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:
a,b,c,d=map(int,input().split())
mod=998244353
dp=[[1 for i in range(d-b+1)] for j in range(c-a+1)]
for i in range(c-a):
    dp[i+1][0]=dp[i][0]*b
    dp[i+1][0]%=mod
for i in range(d-b):
    dp[0][i+1]=dp[0][i]*a
    dp[0][i+1]%=mod
for i in range(c-a):
    for j in range(d-b):
        dp[i+1][j+1]=dp[i+1][j]*(a+i+1)+dp[i][j+1]*(b+j+1)-dp[i][j]*((b+j)*(a+i))
        dp[i+1][j+1]%=mod
print(dp[-1][-1])