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.chomp.to_i
a_arr = n.times.map { gets.chomp.to_i }.sort_by{|a| -a}
a_arr2 = a_arr.reverse

def xxx(arr)
  a = arr.shift
  result = [a]
  while arr.length > 0 do
    b = arr.pop
    if (result[0] - b).abs > (result[-1] - b).abs
      result.unshift(b)
    else
      result.push(b)
    end
    break if arr.length == 0
    c = arr.shift
    if (result[0] - c).abs > (result[-1] - c).abs
      result.unshift(c)
    else
      result.push(c)
    end
  end
  ans = 0
  result.each_cons(2) do |r1, r2|
    ans += (r1 - r2).abs
  end
  ans
end

puts [xxx(a_arr), xxx(a_arr2)].max