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())

    c = C - A
    d = D - B
    mod = 998244353
    dp = [[0]*(d+1) for i in range(c+1)]
    dp[0][0] = 1

    for i in range(c+1):

        for j in range(d+1):
            ret = 0
            if i == 0 and j == 0:
                continue
            if i > 0 and j > 0:
                if i == j == 1:
                    ret -= (A+i-1) * (B+j-1)
                else:
                    ret -= dp[i-1][j-1]
                    ret *= (A+i-1)*(B+j-1)
            ret += dp[i-1][j]*(B+j) + dp[i][j-1]*(A+i)

            ret %= mod
            dp[i][j] = ret
    print(dp[c][d])


main()