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:
Q = 998244353
#import sys
#input = sys.stdin.readline
def main():
    A, B, C, D = map( int, input().split())
    dp = [[0]*3002 for _ in range(3001)]
    dp[C][D] = 1
    for a in range(C-1,A-1,-1):
        dp[a][D] = dp[a+1][D]*D%Q
    for b in range(D-1,B-1,-1):
        dp[C][b] = dp[C][b+1]*C%Q
    for a in range(C-1,A-1,-1):
        z = dp[a+1][D]*a%Q
        for b in range(D-1,B-1,-1):
            dp[a][b] = (b*dp[a+1][b] + z)%Q
            z = (z + dp[a+1][b])*a%Q
    # for i in range(C+1):
    #     print(dp[i][:D+1])
    print(dp[A][B])
if __name__ == '__main__':
    main()