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.*;
public class Main {
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    ArrayList<Integer> a = new ArrayList<Integer>();
    for(int i=0; i<n; i++){
      a.add(sc.nextInt());
    }
    Collections.sort(a);
    if(n==2){
      System.out.println(Math.abs(a.get(0) - a.get(1)));
      System.exit(0);
    }
    int sa_sum = 0;
    int base_c = a.get(0);
    int base_r = a.get(n-1);
    int base_l = a.get(n-2);
    sa_sum = base_r + base_l - base_c*2;
    for(int i=1; i<n-2; i++){
      int sa_r = Math.abs(a.get(i) - base_r);
      int sa_l = Math.abs(a.get(i) - base_l);
      if(sa_r > sa_l){
        sa_sum += sa_r;
        base_r = a.get(i);
      }
      else{
        sa_sum += sa_l;
        base_l = a.get(i);
      }
    }
    System.out.println(sa_sum);
  }
}