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 cmpnum(const void * n1, const void * n2) {
	if (*(long *)n1 > *(long *)n2)
	{
		return 1;
	}
	else if (*(long *)n1 < *(long *)n2)
	{
		return -1;
	}
	else
	{
		return 0;
	}
}

int main(void) {

  long n;
  scanf("%ld", &n);
  long a[n];
  for (long i = 0; i < n; i++) {
    scanf("%ld", &a[i]);
  }
  qsort(a, n, sizeof(long), cmpnum);
  long sum1 = a[n-1]-a[0];
  long head = 0;
  long tail = n-1;
  long generated_top = a[0];
  long generated_bottom = a[n-1];
  while (1) {
    head++;
    if (head >= tail) {
      break;
    }
    if (labs(a[head]-generated_top) > labs(a[head]-generated_bottom)) {
      sum1 += labs(a[head]-generated_top);
      generated_top = a[head];
    } else {
      sum1 += labs(a[head]-generated_bottom);
      generated_bottom = a[head];
    }
    tail--;
    if (head >= tail) {
      break;
    }
    if (labs(a[tail]-generated_top) > labs(a[tail]-generated_bottom)) {
      sum1 += labs(a[tail]-generated_top);
      generated_top = a[tail];
    } else {
      sum1 += labs(a[tail]-generated_bottom);
      generated_bottom = a[tail];
    }
  }
  long sum2 = a[n-1]-a[0];
  head = 0;
  tail = n-1;
  generated_top = a[0];
  generated_bottom = a[n-1];
  while (1) {
    tail--;
    if (head >= tail) {
      break;
    }
    if (labs(a[tail]-generated_top) > labs(a[tail]-generated_bottom)) {
      sum2 += labs(a[tail]-generated_top);
      generated_top = a[tail];
    } else {
      sum2 += labs(a[tail]-generated_bottom);
      generated_bottom = a[tail];
    }
    head++;
    if (head >= tail) {
      break;
    }
    if (labs(a[head]-generated_top) > labs(a[head]-generated_bottom)) {
      sum2 += labs(a[head]-generated_top);
      generated_top = a[head];
    } else {
      sum2 += labs(a[head]-generated_bottom);
      generated_bottom = a[head];
    }
  }
  if (sum1 > sum2) {
    printf("%ld\n", sum1);
  } else {
    printf("%ld\n", sum2);
  }

  return 0;
}