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++ (GCC 9.2.1) (judge verdict: Accepted)

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 */
#include <iostream>
#include <complex>
#include <vector>
#include <string>
#include <algorithm>
#include <cstdio>
#include <numeric>
#include <cstring>
#include <ctime>
#include <cstdlib>
#include <set>
#include <map>
#include <unordered_map>
#include <unordered_set>
#include <list>
#include <cmath>
#include <bitset>
#include <cassert>
#include <queue>
#include <stack>
#include <deque>
#include <random>


using namespace std;
template<typename T1, typename T2> inline void chkmin(T1 &a, T2 b) {if (a > b) a = b;}
template<typename T1, typename T2> inline void chkmax(T1 &a, T2 b) {if (a < b) a = b;}
#define files(FILENAME) read(FILENAME); write(FILENAME)
#define read(FILENAME) freopen((FILENAME + ".in").c_str(), "r", stdin)
#define write(FILENAME) freopen((FILENAME + ".out").c_str(), "w", stdout)
#define all(c) (c).begin(), (c).end()
#define sz(c) (int)(c).size()
#define left left228
#define right right228
#define y1 y1228
#define mp make_pair
#define pb push_back
#define y2 y2228
#define rank rank228
using ll = long long;
using ld = long double;
const string FILENAME = "input";
const int Mod = 998244353;


int sum(int a, int b) {
	return (a + b >= Mod ? a + b - Mod: a + b);
}

int mul(int a, int b) {
	return (ll)a * b % Mod;
}


int a, b, c, d;
int dp[3005][3005];


int main() {
	ios_base::sync_with_stdio(false);
	cin.tie(0);
	cout.tie(0);
 	//read(FILENAME);
 	cin >> a >> b >> c >> d;
 	dp[a][b] = 1;
 	for (int i = a; i <= c; i++) {
 		for (int j = b; j <= d; j++) {
 			int val = dp[i - 1][j - 1];
 			int cnt = mul(val, mul(i - 1, j - 1));
 			dp[i][j] = sum(dp[i][j], Mod - cnt);
 			dp[i + 1][j] = sum(dp[i + 1][j], mul(dp[i][j], j));
 			dp[i][j + 1] = sum(dp[i][j + 1], mul(dp[i][j], i));
 		}
 	}
 	cout << dp[c][d] << endl;
	return 0;	 	
}