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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.util.*;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        long[] a = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = sc.nextLong();
        }
        Arrays.sort(a);
        long ans = 0L;
        int m, sm;
        if(n % 2 == 0){
            m = n/2;
            sm = m-1;
        }else{
            m = n/2;
            sm = Math.abs(a[m-1]-a[m]) < Math.abs(a[m+1]-a[m])
                    ? m-1 : m+1;
        }
        for (int i = 0; i < n; i++) {
            ans += Math.abs(a[m] - a[i]) * 2;
        }
        ans -= Math.abs(a[m] - a[sm]);
        System.out.println(ans);
        sc.close();

    }

}