Problem: 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.

Examples

Input

1 1 2 2


Output

3


Input

2 1 3 4


Output

65


Input

31 41 59 265


Output

387222020

Solution (in JAVA):

Solution:
import java.util.*;
public class Main {

	public static void main(String[] args) {
		int MOD = 998244353;
		Scanner sc = new Scanner(System.in);
		int A = sc.nextInt();
		int B = sc.nextInt();
		int C = sc.nextInt();
		int D = sc.nextInt();
		long[][] dp = new long[C+1][D+1];
		long[][] S = new long[C+1][D+1];
		dp[A][B] = 1;
		for(int i = B; i < D; i++)
			dp[A][i+1] = dp[A][i] * A % MOD;
		for(int i = A; i < C; i++)
			dp[i+1][B] = dp[i][B] * B % MOD;
		for(int i = A+1; i <= C; i++)
			for(int j = B+1; j <= D; j++) {
				S[i][j] = (S[i-1][j] * (j-1) + dp[i-1][j]) % MOD;
				dp[i][j] = (dp[i][j-1] * i + S[i][j]) % MOD;
			}
		System.out.println(dp[C][D]);
	}

}