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]*(D+2) for i in range(C+2)]
    dp[A][B] = 1
    for i in range(A, C+1):
        for j in range(B, D+1):
            ret = dp[i][j]
            if i-A == j-B == 1:
                ret -= (i-1)*(j-1)
            else:
                ret -= dp[i-1][j-1]*(j-1)*(i-1)
            ret %= mod
            dp[i][j] = ret
            dp[i+1][j] += ret * j
            dp[i][j+1] += ret * i

    print(dp[-2][-2])


main()