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 = [[0] * d for _ in range(c)]
dp[a-1][b-1] = 1

for i in range(c):
    for j in range(d):
        if i < a and j < b or i < a-1 or j < b-1:
            pass
        else:
            if i == 0:
                dp[i][j] = 1
            elif j == 0:
                dp[i][j] = 1
            else:
                dp[i][j] = dp[i-1][j] * (j+1) + dp[i][j-1] * (i+1) - dp[i-1][j-1] * i*j
        dp[i][j] %= mod

print(dp[-1][-1])