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 Scala (2.11.7) (judge verdict: Accepted)

import scala.io.StdIn
object Main extends App {
  val n = StdIn.readInt
  val as = (1 to n).map(i => StdIn.readLong).sorted.toArray
  def sum(begin: Int, end: Int) = (begin to end).map(i => as(i)).sum

  val m = n / 2
  println(if (n % 2 == 1) {
    (sum(m + 2, n - 1) * 2 + as(m + 1)) - (sum(0, m - 2) * 2 + as(m - 1)) +
    Math.max(as(m + 1) - as(m), as(m) - as(m - 1))
  } else {
    (sum(m + 1, n - 1) * 2 + as(m)) - (sum(0, m - 2) * 2 + as(m - 1))
  })
}