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<cstdio>
#include<cmath>
#include<math.h>
#include<string>
#include<string.h>
#include<stack>
#include<queue>
#include<vector>
#include<utility>
#include<set>
#include<map>
#include<stdlib.h>
#include<iomanip>

using namespace std;

#define ll long long
#define ld long double
#define EPS 0.0000000001
#define INF 1e9
#define MOD 1000000007
#define rep(i,n) for(i=0;i<(n);i++)
#define loop(i,a,n) for(i=a;i<(n);i++)
#define all(in) in.begin(),in.end()
#define shosu(x) fixed<<setprecision(x)
#define int ll
typedef vector<int> vi;
typedef pair<int,int> pii;

signed main(void) {
  int i,j;
  int n;
  cin>>n;
  vector<pii> p(2*n);
  rep(i,n){
    cin>>p[i].first;
    p[i].second=1;
  }
  rep(i,n){
    cin>>p[i+n].first;
    p[i+n].second=-1;
  }
  sort(all(p));
  ll ans=1;
  int a=0,b=0;
  rep(i,2*n){
    if(p[i].second==1){//pc
      if(a==0)
	b++;
      else
	ans=(ans*a)%MOD,a--; 
    }else{
      if(b==0)
	a++;
      else 
	ans=(ans*b)%MOD,b--;
    }
  }
  cout<<ans<<endl;
}
