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 MOD 1000000007
#define For(i,a,b) for(int i=a;i<=b;i++)
using namespace std;
vector<pair<int,int> > p;
int main(){
	int N,temp;
	cin >> N;
	long long ans = 1;
	For(i,1,N) {
		scanf("%d",&temp);
		p.push_back(make_pair(temp,1));
	}
	For(i,1,N) {
		scanf("%d",&temp);
		p.push_back(make_pair(temp,-1));		
	}
	sort(p.begin(),p.end());
	int currentS = 0;
	For(i,0,p.size()-2){
		if(currentS*p[i].second < 0){
			(ans *= abs(currentS)) %= MOD;
//			cout << i << "==" <<  currentS << endl;
		}
		currentS += p[i].second;
	}
	cout << ans;
}
