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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;

int main(){

    int n;
    cin >> n;
    vector<int> a(n);
    vector<int> ans1(n);
    vector<int> ans2(n);
    for(int i = 0; i < n; i++) cin >> a[i];

    sort(a.begin(), a.end());

    if(n % 2 == 1){
        int half = n / 2;
        int left, right;
        int count;

        ans1[0] = a[half];
        left = 0, right = n - 1;
        count = 1;
        while(true){
            ans1[count] = a[right];
            right--;
            count++;
            if(count == n) break;
            ans1[count] = a[left];
            left++;
            count++;
            if(count == n) break;
        }

        ans2[0] = a[half];
        left = 0, right = n - 1;
        count = 1;
        while(true){
            ans2[count] = a[left];
            left++;
            count++;
            if(count == n) break;
            ans2[count] = a[right];
            right--;
            count++;
            if(count == n) break;
        }
    }else{
        int half = n / 2;
        int left, right;
        int count;

        ans1[0] = a[half];
        left = 0; right = n - 1;
        count = 1;
        while(true){
            ans2[count] = a[left];
            left++;
            count++;
            if(count == n) break;
            ans2[count] = a[right];
            right--;
            count++;
            if(count == n) break;
        }

        ans1[0] = a[half - 1];
        left = 0; right = n - 1;
        count = 1;
        while(true){
            ans1[count] = a[right];
            right--;
            count++;
            if(count == n) break;
            ans1[count] = a[left];
            left++;
            count++;
            if(count == n) break;
        }
    }

    int sum1 = 0, sum2 = 0;
    for(int i = 0; i < n - 1; i++) sum1 += abs(ans1[i + 1] - ans1[i]);
    for(int i = 0; i < n - 1; i++) sum2 += abs(ans2[i + 1] - ans2[i]);
    cout << max(sum1, sum2) << endl;

    return 0;
}