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

dp0 = [[0] * (D + 1) for _ in range(C + 1)]
dp1 = [[0] * (D + 1) for _ in range(C + 1)]


dp0[A][B] = 1

for x in range(A, C + 1):
    for y in range(B, D + 1):
        if x == A and y == B:
            continue
        dp0[x][y] = (dp0[x][y - 1] * x + dp1[x][y - 1] * 1) % MOD
        dp1[x][y] = (dp0[x - 1][y] * y + dp1[x - 1][y] * y) % MOD

# print (dp0)
# print (dp1)        

ans = (dp0[C][D] + dp1[C][D]) % MOD
print (ans)