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 <algorithm>
#include <iostream>
#include <vector>
#include <queue>
#include <set>
#include <map>
#include <list>
#include <cmath>
#include <stack>
#include <string>
#include <cstring>
#include <numeric>
#include <iomanip>
using namespace std;
//
const int inf=1e9+7;//0x3f
//
int main(){
	int N;
	cin>>N;
	vector<pair<int,int>> V;
	for(int i=-1;i<=1;i+=2){
		for(int j=0;j<N;j++){
			int x;
			cin>>x;
			V.push_back(make_pair(x,i));
		}
	}
	sort(V.begin(),V.end());
	int cnt=0;
	long long ans=1;
	for(int i=0;i<2*N;i++){
		if(cnt*V[i].second<0){
			(ans*=abs(cnt))%=inf;
		}
		cnt+=V[i].second;
	}
	cout<<ans<<endl;
	return 0;
}