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:
import sys

readline = sys.stdin.readline
MOD = 10 ** 9 + 7
INF = float('INF')
sys.setrecursionlimit(10 ** 5)


def main():
    MOD = 998244353
    a, b, c, d = map(int, readline().split())
    h, w = c - a, d - b

    dp = [[1] * (d + 1) for _ in range(c + 1)]

    for row in range(a + 1, c + 1):
        dp[row][b] = (dp[row - 1][b] * b) % MOD

    for col in range(b + 1, d + 1):
        dp[a][col] = (dp[a][col - 1] * a) % MOD

    for row in range(a + 1, c + 1):
        for col in range(b + 1, d + 1):
            x = dp[row - 1][col] * col + dp[row][col - 1] * row
            y = dp[row - 1][col - 1] * (row - 1) * (col - 1)
            dp[row][col] = (x - y) % MOD

    print(dp[c][d])


if __name__ == '__main__':
    main()