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():
    import sys
    input = sys.stdin.readline
    mod = 998244353
    A, B, C, D = map(int, input().split())
    dp = [[1] * (D+1) for _ in range(C+1)]
    a = A
    for i, w in enumerate(range(B+1, D+1)):
        dp[A][w] = a
        a *= A
        a %= mod
    b = B
    for i, h in enumerate(range(A+1, C+1)):
        dp[h][B] = b
        b *= B
        b %= mod
    for h in range(A+1, C+1):
        for w in range(B+1, D+1):
            dp[h][w] = (dp[h-1][w]*w%mod + dp[h][w-1]*h%mod - dp[h-1][w-1]*(h-1)*(w-1)%mod) % mod
    print(dp[C][D])

if __name__ == '__main__':
    main()