Problem:
Score : 500 points

Problem Statement

#nck {
width: 30px;
height: auto;
}

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.

Sample Input 1

2
0
10
20
30

Sample Output 1

2

There are two optimal connections: 0-20, 10-30 and 0-30, 10-20.
In both connections the total length of the cables is 40.

Sample Input 2

3
3
10
8
7
12
5

Sample Output 2

1

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
#include <vector>
#define REP(i,n) for(int i=0;i<n;i++)
#define MOD 1000000007
using namespace std;
typedef long long ll;

ll modkai(ll l){
  ll res = 1;
  for(int i=1;i<=l;i++){
    res =res*i%MOD;
  }
  return res%MOD;
}
  
int main(){
  ll n;
  cin>>n;
  ll a[n],b[n];
  REP(i,n){
    cin>>a[i];
  }
  REP(i,n){
    cin>>b[i];
  }
  sort(a,a+n);
  sort(b,b+n);
  
  ll ac,bc,ai,bi;
  ac = 0;
  bc = 0;
  ai=0;
  bi=0;
  ll ans = 1;
  while(ai<n||bi<n){
    if(ai>=n){
      ans = ans*modkai(ac)%MOD;
      break;
    }else if(bi>= n){
      ans = ans*modkai(bc)%MOD;
      break;
    }else if(a[ai]<b[bi]){
      ac++;
      ai++;
    }else{
      bc++;
      bi++;
    }
    if(ac==bc){
      ans = ans*modkai(ac)%MOD;
      ac = 0;
      bc = 0;
    }
  }
  
  
  cout<<ans<<endl;
  
  return 0;
}