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 <algorithm>
#include <vector>
using namespace std;
#define int long long
vector<pair<int, int>>v;
signed main() {
	int n; cin >> n;
	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());
	int c0 = 0, c1 = 0;
	int ans = 1;
	for (int i = 0; i < v.size(); i++) {
		if (v[i].second == 1) {
			if (c0 == 0)c1++;
			else {
				ans *= c0;
				c0--;
				ans %= 1000000007;
			}
		}
		else {
			if (c1 == 0)c0++;
			else {
				ans *= c1;
				c1--;
				ans %= 1000000007;
			}
		}
	}
	cout << ans << endl;
}