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: Accepted)

import java.util.*;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        long[] odd = new long[n - n/2];
        long[] even = new long[n/2];
        Long[] nums = new Long[n];
        for(int i = 0; i < n; i++) {
            nums[i] = sc.nextLong();
        }
        Arrays.sort(nums);
        int oddIndex = 0;
        int evenIndex = 0;
        for(int i = 0; i < n; i++) {
            if(i % 2 == 0) {
                odd[oddIndex] = nums[i];
                oddIndex++;
            } else {
                even[evenIndex] = nums[i];
                evenIndex++;
            }
        }
        long[] newNums = new long[n];
        int middle = n - n/2;
        long count = 0;
        int evenStart = 0;
        int evenEnd = even.length-1;
        for(int i = middle; i < n; i++) {
            if(count % 2 == 0) {
                newNums[i] = even[evenEnd];
                evenEnd--;
            } else {
                newNums[i] = even[evenStart];
                evenStart++;
            }
            count++;
        }
        count = 0;
        int oddStart = 0;
        int oddEnd = odd.length-1;
        for(int i = middle-1; i >= 0; i--) {
            if(count % 2 == 0) {
                newNums[i] = odd[oddStart];
                oddStart++;
            } else {
                newNums[i] = odd[oddEnd];
                oddEnd--;
            }
            count++;
        }
        long sum1 = 0;
        long prev = newNums[0];
        for(int i = 1; i < n; i++) {
            long current = newNums[i];
            sum1 += Math.abs(prev - current);
            prev = current;
        }


        Arrays.sort(nums, Collections.reverseOrder());
        oddIndex = 0;
        evenIndex = 0;
        for(int i = 0; i < n; i++) {
            if(i % 2 == 0) {
                odd[oddIndex] = nums[i];
                oddIndex++;
            } else {
                even[evenIndex] = nums[i];
                evenIndex++;
            }
        }
        middle = n - n/2;
        count = 0;
        evenStart = 0;
        evenEnd = even.length-1;
        for(int i = middle; i < n; i++) {
            if(count % 2 == 0) {
                newNums[i] = even[evenEnd];
                evenEnd--;
            } else {
                newNums[i] = even[evenStart];
                evenStart++;
            }
            count++;
        }
        count = 0;
        oddStart = 0;
        oddEnd = odd.length-1;
        for(int i = middle-1; i >= 0; i--) {
            if(count % 2 == 0) {
                newNums[i] = odd[oddStart];
                oddStart++;
            } else {
                newNums[i] = odd[oddEnd];
                oddEnd--;
            }
            count++;
        }
        long sum2 = 0;
        prev = newNums[0];
        for(int i = 1; i < n; i++) {
            long current = newNums[i];
            sum2 += Math.abs(prev - current);
            prev = current;
        }

        System.out.println(Math.max(sum1, sum2));
    }
}