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<algorithm>
#include<iostream>

using namespace std;

typedef long long ll;
typedef pair<ll, bool> P;

const ll MOD = 1000000007;

int N;
P ab[100000 * 2];

int main() {

	cin >> N;
	for (int i = 0; i < N; i++) {
		ll a;
		cin >> a;
		ab[i].first = a, ab[i].second = true;
	}
	for (int i = 0; i < N; i++) {
		ll b;
		cin >> b;
		ab[i + N].first = b, ab[i + N].second = false;
	}

	sort(ab, ab + 2 * N);

	ll ans = 1;
	ll cnt = 1;
	bool base = ab[0].second;
	for (int i = 1; i < 2 * N; i++) {
		if (cnt == 0) {
			cnt = 1;
			if (ab[i].second != base)base = !base;
		}else if (base != ab[i].second) {
			ans *= cnt;
			ans %= MOD;
			cnt--;
		}
		else {
			cnt++;
		}
	}

	cout << ans << endl;

	return 0;
}