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>
#include<queue>
#define lol(i,n) for(int i=0;i<n;i++)
#define mod 1000000007
typedef long long ll;
using namespace std;
#define N 100010
int n,x;
vector<pair<int,int> >v;

int main(){
  cin>>n;
  lol(i,n){cin>>x;v.push_back(make_pair(x,0));}
  lol(i,n){cin>>x;v.push_back(make_pair(x,1));}
  sort(v.begin(),v.end());
  ll ans=1,cnt=0;
  lol(i,v.size()){
    if(v[i].second==0){
      if(cnt>0)ans=ans*cnt%mod;
      cnt--;
    }
    if(v[i].second==1){
      if(-cnt>0)ans=ans*(-cnt)%mod;
      cnt++;
    }
  }
  cout<<ans<<endl;
  return 0;
}
