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:
# でつoO(YOU PLAY WITH THE CARDS YOU'RE DEALT..)
import sys
MOD = 998244353
def main(A, B, C, D):
    I, J = C - A, D - B
    dp = [[0] * (I + 1) for _ in range(I + J + 1)]
    dp[0][0] = 1
    for k in range(1, I + J + 1):
        for i in range(min(I, k) + 1):
            j = k - i
            v = dp[k - 1][i - 1] * (j + B) % MOD if i >= 1 else 0
            h = dp[k - 1][i] * (i + A) % MOD
            d = dp[k - 2][i - 1] * (i + A - 1) * (j + B - 1) if k >= 2 and i >= 1 else 0
            dp[k][i] = (v + h - d) % MOD
    print(dp[I + J][I])

if __name__ == '__main__':
    input = sys.stdin.readline
    A, B, C, D = map(int, input().split())
    main(A, B, C, D)