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:
#!/usr/bin/env python3
import sys
sys.setrecursionlimit(10**8)
from functools import lru_cache
INF = float("inf")

MOD = 998244353  # type: int


def main():
    A, B, C, D = map(int, input().split())
    DP = [[1]*(D-B+1) for _ in range(C-A+1)]

    for i in range(C-A+1):
        for j in range(D-B+1):
            if i == j == 0:
                continue
            DP[i][j] = 0
            if 0 <= i-1:
                DP[i][j] += (DP[i-1][j]*(j+B)) % MOD
                DP[i][j] %= MOD
            if 0 <= j-1:
                DP[i][j] += (DP[i][j-1]*(i+A)) % MOD
                DP[i][j] %= MOD
            if 0 <= i-1 and 0 <= j-1:
                DP[i][j] -= (DP[i-1][j-1]*(i+A-1)*(j+B-1)) % MOD
                DP[i][j] %= MOD
            # print(i, j, DP[i][j])
    print(DP[-1][-1] % MOD)
    # print(DP)

    # @lru_cache(maxsize=None)
    # def f(a, b):
    #     if a < A or b < B:
    #         return 0
    #     if a == A and b == B:
    #         return 1
    #     elif a == A:
    #         return pow(A, b-B, MOD)
    #     elif b == B:
    #         return pow(B, a-A, MOD)
    #     ans = (f(a-1, b)*b) % MOD
    #     ans += (f(a, b-1)*a) % MOD
    #     ans -= (f(a-1, b-1)*(a-1)*(b-1)) % MOD
    #     ans %= MOD
    #     return ans

    # print(f(C, D))

    return


if __name__ == '__main__':
    main()