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;

long long MOD=1000000007LL;

int main(){
	int N;
	cin >> N;
	vector<pair<int,int>> ab;
	for(int i=0;i<N;i++){
		int a;
		cin >> a;
		ab.push_back(make_pair(a,1));
	}
	for(int i=0;i<N;i++){
		int b;
		cin >> b;
		ab.push_back(make_pair(b,2));
	}
	
	sort(ab.begin(),ab.end());
	long long ans=1LL;
	long long a=0LL,b=0LL;
	for(int i=0;i<2*N;i++){
		if(ab[i].second==1){
			if(b==0LL)a++;
			else{
				ans*=b;
				b--;
			}
		}
		else{
			if(a==0LL)b++;
			else{
				ans*=a;
				a--;
			}
		}
		if(ans>=MOD)ans%=MOD;
	}
	cout << ans << endl;
	return 0;
}