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<bits/stdc++.h>
using namespace std;
 
const int mod = 1e9+7;
 
int main(){
	int n,a,cnt=0;
	long long ans=1;
	vector<pair<int,int> > v;
	
	cin >> n;
	for(int i=0;i<2;i++){
		for(int j=0;j<n;j++){
			cin >> a;
			v.push_back(pair<int,int>(a,i));
		}
	}
	sort(v.begin(),v.end());
	
	for(int i=0;i<v.size();i++){
		if(v[i].second==1){
			if(cnt < 0) ans = ans * -cnt % mod;
			cnt++;
		}
		else{
			if(cnt > 0) ans = ans * cnt % mod;
			cnt--;
		}
	}
	
	cout << ans << endl;
	return 0;
}