There are N computers and N sockets in a one-dimensional world. The coordinate of the i-th computer is a_i, and the coordinate of the i-th socket is b_i. It is guaranteed that these 2N coordinates are pairwise distinct.

Snuke wants to connect each computer to a socket using a cable. Each socket can be connected to only one computer.

In how many ways can he minimize the total length of the cables? Compute the answer modulo 10^9+7.

Constraints

* 1 ≤ N ≤ 10^5
* 0 ≤ a_i, b_i ≤ 10^9
* The coordinates are integers.
* The coordinates are pairwise distinct.

Input

The input is given from Standard Input in the following format:


N
a_1
:
a_N
b_1
:
b_N


Output

Print the number of ways to minimize the total length of the cables, modulo 10^9+7.

Examples

Input

2
0
10
20
30


Output

2


Input

3
3
10
8
7
12
5


Output

1
#include <iostream>
#include <utility>
#include <algorithm>
using namespace std;
int main(){
	pair<int,int> p[200010];
	int i,n,a,b;
	cin >> n;
	for(i=0;i<n;i++){
		cin >> a;
		p[i] = make_pair(a,0);
	}
	for(i=0;i<n;i++){
		cin >> b;
		p[i+n] = make_pair(b,1);
	}
	
	sort(p,p+2*n);
	long long ans = 1;
	int s=0,t=0;
	for(i=0;i<2*n;i++){
		if(p[i].second==0){
			if(t==0){
				s++;
			}else{
				ans *= t;
				ans = ans%1000000007;
				t--;
			}
		}else{
			if(s==0){
				t++;
			}else{
				ans *= s;
				ans = ans%1000000007;
				s--;
			}
		}
	}
	cout << ans << endl;
}