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.buffer.readline
sys.setrecursionlimit(10**7)
from collections import defaultdict
con = 998244353; INF = float("inf")

def getlist():
	return list(map(int, input().split()))

#処理内容
def main():
	A, B, C, D = getlist()
	DP = [[0] * (D + 1) for i in range(C + 1)]
	DP[A][B] = 1
	for i in range(B + 1, D + 1):
		DP[A][i] = (DP[A][i - 1] * A) % con

	for i in range(A + 1, C + 1):
		DP[i][B] = (DP[i - 1][B] * B) % con

	#DP
	for i in range(A + 1, C + 1):
		for j in range(B + 1, D + 1):
			DP[i][j] = (DP[i][j - 1] * i + DP[i - 1][j] * j - DP[i - 1][j - 1] * (i - 1) * (j - 1)) % con

	ans = DP[C][D]
	print(ans)

if __name__ == '__main__':
	main()