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>
typedef long long ll;
using namespace std;
int main() {
	int n;
	scanf("%d", &n);
	int a[n], b[n];
	for (int i = 0; i < n; ++i)
		scanf("%d", a + i);
	for (int i = 0; i < n; ++i)
		scanf("%d", b + i);
	pair<int, int> v[2 * n];
	for (int i = 0; i < n; ++i) {
		v[i] = make_pair(a[i], 1);
		v[i + n] = make_pair(b[i], 2);
	}
	n += n;
	sort(v, v + n);
	ll ans = 1;
	int m = 1000000007;
	for (int i = 0, cnt = 0; i < n; ++i) {
		if (v[i].second == 1) {
			if (cnt > 0)
				ans = ans * cnt % m;
			--cnt;
		} else {
			if (cnt < 0)
				ans = ans * -cnt % m;
			++cnt;
		}
	}
	cout << ans;
	return 0;
}
