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
sys.setrecursionlimit(10000000)
MOD = 998244353
INF = 10 ** 9

def main():
    A,B,C,D = map(int,input().split())
    dp = [[0]*(1+D) 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 == A - 1 and j == B - 1:
                continue
            dp[i + 1][j + 1] = (i + 1)*dp[i + 1][j] + (j + 1)*dp[i][j + 1] - dp[i][j] * i*j
            dp[i + 1][j + 1] %= MOD
    print(dp[C][D])
if __name__ == '__main__':
    main()