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: Wrong Answer)

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

int int_sort( const void * a , const void * b ) {
  if( *( int * )a < *( int * )b ) {
    return -1;
  } else if( *( int * )a == *( int * )b ) {
    return 0;
  }
  return 1;
}

int main(void) {
  int N;
  scanf("%d", &N);

  int A[100000];
  for(int i = 0; i < N; i++) {
    scanf("%d", &A[i]);
  }
  if(N == 2) {
    printf("%d\n", abs(A[0] - A[1]));
    return 0;
  }
  qsort((void*)A, N, sizeof(A[0]), int_sort);

  int B[100000];
  int C[100000];
  int pos = N / 2;
  int beg, end;
  int flag;
  int offset;
  B[pos] = A[0];
  beg = 1;
  end = N - 1;
  flag = 1;
  offset = 1;
  while(1) {
    if(flag == 1) {
      B[pos-offset] = A[end--];
      if(end < beg) break;
      B[pos+offset] = A[end--];
      if(end < beg) break;
      offset++;
      flag = 0;
    } else {
      B[pos-offset] = A[beg++];
      if(end < beg) break;
      B[pos+offset] = A[beg++];
      if(end < beg) break;
      offset++;
      flag = 1;
    }
  }
  
  C[pos] = A[N-1];
  beg = 0;
  end = N - 2;
  flag = 0;
  offset = 1;
  while(1) {
    if(flag == 1) {
      C[pos-offset] = A[end--];
      if(end < beg) break;
      C[pos+offset] = A[end--];
      if(end < beg) break;
      offset++;
      flag = 0;
    } else {
      C[pos-offset] = A[beg++];
      if(end < beg) break;
      C[pos+offset] = A[beg++];
      if(end < beg) break;
      offset++;
      flag = 1;
    }
  }
  
  int sumB = 0;
  int x = B[0];
  for(int i = 1; i < N; i++) {
    int y = B[i];
    sumB += abs(x - y);
    x = y;
  }

  int sumC = 0;
  x = C[0];
  for(int i = 1; i < N; i++) {
    int y = C[i];
    sumC += abs(x - y);
    x = y;
  }

  if(sumB < sumC)
    printf("%d\n", sumC);
  else
    printf("%d\n", sumB);
    
  return 0;
}