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())

dp = [[0] * (D-B+1) for _ in range(C-A+1)]
dp[0][0] = 1
for i in range(1, C-A+1):
    dp[i][0] = dp[i-1][0] * B
    dp[i][0] %= MOD
for i in range(1, D-B+1):
    dp[0][i] = dp[0][i-1] * A
    dp[0][i] %= MOD

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

print(dp[C-A][D-B])