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;

int n;
typedef pair<int, int> P;
vector<P> v;
long long ans = 1, mod = 1e9+7;
int a[2];

int main(){
	cin.tie(0);
	ios::sync_with_stdio(false);
	cin >> n;
	for(int i=0; i<n; ++i){
		int t;
		cin >> t;
		v.push_back(P(t, 0));
	}
	for(int i=0; i<n; ++i){
		int t;
		cin >> t;
		v.push_back(P(t, 1));
	}
	sort(v.begin(), v.end());
	for(int i=0; i<2*n; ++i){
		if(a[1-v[i].second] > 0){
			ans = ans * a[1-v[i].second] % mod;
			--a[1-v[i].second];
		}else{
			++a[v[i].second];
		}
	}
	cout << ans << "\n";
}