(int,input().split())
	mod=998244353
	dp=[[0 for _ in range(d)]for _ in range(c)]
	dp[a-1][b-1]=1
	for i in range(a-1,c):
		for j in range(b-1,d):
			if i!=a-1:
				dp[i][j]+=dp[i-1][j]*(j+1)%mod
			if j!=b-1:
				dp[i][j]+=dp[i][j-1]*(i+1)%mod
			if i!=a-1 and j!=b-1:
				dp[i][j]-=dp[i-1][j-1]*i*j%mod
			dp[i][j]%=mod
	print(dp[-1][-1])

if __name__ == '__main__':
	main()