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>
using namespace std;

const int mod = 1e9+7;
int A[100105],B[100105];

int main(){
	int n,a=0,b=0,cnt=0,cnt2=0;
	long long ans = 1;
	cin >> n;
	for(int i=0;i<n;i++) cin >> A[i];
	for(int i=0;i<n;i++) cin >> B[i];
	sort(A,A+n);
	sort(B,B+n);
	
	for(int i=0;i<2*n;i++){
		if(a<n && (b==n || A[a]<B[b]) ){
			if(cnt2 > 0){
				ans = ans*cnt2%mod;
				cnt2--;
			}
			else
				cnt++;
			a++;
		}
		else{
			if(cnt > 0){
				ans = ans * cnt%mod;
				cnt--;
			}
			else
				cnt2++;
			b++;
		}
	}
	
	cout << ans << endl;
	return 0;
}