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():
    mod=998244353
    a,b,c,d=map(int,input().split())
    dx,dy=c-a,d-b
    if dx==0:
        return pow(a,dy,mod)
    if dy==0:
        return pow(b,dx,mod)
    DP=[[0]*(d+1) for _ in range(c+1)]
    DP[a][b]=1
    for x in range(a+1,c+1):
        DP[x][b]=pow(b,x-a,mod)
    for y in range(b+1,d+1):
        DP[a][y]=pow(a,y-b,mod)
    #print(DP)
    for x in range(a+1,c+1):
        for y in range(b+1,d+1):
            DP[x][y]=DP[x-1][y]*y+DP[x][y-1]*x
            DP[x][y]-=DP[x-1][y-1]*(x-1)*(y-1)
            DP[x][y]%=mod
    #print(DP)
    return DP[-1][-1]

if __name__=='__main__':
    print(main())