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>
#include <set>
#include <math.h>
#include <numeric>
using namespace std;
typedef long long int ll;

ll mod=1e9+7;

int main(){
	cin.tie(nullptr);
	ios::sync_with_stdio(false);
	int n; cin >> n;
	vector<pair<int,int> > v;
	for(int i=0;i<n;i++){
		int a; cin >> a;
		v.push_back(make_pair(a,0));
	}
	for(int i=0;i<n;i++){
		int a; cin >> a;
		v.push_back(make_pair(a,1));
	}
	sort(v.begin(),v.end());
	ll ans=1;
	ll aleft=0;
	ll bleft=0;
	for(auto p:v){
		if(p.second==0){
			if(bleft){
				ans*=bleft;
				ans%=mod;
				bleft--;
			}
			else{
				aleft++;
			}
		}
		else{
			if(aleft){
				ans*=aleft;
				ans%=mod;
				aleft--;
			}
			else{
				bleft++;
			}
		}
	}
	cout << ans << endl;
}