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>

using namespace std;

int main()
{
	int n;
	cin >> n;
	vector<vector<int>> v(n * 2, vector<int>(2));
	for (int i = 0; i < n; i++)
	{
		cin >> v[i][0];
		v[i][1] = 1;
	}
	for (int i = n; i < n * 2; i++)
	{
		cin >> v[i][0];
		v[i][1] = -1;
	}
	sort(v.begin(), v.end());
	long long ret = 1;
	long long count = 0;
	for (auto x : v)
	{
		if (x[1] < 0)ret *= max(count, -(count - 1));
		ret %= (int)1e9 + 7;
		count += x[1];
	}
	cout << ret << endl;
	return 0;
}
