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 EM 100000000
using namespace std;
using LL = long long;
using P = pair<LL, LL>;
LL LINF = 1e18;
int INF = 1e9;
LL mod = 1e9+7;
using vint = vector<int>;
using vLL = vector<LL>;
using vvint = vector<vector<int>>;
using vvLL = vector<vector<LL>>;
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }

int main(){
	int N;
	cin >> N;
	vint a(N), b(N), c(2*N, 0);
	vector<P>	ab(2*N);
	for(int i = 0;i < N;i++)	cin >> a[i];
	for(int i = 0;i < N;i++)	cin >> b[i];
	for(int i = 0;i < 2*N;i+=2){ab[i] = P(a[i/2], 1);ab[i+1] = P(b[i/2], 0);}
	sort(ab.begin(), ab.end());
	int d = 0;
	LL ans = 1;
	for(int i = 0;i < 2*N;i++){
		if(ab[i].second == 1){if(d < 0) ans *= -d;ans %= mod;d++;}
		else{if(d > 0) ans *= d;ans %= mod;d--;}
	}
	cout << ans << endl;
}