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:
import sys
input = sys.stdin.readline
input = sys.stdin.buffer.readline


#sys.setrecursionlimit(10**9)
#from functools import lru_cache

def RD(): return sys.stdin.read()
def II(): return int(input())
def MI(): return map(int,input().split())
def MF(): return map(float,input().split())
def LI(): return list(map(int,input().split()))
def LF(): return list(map(float,input().split()))
def TI(): return tuple(map(int,input().split()))
# rstrip().decode()

#import numpy as np


def main():
	a,b,c,d=MI()
	dp=[[0]*(d+1) for _ in range(c+1)]
	dp[a][b]=1

	for i in range(a-1,c):
		for j in range(b-1,d):
			if i+1==a and j+1==b:
				continue
			#print(i,j)
			dp[i+1][j+1]=dp[i][j+1]*(j+1)+dp[i+1][j]*(i+1)-i*j*dp[i][j]
			dp[i+1][j+1]%=998244353

	print(dp[c][d])
















if __name__ == "__main__":
	main()