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 (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#include <stdlib.h>

int compare_int(const void *a, const void *b)
{
    return *(long long int*)a - *(long long int*)b;
}

int main(){
  int N;
  scanf("%d",&N);
  long long int A[N];
  int i;
  for(i=0;i<N;i++){
    scanf("%lld",&A[i]);
  }
  qsort(A, N, sizeof(long long int), compare_int);
  long long int ans=0;
  if(N%2==0){
    for(i=0;i<N/2-1;i++){
      ans=ans-2*A[i]+2*A[N/2+i+1];
    }
    ans=ans-A[N/2-1];
    ans=ans+A[N/2];
    printf("%lld",ans);
  }else{
    for(i=0;i<(N-3)/2;i++){
      ans=ans-2*A[i]+2*A[i+(N+3)/2];
    }
    if(2*A[(N+1)/2]-A[(N-3)/2]-A[(N-1)/2]>A[(N+1)/2]-2*A[(N-3)/2]+A[(N-1)/2]){
      ans=ans+2*A[(N+1)/2]-A[(N-3)/2]-A[(N-1)/2];
    }else{
      ans=ans+A[(N+1)/2]-2*A[(N-3)/2]+A[(N-1)/2];
    }
    printf("%lld",ans);
  }
  return 0;
}