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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;

long long dp[3010][3010];
constexpr int mod = 998244353;

int main() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    int A, B, C, D; cin >> A >> B >> C >> D;
    dp[A][B] = 1;
    for (int i = A; i <= C; i++) {
        for (int j = B; j <= D; j++) {
            dp[i][j] %= mod;
            dp[i+1][j] += dp[i][j] * j % mod;
            dp[i][j+1] += dp[i][j] * i % mod;
            dp[i+1][j+1] += mod - dp[i][j] * i % mod * j % mod;
        }
    }
    cout << dp[C][D] % mod << "\n";
    return 0;
}