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 int long long
#define MOD 1000000007
using namespace std;

typedef pair<int,int> P;

signed main(){
	vector<P> vec;
	int n,cnt = 0,ans = 1;
	cin >> n;
	for(int i = -1;i <= 1;i += 2){
		for(int j = 0;j < n;j++){
			int a;
			cin >> a;
			vec.push_back(P(a,i));
		}
	}
	sort(vec.begin(),vec.end());
	for(int i = 0;i < n * 2;i++){
		if(cnt * vec[i].second < 0) ans = ans * abs(cnt) % MOD;
		cnt += vec[i].second;
	}
	cout << ans << endl;
	return 0;
}