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<set>
#include<algorithm>
using namespace std;
typedef long long int ll;
static const int MOD = 1000000007;
int main(){
	int N;
	pair<int, int> p[200000];
	cin >> N;
	for(int i = 0; i < N; i++){
		int a;
		cin >> a;
		p[i] = make_pair(a, 1);
	}
	for(int i = 0; i < N; i++){
		int b;
		cin >> b;
		p[N + i] = make_pair(b, 2);
	}
	sort(p, p + 2 * N);
	ll cnt_a = 0, cnt_b = 0, ans = 1;
	for(int i = 0; i < 2 * N; i++){
		if(p[i].second == 1){
			if(cnt_b == 0) cnt_a++;
			else{
				ans *= cnt_b;
				ans %= MOD;
				cnt_b--;
			}
		}else if(p[i].second == 2){
			if(cnt_a == 0) cnt_b++;
			else{
				ans *= cnt_a;
				ans %= MOD;
				cnt_a--;
			}
		}
	}
	cout << ans << endl;
}