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():
    MOD = 998244353

    A, B, H, W = map(int, input().split())

    dp = [[0] * (W + 1) for _ in range(H + 1)]
    dp[A][B] = 1

    for h in range(A, H + 1):
        for w in range(B, W + 1):
            if h == A and w == B: continue
            t = 0
            if h > A:
                t += dp[h - 1][w] * w
            if w > B:
                t += dp[h][w - 1] * h
            if h > A and w > B:
                t -= dp[h - 1][w - 1] * (h - 1) * (w - 1)
            dp[h][w] = t % MOD

    print(dp[H][W])


if __name__ == '__main__':
    main()