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:
from sys import stdin
# stdin = open('b_1.txt')

input = stdin.readline

MOD = 998244353
def main():
    A, B, C, D = map(int, input().rstrip().split())
    DP = [[0 for _ in range(D + 1)] for _ in range(C + 1)]
    for i in range(A, C + 1):
        for j in range(B, D + 1):
            if i == A and j == B:
                DP[i][j] = 1
                continue
            DP[i][j] = ((DP[i -1][j] * j) + (DP[i][j -1] * i) - (DP[i -1][j - 1] * (i - 1) * (j  - 1))) % MOD
    print(DP[C][D] % MOD)

if __name__ == "__main__":
    main()