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;

int main() {
	int N;
	long long ans = 1, count = 0, A, MOD = 1000000007;
	vector<pair<long long, int> > V;
	cin >> N;
	for (int i = 0; i < N * 2; i++) {
		cin >> A;
		if (i < N) V.push_back({ A, 1 });
		else V.push_back({ A, -1 });
	}
	sort(V.begin(), V.end());
	for (auto it = V.begin(); it != V.end(); it++) {
		if ((count < 0 && it->second > 0) || (count > 0 && it->second < 0)) {
			ans *= abs(count);
			ans = ans % MOD;
		}
		count += it->second;
	}
	cout << ans;
}