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 Ruby (2.7.1) (judge verdict: Runtime Error)

class Problem
  attr_accessor *(?a..?z).to_a.map(&:to_sym)
  def initialize
    @n = gets.to_s.to_i
    @m = n / 2
    @a = Array.new(n){ gets.to_s.to_i }.sort
    @top_heavy = a[m+1] - a[m] < a[m] - a[m-1]
  end

  def solve
    ans = 0
    n.times do |i|
      ans += a[i] * weight(i)
      # print "(#{a[i]} * #{weight(i)}) + "
    end
    ans
  end

  def weight(i)
    return weight_even(i) if n.even?
    return weight_odd_top(i) if @top_heavy
    return weight_odd_bottom(i)
  end
    
  def weight_even(i)
    return -2 if i < n / 2 - 1
    return -1 if i == n / 2 - 1
    return 1 if i == n / 2
    return 2
  end
  
  def weight_odd_top(i)
    return -2 if i < m
    return 1 if i == m
    return 1 if i == m + 1
    return 2
  end
  
  def weight_odd_bottom(i)
    return -2 if i < m - 1
    return -1 if i == m - 1
    return -1 if i == m
    return 2
  end

  def show(ans)
    puts ans
  end
end

Problem.new.instance_eval do
  show(solve)
end