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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.Scanner;
import java.util.Arrays;
public class Main{
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		long[] a=new long[n];
		long[] b=new long[n];
		long mod=1000000007;
		for(int i=0; i<n; i++){
			a[i]=sc.nextLong();
		}
		for(int i=0; i<n; i++){
			b[i]=sc.nextLong();
		}
		Arrays.sort(a);
		Arrays.sort(b);
		int oa=0;
		int ob=0;
		int ca=0;
		int cb=0;
		long ans=1;
		for(int i=0; i<2*n; i++){
			if(a[oa]<b[ob]){
				if(oa==n-1){
					oa=0;
					a[oa]=Long.MAX_VALUE;
				}else{
					oa++;
				}
				ca++;
			}else{
				if(ob==n-1){
					ob=0;
					b[ob]=Long.MAX_VALUE;
				}else{
					ob++;
				}
				cb++;
			}
			if(ca==cb){
				
				while(ca>0){
					ans*=ca;
					ca--;
					ans%=mod;
				}
				ca=0;
				cb=0;
			}
		}
		System.out.println(ans);
	}
}