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# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Collections;
using System.Linq;
using System.Numerics;




namespace contest
{

    class contest
    {


        static void Main(string[] args)
        {


            //int n = int.Parse(Console.ReadLine());
            //var input = Console.ReadLine().Split().Select(int.Parse).ToArray();

            //var num = Console.ReadLine().Split().Select(int.Parse).ToArray();




            int n = int.Parse(Console.ReadLine());
            
            
            
            var pc = new int[n];
            for (int i =0; i< n; i++)
            {
                pc[i] = int.Parse(Console.ReadLine());
            }
            var plug = new int[n];
            for (int i = 0; i < n; i++)
            {
                plug[i] = int.Parse(Console.ReadLine());
            }

            var arr = new int[n * 2];
            pc.CopyTo(arr, 0);
            plug.CopyTo(arr, pc.Length);
            Array.Sort(arr);

            var setPC = new HashSet<int>(pc);
            var setPL = new HashSet<int>(plug);

            BigInteger count = 1;

            var que = new Queue<int>();
            bool pl = false;
            bool first = true;



   


            int countPC = 0;
            int countPL = 0;
            for(int i=0; i<2* n; i++)
            {
                int cur = arr[i];

                if(setPC.Contains(cur))
                {
                    if (countPL > 0)
                    {
                        int countTmp = 0;
                        while(i<2*n && setPC.Contains(arr[i]) && countTmp<countPL)
                        {
                            countTmp++;
                            i++;
                        }
                        if (countTmp > 1) count *= calc(countTmp);
                          
                        countPC -= countTmp;

                    }
                    else countPC++;
                }
                else
                {
                    if (countPC > 0)
                    {
                        int countTmp = 0;
                        while (i < 2 * n && setPL.Contains(arr[i]) && countTmp < countPC)
                        {
                            countTmp++;
                            i++;
                        }
                        if (countTmp > 1) count *= calc(countTmp);

                        countPL -= countTmp;
                    }
                    else countPL++;
                }
            }



            long mod = 1000000007;

            count %= mod;

            Console.WriteLine(count);






        }

       public static long calc(int a)
        {
            long result = 1;
            for(int i= a; i>=2; i--)
            {
                result *= (long)i;
            }
            return result;
        }
       

    }

   
    
}