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();
        Deque<Long> deque1 = new ArrayDeque<>();
        Deque<Long> deque2 = new ArrayDeque<>();
        long[] a = new long[n];
        long[] b = new long[n];
        long[] c = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = scanner.nextInt();
            deque1.add(a[i]);
            deque2.add(a[i]);
        }
        Arrays.sort(a);
        b[0] = c[0] = a[n / 2];
        b[n - 1] = c[n - 1] = n % 2 == 0 ? a[n / 2 - 1] : a[n / 2] - a[n / 2 - 1] > a[n / 2 + 1] - a[n / 2] ? a[n / 2 + 1] : a[n / 2 - 1];
        deque1.remove(b[0]);
        deque1.remove(b[n - 1]);
        deque2.remove(b[0]);
        deque2.remove(b[n - 1]);

        boolean f = true;
        for (int i = 1; i < n - 1; i++) {
            long j = f ? deque1.pollFirst() : deque1.pollLast();
            long k = f ? deque2.pollLast() : deque2.pollFirst();
            b[i] = j;
            c[i] = k;
            f = !f;
        }

        long ans1 = 0, ans2 = 0;
        for (int i = 1; i < n; i++) {
            ans1 += Math.abs(b[i - 1] - b[i]);
            ans2 += Math.abs(c[i - 1] - c[i]);
        }

        System.out.println(Math.max(ans1, ans2));
    }
}