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;
using ll = long long;
using ull = unsigned long long;
#define REP(i,a) for(int i=0;i<(a);i++)
#define MOD 1000000007

int main(){
  int N;
  cin>>N;
  vector<pair<int,bool>> v(2*N);
  for(int i=0;i<2*N;i++){
    int x;
    cin>>x;
    bool y=(i<N);
    v[i]={x,y};
  }
  sort(v.begin(),v.end());
  ll ans=1;
  int cnt=0;
  for(int i=0;i<2*N;i++){
    int tmp=cnt+(v[i].second?1:-1);
    if(abs(tmp)<abs(cnt)) (ans*=cnt)%=MOD;
    cnt=tmp;
  }
  cout<<abs(ans)<<endl;
  return 0;
}
