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: Accepted)

def pop_back_gen(nums)
  Fiber.new do
    nums.reverse_each do |i|
      Fiber.yield(i)
    end
  end
end

def pop_front_gen(nums)
  Fiber.new do
    nums.each do |i|
      Fiber.yield(i)
    end
  end
end

def main
  n = gets.chomp.to_i

  nums = Array.new(n)
  n.times do |i|
    nums[i] = gets.chomp.to_i
  end
  # puts nums

  nums.sort!

  # 先頭と末尾から値を取り出すgenerator
  front_gen = pop_front_gen(nums)
  back_gen = pop_back_gen(nums)

  # 中央値からスタート
  last_num = nums[n / 2]

  # 先頭（最小値）から取るパターン
  len_min_first = 0
  0.upto(n-2) do |i|
    cur_num = if i.even?
                # 前を取る
                front_gen.resume
              else
                # 後ろを取る
                back_gen.resume
              end
    len_min_first += (last_num - cur_num).abs
    last_num = cur_num
  end

  front_gen = pop_front_gen(nums)
  back_gen = pop_back_gen(nums)

  # 中央値からスタート
  last_num = nums[n / 2]

  # 末尾（最大値）から取るパターン
  len_max_first = 0
  1.upto(n-1) do |i|
    cur_num = if i.even?
                # 前を取る
                front_gen.resume
              else
                # 後ろを取る
                back_gen.resume
              end
    len_max_first += (last_num - cur_num).abs
    last_num = cur_num
  end

  puts [len_min_first, len_max_first].max
end

if __FILE__ == $0
  main
end