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 main(){
	int N;
	cin >> N;
	int a[N], b[N];
	for(int i=0; i<N; i++){
		cin >> a[i];
	}
	for(int i=0; i<N; i++){
		cin >> b[i];
	}
	vector<pair<int , int>> P;
	for(int i=0; i<2*N; i++){
		if(i < N){
			P.push_back({a[i], 0});
		}else{
			P.push_back({b[i-N], 1});
		}
	}
	sort(P.begin(), P.end());
	long long ans = 1;
	int cnt = 0, c;
	for(int i=2*N-1; i>=0; i--){
		if(cnt == 0){
			c = P[i].second;
		}
		if(P[i].second != c){
			ans = (ans * cnt) % mod;
			cnt--;
		}else{
			cnt++;
		}
	}
	cout << ans << endl;
	return 0;
}
