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: Wrong Answer)

N = gets.to_i
A = Array.new(N)
N.times do |n|
  A[n] = gets.to_i
end

A.sort!

a = A.clone

size = A.size

is_even = (size % 2 == 0)

if is_even
  c = size / 2
  r = c
  l = c-1
  c.times do |i|
    if i % 2 == 0
      a[r] = A.pop
      a[l] = A.shift
      r += 1
      l -= 1
    else
      a[r] = A.shift
      a[l] = A.pop
      r += 1
      l -= 1
    end
  end
else
  c = size / 2
  r = c+1
  l = c-1
  a[c] = A.shift
  c.times do |i|
    if i % 2 == 0
      a[r] = A.pop
      a[l] = A.pop
    else
      a[r] = A.shift
      a[l] = A.shift
    end
    r += 1
    l -= 1
  end
end

sum = 0
(1...size).each do |i|
  sum += (a[i] - a[i-1]).abs
end

puts sum