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<algorithm>
#include<vector>
using namespace std;
long ans=1,mod=1e9+7,cnt;
int main()
{
	int N;cin>>N;
	vector<pair<int,int> >A;
	for(int i=0;i<2*N;i++)
	{
		int a;cin>>a;
		A.push_back(make_pair(a,i<N));
	}
	sort(A.begin(),A.end());
	for(pair<int,int>p:A)
	{
		if(p.second)
		{
			if(cnt>0)ans=ans*cnt%mod;
			cnt--;
		}
		else
		{
			if(cnt<0)ans=ans*-cnt%mod;
			cnt++;
		}
	}
	cout<<ans<<endl;
}
