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:
mod = 998244353
a, b, c, d = map(int, input().split())

dp0 = [0] * (c-a+1)
dp1 = [1]
for i in range(c-a):
    dp1.append(dp1[-1] * b % mod)

for j in range(1, d-b+1):
    new_dp0 = [(dp0[0] * a + dp1[0]) % mod]
    new_dp1 = [dp1[0] * (a-1) % mod]
    for i in range(1, c-a+1):
        new_dp0.append((dp0[i] * (a+i) + dp1[i]) % mod)
        new_dp1.append((new_dp0[-2] + new_dp1[-1]) * (b+j) % mod)

    dp0 = new_dp0
    dp1 = new_dp1

print((dp0[-1] + dp1[-1]) % mod)