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 MOD 1000000007
using namespace std;
typedef pair<int,int>P;
typedef long long ll;

int main(){
	int n;scanf("%d",&n);
	vector<P>v;
	rep(i,n){
		int a;scanf("%d",&a);
		v.push_back(P(a,0));
	}
	rep(i,n){
		int b;scanf("%d",&b);
		v.push_back(P(b,1));
	}
	sort(v.begin(),v.end());
	ll cnt=0,ty=-1;
	ll ans=1;
	for(auto p:v){
		if(ty==!p.second){
			(ans*=cnt)%=MOD;
			cnt--;
			if(cnt==0)ty=-1;
		}
		else{
			cnt++;
			ty=p.second;
		}
	}
	cout<<ans<<endl;
}