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, c, d = map(int, input().split())
    dp = [[0]*(d+1) for _ in [0]*(c+1)]
    dp[a][b] = 1
    for i in range(a+b+1, c+d+1):
        for p in range(c, a-1, -1):
            q = i-p
            if q > d:
                break
            if q < 0:
                continue
            dp[p][q] = (q*dp[p-1][q]+p*dp[p][q-1] -
                        (p-1)*(q-1)*dp[p-1][q-1]) % mod
    print(dp[c][d])


main()