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: Accepted)

using System;

namespace CODE_FESTIVAL_2016_Grand_Final_Parallel__A___1D_Matching
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = int.Parse(Console.ReadLine());
            long MOD = 1000000007;

            var computers = new int[N];
            for (int i = 0; i < N; i++) computers[i] = int.Parse(Console.ReadLine());
            Array.Sort(computers);

            var powers = new int[N];
            for (int i = 0; i < N; i++) powers[i] = int.Parse(Console.ReadLine());
            Array.Sort(powers);

            var isPower = new bool[2 * N];
            var p = 0; var c = 0;
            for (int i = 0; i < 2 * N; i++)
            {
                if (p == N)
                {
                    isPower[i] = false;
                    continue;
                }
                if (c == N)
                {
                    isPower[i] = true;
                    continue;
                }

                if (powers[p] < computers[c])
                {
                    isPower[i] = true;
                    p++;
                }
                else
                {
                    isPower[i] = false;
                    c++;
                }
            }

            long match = 1;
            var pow = 0; var comp = 0;
            for (int i = 0; i < 2 * N; i++)
            {
                if (isPower[i])
                {
                    if (pow < comp) match = match * (comp - pow) % MOD;
                    pow++;
                }
                else
                {
                    if (comp < pow) match = match * (pow - comp) % MOD;
                    comp++;
                }
            }
            Console.WriteLine(match);
        }
    }
}