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 N=3005,p=998244353,inf=0x3f3f3f3f;
int read(){
	int f=1,g=0;
	char ch=getchar();
	for (;!isdigit(ch);ch=getchar()) if (ch=='-') f=-1;
	for (;isdigit(ch);ch=getchar()) g=g*10+ch-'0';
	return f*g;
}
int A,B,C,D,f[N][N],g[N][N];
void check(int &x,int y){if ((x+=y)>=p) x-=p;}
int main(){
//	freopen("a.txt","r",stdin);
	A=read();B=read();C=read();D=read();
	f[A][B]=1;
	for (int i=A;i<=C;i++)
	for (int j=B+(i==A);j<=D;j++){
		f[i][j]=((ll)f[i-1][j]*j+g[i-1][j])%p;
		g[i][j]=(ll)(g[i][j-1]+f[i][j-1])*i%p;
	}
	int ans=(f[C][D]+g[C][D])%p;
	printf("%d\n",ans);
	return 0;
}