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>
#define rep(i,n) for(int i=0;i<(n);++i)
#define ALL(A) A.begin(), A.end()

using namespace std;

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

const ll MOD = (ll)1e9 + 7LL;

int main()
{
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	int N; cin >> N;
	vector<P> v(2*N);
	rep (i, N){
		int a; cin >> a;
		v[i].first = a;
		v[i].second = 1;
	} // end rep
	rep (i, N){
		int b; cin >> b;
		v[i+N].first = b;
		v[i+N].second = -1;
	} // end rep

	sort(ALL(v));

	ll sum = 0LL;
	ll ans = 1LL;
	for (int i = 0; i < v.size(); ++i){
		if ((sum > 0LL && v[i].second < 0) || (sum < 0LL && v[i].second > 0)){
			ans = (ans * abs(sum)) % MOD;
		} // end if
		sum += v[i].second;
	} // end for
	cout << ans << endl;

	return 0;
}