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 <algorithm>
#include <utility>
using namespace std;

int main() {
	int N;
	cin >> N;
	vector<pair<long, long>> v(N*2);
	for(int i=0; i<N; ++i){
	    int a;
	    cin >> a;
	    v[i]=make_pair(a, 1);
	}
	for(int i=0; i<N; ++i){
	    int a;
	    cin >> a;
	    v[N+i]=make_pair(a, -1);
	}
	sort(v.begin(), v.end());
	long ans=1, now=0, mod=1000000007;
	for(int i=0; i<N*2; ++i){
	    if(now*v[i].second<0) ans=(ans*abs(now))%mod;
	    now += v[i].second;
	}
	cout << ans << endl;
	return 0;
}
