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 <iostream>
#include <algorithm>
#include <string>
#include <vector>
#include <cmath>
#include <map>
#include <queue>
#include <iomanip>
#define MOD 1000000007
typedef long long ll;
using namespace std;

int N;
vector<int> A,B;

vector<pair<int,int>> v;

int main(){
  cin>>N;
  for(int i=0;i<N;i++){
      int x;
      cin>>x;
      A.push_back(x);
      v.push_back(make_pair(x,0));
  }
  for(int i=0;i<N;i++){
      int x;
      cin>>x;
      B.push_back(x);
      v.push_back(make_pair(x,1));
  }
  sort(v.begin(),v.end());

  ll ans=1;
  for(int i=0;i<v.size();i++){
      int start=v[i].second;
      int a=1,b=0;
      int rest=1;
      for(i=i+1;i<v.size();i++){
          if(v[i].second==start){
              a++;
              rest++;
          }else{
              ans=(ans*rest)%MOD;
              b++;
              rest--;
          }
          if(a==b) break;
      }
  }

  cout<<ans<<endl;

  return 0;
}
