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 Rust (1.42.0) (judge verdict: Accepted)

use std::io::*;

const MOD: usize = 998244353;

fn main() {
    let mut s: String = String::new();
    std::io::stdin().read_to_string(&mut s).ok();
    let mut itr = s.trim().split_whitespace();
    let a: usize = itr.next().unwrap().parse().unwrap();
    let b: usize = itr.next().unwrap().parse().unwrap();
    let c: usize = itr.next().unwrap().parse().unwrap();
    let d: usize = itr.next().unwrap().parse().unwrap();

    let mut dp = vec![vec![0; d + 1]; c + 1];
    dp[a][b] = 1usize;
    for i in a..=c {
        for j in b..=d {
            dp[i][j] += dp[i - 1][j] * j % MOD;
            dp[i][j] += dp[i][j - 1] * i % MOD;
            dp[i][j] += MOD - dp[i - 1][j - 1] * (i - 1) * (j - 1) % MOD;
            dp[i][j] %= MOD;
        }
    }
    println!("{}", dp[c][d]);
}