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 (2.3.3) (judge verdict: Runtime Error)

n = gets.to_i
a = Array.new(n)
(0..(n-1)).each do |i|
  a[i] = gets.to_i
end


if n == 2
  a = a.sort
  p a[1]-a[0]
  return
end

if n == 3
  a = a.sort
  p [(a[2]*2-a[0]-a[1]), (a[2]+a[1]-a[0]*2)].max
  return
end

if a.length.odd?
  a = a.sort!.each_slice(a.length / 2 + 1).to_a
else
  a = a.sort!.each_slice(a.length / 2).to_a
end

a1 = a[0]
a2 = a[1].sort! {|x,y| y<=>x}

sum = 0
l = a1.length
if n.odd?
  (0..l-1).each do |i|
    if i == 0
      sum += (a2[0] + a2[1] - a1[0]*2)
    elsif i == (l-1) || i == (l-2)
      sum += (a2[i-1] - a1[i])
    else
      sum += (a2[i+1] + a2[i-1] - a1[i]*2)
    end
  end
else
  (0..l-1).each do |i|
    if i == 0
      sum += (a2[0] + a2[1] - a1[0]*2)
    elsif i == (l-1)
      sum += (a2[i-1] - a1[i])
    else
      sum += (a2[i+1] + a2[i-1] - a1[i]*2)
    end
  end
end

p sum