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;
typedef long long ll;
const int maxn = 3e3 + 10;
const int maxm = 2e3 + 10;
const int inf = 1e9 + 9;
const int mod = 998244353;

ll dp[maxn][maxn];
int main()
{
    ios::sync_with_stdio(0); cin.tie(0); //C++关同步
    int a, b, c, d;
    cin >> a >> b >> c >> d;
    dp[a][b] = 1;
    for(int i = 1; i <= c; ++i){
        for(int j = 1; j <= d; ++j){
            if((i > a && j >= b) || (i >= a && j > b)){
                dp[i][j] = (i * dp[i][j - 1] + j * dp[i - 1][j] - dp[i - 1][j - 1] * (i - 1) % mod * (j - 1) % mod + mod) % mod;
            }
        }
    }
    cout << dp[c][d] << '\n';
    return 0;
}