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 = list(map(int, input().split()))
    mod = 998244353
    u = [0] * (D + 1)
    v = [0] * (D + 1)
    u[B] = 1
    for b in range(B + 1, D + 1):
        u[b] = u[b - 1] * A
    for a in range(A + 1, C + 1):
        v[B] = u[B] * B % mod
        for b in range(B + 1, D + 1):
            v[b] = (u[b] * b + v[b - 1] * a - u[b - 1] * (a - 1) * (b - 1)) % mod
        u, v = v, u

    return u[D]

print(main())