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;
#define MOD 1000000007

int main() {
	int n;
	cin >> n;
	vector<pair<long long, int>> v(2*n);
	for(int i = 0; i < n; ++i){
		long long tmp;
		cin >> tmp;
		v[i] = make_pair(tmp, 1);
	}
	for(int i = 0; i < n; ++i){
		long long tmp;
		cin >> tmp;
		v[n+i] = make_pair(tmp, -1);
	}
	
	sort(v.begin(), v.end());
	
	long long ans = 1;
	long long sum = 0;
	for(int i = 0; i < 2*n; ++i){
		if(v[i].second == 1 && sum < 0) ans = (ans * (-sum)) % MOD;
		if(v[i].second == -1 && sum > 0) ans = (ans * sum) % MOD;
		sum += v[i].second;
	}
	
	assert(sum == 0);
	cout << ans << endl;
	
	return 0;
}