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;
typedef long long ll;
#define FOR(I,A,B) for(ll I = int(A); I < int(B); ++I)
const ll MOD=1e9+7;
int main(){
	ll N,ans=1,a;
	cin >> N;
	priority_queue<pair<ll,ll>> Q;
	FOR(i,0,N)cin>>a,Q.push({-a,-1});
	FOR(i,0,N)cin>>a,Q.push({-a,1});
	a = 0;
	while(!Q.empty()){
		if(a != Q.top().second*llabs(a))
			(ans *= llabs(a) )%=MOD;
		a+=Q.top().second;
		Q.pop();
	}
	cout << ans << endl;
}