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>
#define pb push_back
#define mp make_pair
#define int long long
#define inf 1000000007
#define LINF 100000000000000007LL
#define ll long long
using namespace std;
signed main(){
	int n;
	cin>>n;
	vector<int> a(n),b(n);
	vector< pair<int,int> > p;
	for(int i=0;i<n;i++){
		cin>>a[i];
		p.pb( mp(a[i],0) );
	}
	for(int i=0;i<n;i++){
		cin>>b[i];
		p.pb( mp(b[i],1) );
	}
	sort( p.begin(), p.end() );
	int ac = 0, bc = 0;
	int ans = 1;
	for(int i=0;i<p.size();i++){
		int tp = p[i].second;
		if( tp == 1 ){
			if( bc == 0 ){
				ac++;
			}
			else{
				ans *= bc;
				ans %= inf;
				bc--;
			}
		}
		else{
			if( ac == 0 ){
				bc++;
			}
			else{
				ans *= ac;
				ans %= inf;
				ac--;
			}
		}
	}
	cout<<ans<<endl;
	return 0;
}