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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.util.Scanner;

public class Main {
	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		int a = sc.nextInt();
		int b = sc.nextInt();
		int c = sc.nextInt();
		int d = sc.nextInt();
		sc.close();

		int mod = 998244353;
		long[][] dp1 = new long[c + 1][d + 1];
		long[][] dp2 = new long[c + 1][d + 1];
		for (int i = 1; i <= b; i++) {
			dp1[a][i] = 1;
		}
		for (int i = b + 1; i <= d; i++) {
			dp1[a][i] = dp1[a][i - 1] * a % mod;
		}

		for (int i = a + 1; i <= c; i++) {
			for (int j = 1; j <= d; j++) {
				dp1[i][j] = (dp1[i - 1][j] + dp2[i - 1][j]) * j % mod;
				if (j > b) {
					dp2[i][j] = (dp2[i][j - 1] * i + dp1[i][j - 1]) % mod;
				}
			}
		}
		System.out.println((dp1[c][d] + dp2[c][d]) % mod);
	}
}