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

a = 1
arr = []
for j in range(D-B+1):
    arr.append(a)
    a *= A
    a %= MOD
dp = [arr]

b = B
for i in range(1, C-A+1):
    arr = [b]
    for j in range(1, D-B+1):
        # tate: A+i  yoko: B+j
        x = arr[-1]
        y = dp[-1][j]
        z = dp[-1][j-1]
        h = A+i
        w = B+j
        arr.append((x*h + y*w - z*((h-1)*(w-1))) % MOD)
    b *= B
    b %= MOD
    dp.append(arr)
print(dp[C-A][D-B])