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:
MOD = 998244353

def solve(A,B,C,D):
    H,W = C-A, D-B
    dp = [[0]*(W+1) for _ in range(H+1)]

    t = 1
    for i in range(W+1):
        dp[0][i] = t
        t *= A
        t %= MOD

    for j in range(1,H+1):
        dp[j][0] = (dp[j-1][0]*B)%MOD

        for i in range(1,W+1):
            dp[j][i] = dp[j-1][i]*(B+i) + dp[j][i-1]*(A+j) - dp[j-1][i-1]*(B+i-1)*(A+j-1)
            dp[j][i] %= MOD

    return dp[-1][-1]


if __name__ == '__main__':
    print(solve(*map(int,input().split())))