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: Time Limit Exceeded)

#include<iostream>
#include<algorithm>
using namespace std;
#define N 100010
int a[N];
int b[N];
int n;
void test()
{
    int max_ans=0;
    int temp_ans;
    sort(a+1,a+1+n);
    do
    {
        temp_ans=0;
        for(int i=2;i<=n;i++) temp_ans+=abs(a[i]-a[i-1]);
        if(max_ans<temp_ans)
        {
            max_ans=temp_ans;
            for(int i=1;i<=n;i++) b[i]=a[i];
        }

    }while(next_permutation(a+1,a+1+n));
    /*
    for(int i=1;i<=n;i++)
    {
        cout<<b[i]<<" ";
    }
    cout<<endl<<max_ans<<endl;
    */
    cout<<max_ans<<endl;
}
int main()
{
    ios::sync_with_stdio(false);
    while(cin>>n)
    {
        for(int i=1;i<=n;i++)
        {
            cin>>a[i];
        }
        test();
    }
}