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;
using System.Linq;
using static Constans;

public static class Constans
{
    public const long Mod = 998244353;
}

public struct ModInt
{
    public long Num;

    public ModInt(long num)
    {
        Num = num;
    }

    public override string ToString()
    {
        return Num.ToString();
    }

    public static ModInt operator +(ModInt l, ModInt r)
    {
        l.Num += r.Num;
        if (l.Num >= Mod)
        {
            l.Num -= Mod;
        }
        return l;
    }

    public static ModInt operator -(ModInt l, ModInt r)
    {
        l.Num -= r.Num;
        if (l.Num < 0)
        {
            l.Num += Mod;
        }
        return l;
    }

    public static ModInt operator *(ModInt l, ModInt r)
    {
        return new ModInt(l.Num * r.Num % Mod);
    }

    public static implicit operator ModInt(long n)
    {
        n %= Mod;
        if (n < 0)
        {
            n += Mod;
        }
        return new ModInt(n);
    }
}

public class Solution
{
    public static void Main()
    {
        var vals = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
        var A = vals[0];
        var B = vals[1];
        var C = vals[2];
        var D = vals[3];

        var dp = new ModInt[C + 1, D + 1, 2];
        for (int i = A; i <= C; i++)
        {
            for (int j = B; j <= D; j++)
            {
                if (i == A && j == B)
                {
                    dp[A, B, 0] = 1;
                    continue;
                }

                dp[i, j, 0] = dp[i, j - 1, 0] * i + dp[i, j - 1, 1];
                dp[i, j, 1] = (dp[i - 1, j, 0] + dp[i - 1, j, 1]) * j;
            }
        }

        var answer = dp[C, D, 0] + dp[C, D, 1];
        Console.WriteLine(answer);
    }
}