Problem:
Score : 400 points

Problem Statement

You are given N integers; the i-th of them is A_i.
Find the maximum possible sum of the absolute differences between the adjacent elements after arranging these integers in a row in any order you like.

Constraints

2 \leq N \leq 10^5

1 \leq A_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1
:
A_N

Output

Print the maximum possible sum of the absolute differences between the adjacent elements after arranging the given integers in a row in any order you like.

Sample Input 1

5
6
8
1
2
3

Sample Output 1

21

When the integers are arranged as 3,8,1,6,2, the sum of the absolute differences between the adjacent elements is |3 - 8| + |8 - 1| + |1 - 6| + |6 - 2| = 21. This is the maximum possible sum.

Sample Input 2

6
3
1
4
1
5
9

Sample Output 2

25

Sample Input 3

3
5
5
1

Sample Output 3

8

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

import java.util.*;

class Main{
	public static void main(String[] $){
		Scanner s=new Scanner(System.in);
		int n=s.nextInt();

		int[] a=new int[n];
		Arrays.setAll(a,i->Integer.parseInt(s.next()));
		Arrays.sort(a);
		int b=a[0],c=a[n-1];

		int l=1,r=n-2;

		int v=c-b;

		while(l<=r){
			int w=0;
			w=Math.max(w,Math.abs(b-a[l]));
			w=Math.max(w,Math.abs(b-a[r]));
			w=Math.max(w,Math.abs(c-a[l]));
			w=Math.max(w,Math.abs(c-a[r]));
			v+=w;
			//System.err.println(w);
			if(w==Math.abs(b-a[l])){
				b=a[l++];
				continue;
			}
			if(w==Math.abs(b-a[r])){
				b=a[r--];
				continue;
			}
			if(w==Math.abs(c-a[l])){
				c=a[l++];
				continue;
			}
			if(w==Math.abs(c-a[r])){
				c=a[r--];
				continue;
			}
		}
		System.out.println(v);
	}
}