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 = [int(_) for _ in input().split()]
mod = 998244353
dp = [0] * 3005
dp[b] = 1

for y in range(b + 1, d + 1):
    dp[y] = dp[y - 1] * a % mod
for x in range(a + 1, c + 1):
    dp2 = [0] * 3005
    dp2[b] = dp[b] * b % mod
    for y in range(b + 1, d + 1):
        dp2[y] = (dp[y] * y + dp2[y - 1] * x - dp[y - 1] * (x - 1) *
                  (y - 1)) % mod
    dp = dp2
print(dp[d])