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 {
    static Scanner scanner = new Scanner(System.in);

    public static void main(String[]$) {
        int n = scanner.nextInt();
        long[] a = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = scanner.nextInt();
        }
        Arrays.sort(a);

        long ans = 0;
        for (int i = 0; i < n / 2; i++) {
            if (n % 2 == 0) {
                ans += a[n - i - 1] - a[n / 2 - i - 1] + (i == n / 2 - 1 ? 0 : a[n - i - 1] - a[n / 2 - i - 2]);
            } else if (a[n / 2 + 1] - a[n / 2] == a[n / 2] - a[n / 2 - 1]) {
                ans += 2 * a[n - i - 1] - a[i] - a[i + 1];
            } else if (a[n / 2 + 1] - a[n / 2] > a[n / 2] - a[n / 2 - 1]) {
                ans += 2 * a[n - i - 1] - (i == 0 ? a[n / 2] : a[i - 1]) - a[i];
            } else {
                ans += -2 * a[i] + (i == 0 ? a[n - 1] : a[n / 2 + i - 1]) + a[n / 2 + i];
            }
        }
        System.out.println(ans);
    }
}