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 <cstdio>
#include <cstring>
#include <iostream>
#include <string>
#include <cmath>
#include <bitset>
#include <vector>
#include <map>
#include <set>
#include <queue>
#include <deque>
#include <algorithm>
#define MOD 1000000007LL

using namespace std;
typedef long long int ll;
typedef pair<int, int> P;

int main()
{
	int n;
  cin>>n;
  vector<P> p;
  for(int i=0; i<n; i++){
    int a;
    cin>>a;
    p.push_back(P(a, 1));
  }
  for(int i=0; i<n; i++){
    int b;
    cin>>b;
    p.push_back(P(b, -1));
  }
  sort(p.begin(), p.end());
  ll ans=1;
  int s=0;
  int x;
  for(auto p0:p){
    int t=p0.second;
    if(s==0) x=t;
    s+=t;
    if(x==t){
      ans*=((ll)(abs(s)));
      ans%=MOD;
    }
  }
  cout<<ans<<endl;
	return 0;
}