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())
#print(d-b,c-a)
dp=[[1]*(d-b+1) for _ in range(c-a+1)]
mod=998244353 
for h in range(1,c-a+1):
    dp[h][0]=pow(b,h,mod)
for w in range(1,d-b+1):
    dp[0][w]=pow(a,w,mod)
for w in range(1,d-b+1):
    for h in range(1,c-a+1):
        #print(dp[h][w-1]*(h+b+1),dp[h-1][w]*(w+a+1),dp[h-1][w-1]*(h+b-1)*(w+a-1))
        dp[h][w]=dp[h][w-1]*(h+a)+dp[h-1][w]*(w+b)-dp[h-1][w-1]*(w+b-1)*(h+a-1)
        dp[h][w]%=mod
#print(*dp)
print(dp[c-a][d-b])