Problem:
Score : 600 points

Problem Statement

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.

Sample Input 1

1 1 2 2

Sample Output 1

3

Any two of the three squares other than the bottom-left square can be painted black.

Sample Input 2

2 1 3 4

Sample Output 2

65

Sample Input 3

31 41 59 265

Sample Output 3

387222020

Solution in Haskell (GHC 8.8.3) (judge verdict: Wrong Answer)

import Control.Applicative

calc :: Int -> Int -> Int -> Int -> Int
calc a b c d
    | a == c = a ^ (d - b)
    | b == d = b ^ (c - a)
    | otherwise = (calc' (c - 1) d) * d + (calc' c (d - 1)) * c - duplicate
    where
        calc' = calc a b
        duplicate = calc' (c - 1) (d - 1) * (c - 1) * (d - 1)

main :: IO ()
main = do 
    [a, b, c, d] <- map read . words <$> getLine
    print $ calc a b c d