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 <sstream>
#include <fstream>
#include <string>
#include <vector>
#include <deque>
#include <queue>
#include <stack>
#include <set>
#include <map>
#include <algorithm>
#include <functional>
#include <utility>
#include <bitset>
#include <cmath>
#include <cstdlib>
#include <ctime>
#include <cstdio>

using namespace std;

int n;
pair<int, int> p[200005];
long long MOD = 1000000007;

int dir(long long a){
	if(a > 0) return 1;
	else if(a < 0) return -1;
	else return 0;
}

int main(){
	cin>>n;
	for(int i=0;i<n;i++){
		int pp; cin>>pp;
		p[i] = make_pair(pp,1);
	}
	for(int i=0;i<n;i++){
		int pp; cin>>pp;
		p[i+n] = make_pair(pp,-1);
	}
	sort(p,p+2*n);

	long long ans = 1;
	long long tmp = 0;

	for(int i=0;i<2*n;i++){
		if(tmp == 0) tmp += p[i].second;
		else {
			if(dir(tmp) == dir(p[i].second)) tmp += p[i].second;
			else {
				ans *= abs(tmp);
				ans %= MOD;
				tmp += p[i].second;
			}
		}
	}

	cout<<ans<<endl;
	return 0;

}
