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>
using namespace std;
long long a[300000],b[300000],n;
vector<pair<long long,long long> > vec;
int main(){
	cin>>n;
	for(int i=0;i<n;i++){cin>>a[i];vec.push_back(make_pair(a[i],i));}
	for(int i=0;i<n;i++){cin>>b[i];vec.push_back(make_pair(b[i],i+n));}
	sort(vec.begin(),vec.end());
	long long v=1;long long cnt=0;
	for(int i=0;i<vec.size();i++){
		if(vec[i].second<n){
			if(cnt<0){v*=1LL*-cnt;}
			cnt++;
		}
		if(vec[i].second>=n){
			if(cnt>0){v*=1LL*cnt;}
			cnt--;
		}
		v%=1000000007LL;
	}
	cout<<v<<endl;
	return 0;
}