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.*;
import java.util.Arrays;
public class Main {
    public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] a = new int[n];
        for(int i = 0; i < n; i++){
            a[i] = sc.nextInt();
        }
        Arrays.sort(a);
        int ans = 0;
        int x = 1; 
        int y = n-1;
        if(n%2 == 0){
            int max1 = Math.max(a[n/2 - 1] - a[0], a[n-1] - a[n/2 - 1]);
            int max2 = Math.max(a[n/2] - a[0], a[n-1] - a[n/2]);
            int max = Math.max(max1, max2);
            if(max == a[n/2 - 1] - a[0]){
                a[n/2 - 1] = 0;
                Arrays.sort(a);
                ans += max;
                while(x < y){
                    ans += a[y] - a[x];
                    x++;
                    if(x < y){
                        ans += a[y] - a[x];
                        y--;
                    }
                }
            }else if(max == a[n/2] - a[0]){
                a[n/2] = 0;
                Arrays.sort(a);
                ans += max;
                while(x < y){
                    ans += a[y] - a[x];
                    x++;
                    if(x < y){
                        ans += a[y] - a[x];
                        y--;
                    }
                }
            }else if(max == a[n-1] - a[n/2 - 1]){
                a[n/2 - 1] = 0;
                Arrays.sort(a);
                ans += max;
                while(x < y){
                    ans += a[y] - a[x];
                    y--;
                    if(x < y){
                        ans += a[y] - a[x];
                        x++;
                    }
                    
                }
            }else{
                a[n/2] = 0;
                Arrays.sort(a);
                ans += max;
                while(x < y){
                    ans += a[y] - a[x];
                    y--;
                    if(x < y){
                        ans += a[y] - a[x];
                        x++;
                    }
                }
            }
        }else{
            int max3 = Math.max(a[n/2] - a[0], a[n-1] - a[n/2]);
            ans += max3;
            if(max3 == a[n/2] - a[0]){
                a[n/2] = 0;
                Arrays.sort(a);
                while(x < y){
                    ans += a[y] - a[x];
                    x++;
                    if(x < y){
                        ans += a[y] - a[x];
                        y--;
                    }
                }
            }else{
                a[n/2] = 0;
                Arrays.sort(a);
                while(x < y){
                    ans += a[y] - a[x];
                    y--;
                    if(x < y){
                        ans += a[y] - a[x];
                        x++;
                    }
                }
            }
        }
        System.out.println(ans);
    }
}