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 = N.times.map { gets.to_i }.sort

list = Array.new(N)
n = N / 2
list[n] = A.shift

a = -1
d = 1

1.upto(N - 1) do |i|
  if d.even?
    list[n + a * d] = A.shift
  else
    list[n + a * d] = A.pop
  end

  if i.even?
    d += 1
  end

  a *= -1
end

ans = 0

list.each_cons(2) do |a, b|
  ans += (a - b).abs
end

puts ans