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 <map>
#include <algorithm>

using namespace std;

#define rep(i, n) for (int i = 0; i < (int)n; i++)
#define vec vector
#define ll long long
#define mp make_pair
#define pb push_back

ll INF = 1000000007;

int ret(int get)
{
	if (!get) return 1;
	else if (get < 0) return - get;
	else return get;
}

int main(void)
{
	int n;
	cin >> n;
	vec<pair<int, int>> a(2 * n);
	rep(i, n) {
		cin >> a[i].first;
		a[i].second = 1;
	}
	rep(i, n) {
		cin >> a[i + n].first;
		a[i + n].second = - 1;
	}

	sort(a.begin(), a.end());

	vec<int> cur;
	int count = 0;
	ll ans = 1;
	rep(i, n * 2) {
		count += a[i].second;
		cur.pb(a[i].second);
		if (!count) {
			int start = cur[0];
			ll c = 0;
			rep(j, cur.size()) {
				if (start == cur[j]) c++;
				else {
					ans *= c;
					ans %= INF;
					c--;
				}
			}
			cur.clear();
		}
	}
	cout << ans << endl;
	return 0;
}