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: Wrong Answer)

n = gets.to_i

arr = Array.new(n)
n.times do |i|
  arr[i] = gets.to_i
end

arr = arr.sort
sum = 0
((n-1)/2).times do |i|
  sum += 2 * (arr[-i - 1] - arr[i])
end

i = n / 2
if n % 4 == 0
  # 最後の2つは端として1回ずつ計算する
  sum += arr[i + 1] - arr[i]
elsif n % 4 == 2
  sum += arr[i] - arr[i - 1]
elsif n % 4 == 1
  sum += arr[i - 1] - arr[i]
elsif n % 4 == 3
  sum += arr[i] - arr[i + 1]
end
puts sum