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

int main(void){
  int n,i,x;
  const int mod=1e9+7;
  vector<P> px;
  
  cin >> n;
  for (i=0;i<n*2;i++){
    cin >> x;
    px.push_back(P(x,i));
  }
  
  sort(px.begin(),px.end());
  
  ll ans=1,an,bn;
  an=bn=0;
  for (i=0;i<n*2;i++){
    if (px[i].second < n){
      if (bn>0){
        ans=ans*bn%mod;
        bn--;
      }else{
        an++;
      }
    }else{
      if (an>0){
        ans=ans*an%mod;
        an--;
      }else{
        bn++;
      }
    }
  }
  
  cout << ans << endl;
  
  return 0;
}