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;

#define rep(i,n) for(int i=0;i<(int)(n);i++)
#define repe(i,n) rep(i,(n)+1)
#define per(i,n) for(int i=(int)(n)-1;i>=0;i--)
#define pere(i,n) rep(i,(n)+1)
#define all(x) (x).begin(),(x).end()
#define SP <<" "<<
#define MOD 1000000007
#define TIF 1000000000
#define LIF 1000000000000000000

typedef long long LL;
typedef long double LD;

int main(){
  int n;
  cin >> n;
  vector<pair<int,int>> p(2*n);
  int x;
  for(int i=0;i<n;i++){
    cin >> x;
    p[i]={x,1};
  }
  for(int i=0;i<n;i++){
    cin >> x;
    p[i+n]={x,-1};
  }
  sort(all(p));
  LL ans=1;
  LL t=0;
  for(int i=0;i<2*n;i++){
    if(t>0){
      if(p[i].second==1){
        ans=ans*(t+1)%MOD;
      }
    }else{
      if(p[i].second==-1){
        ans=ans*(-t+1)%MOD;
      }
    }
    t+=p[i].second;
  }
  cout << ans << endl;
  return 0;
}