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 C# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections.Generic;

class Program
{
	static void Main(string[] args)
	{
		string[] input = Console.ReadLine().Split(' ');
		int a = int.Parse(input[0]);
		int b = int.Parse(input[1]);
		int c = int.Parse(input[2]);
		int d = int.Parse(input[3]);
		long mod = 998244353;

		long[][] dp = new long[c+1][];
		for(int i=0; i<=c; i++) dp[i] = new long[d+1];
		dp[a][b] = 1;

		for(int col = b; col <= d; col++)
		{
			for(int row = a; row <= c; row++)
			{
				if(col == b && row == a) continue;
				long dpTmp = (dp[row-1][col] * (long)col) % mod;
				dpTmp = (dpTmp + (dp[row][col-1] * (long)row) % mod) % mod;
				dpTmp = (dpTmp + mod - ((dp[row-1][col-1] * ((long)row - 1) * ((long)col - 1)) % mod)) % mod;
				dp[row][col] = dpTmp;
			}
		}
		Console.WriteLine(dp[c][d]);
	}
}