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;

typedef long long ll;
typedef vector<ll> vll;
typedef vector<bool> vb;
typedef pair<ll,ll> pll;

const ll mod=1000000007;
const ll inf=1000000000000; 

#define rep(i,m,n) for(ll i=m;i<n;i++)

int main(){
   cin.tie(nullptr);
  ios::sync_with_stdio(false);

 ll n;
  cin >> n;
  vector<pll> p(2*n);
  rep(i,0,n) {
    cin >> p[i].first;
    p[i].second=-1; 
  }
  rep(i,n,2*n) {
    cin >> p[i].first;
    p[i].second=1; 
  }
  sort(p.begin(),p.end());
  
 ll res=1; 
  stack<ll> a,b;
  
  rep(i,0,2*n){
   if(p[i].second==-1){
    if(!b.empty()) {
      res*=b.size();
      res%=mod;
      b.pop();
   }
     else a.push(p[i].first);
   }
     else if(p[i].second==1){
    if(!a.empty()) {
      res*=a.size();
      res%=mod;
      a.pop();
   }
     else b.push(p[i].first);
   }
     
  }
  
  cout << res << endl;
  
}
