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


def solve(A, B, C, D):
    numWays = [[None for c in range(D + 1)] for r in range(C + 1)]

    numWays[A][B] = 1

    for rows in range(A, C + 1):
        for cols in range(B, D + 1):
            if rows == A and cols == B:
                continue
            ways = 0
            if rows > A:
                ways += cols * numWays[rows - 1][cols] % MOD
            if cols > B:
                ways += rows * numWays[rows][cols - 1] % MOD
            if rows > A and cols > B:
                ways -= (cols - 1) * (rows - 1) * numWays[rows - 1][cols - 1] % MOD
            numWays[rows][cols] = ways % MOD

    return numWays[C][D] % MOD


A, B, C, D = [int(x) for x in input().split()]
print(solve(A, B, C, D))