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
inpl = lambda: list(map(int,input().split()))
A, B, C, D = inpl()
dp = [ [0]*(D+1) for _ in range(C+1) ]
dp[A][B] = 1
for a in range(A+1, C+1):
    dp[a][B] = (dp[a-1][B] * B) % MOD
for b in range(B+1, D+1):
    dp[A][b] = (dp[A][b-1] * A) % MOD

for a in range(A+1,C+1):
    for b in range(B+1,D+1):
        dp[a][b] = (b * dp[a-1][b] + a * dp[a][b-1] - (a-1)*(b-1)*dp[a-1][b-1]) % MOD

print(dp[C][D])