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())

dp = [[1 for i in range(d+1)] for j in range(c+1)]

mod = 998244353

for y in range(c+1):
    if y < a:
        continue
    for x in range(d+1):
        if x < b:
            continue
        if y == a and x == b:
            continue
        py = 0
        px = 0
        m = 0
        if y > a:
            py = dp[y-1][x] * x
        if x > b:
            px = dp[y][x-1] * y
        if y > a and x > b:
            m = dp[y-1][x-1] * (y-1) * (x-1)
        dp[y][x] = py + px - m
        dp[y][x] %= mod


print(dp[c][d])