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<vector>
#include<algorithm>
#define mod 1000000007
using namespace std;
typedef long long int ll;
typedef pair<ll,int> mypair;
int main(void){
	int n;
	cin>>n;
	vector<ll> a(n),b(n);
	vector<mypair> l;
	for(int i=0;i<n;i++){
		cin>>a[i];
	l.push_back(mypair(a[i],-1));
	
	}
	for(int i=0;i<n;i++){	
		cin>>b[i];
	l.push_back(mypair(b[i],1));
	
	}
	
	sort(l.begin(),l.end());
	ll ans=1;
	int f=0;
	for(int i=0;i<2*n;i++){
		int c=l[i].second;
		if(f==0){
			f+=c;
		}else if(f<0){
			if(c<0){
				f+=c;
			}else{
				ans*=-1*f;
				ans%=mod;
				f+=c;
			}
		}else{
			if(c>0){
				f+=c;
			}else{
				ans*=f;
				ans%=mod;
				f+=c;
			}
		}

	}

	cout<<ans<<endl;
	
	return  0;
}