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.chomp.to_i
a = []
n.times do
  a << gets.chomp.to_i
end

if n == 2
  puts (a[1] - a[0]).abs
  exit
end

a.sort!
center = a.shift
left = a.pop
right = a.pop

ans = 0
ans += (center - left).abs
ans += (center - right).abs

flag = true
loop do
  break if a.empty?
  if a.length == 1
    sum1 = (left - a[0]).abs
    sum2 = (right - a[0]).abs
    if sum1 >= sum2
      ans += sum1
    else
      ans += sum2
    end
    break
  end
  if flag
    nl = a.shift
    nr = a.shift
    sum1 = (left - nl).abs + (right - nr).abs
    sum2 = (left - nr).abs + (right - nl).abs
    if sum1 >= sum2
      ans += sum1
    else
      ans += sum2
    end
    left = nl
    right = nr
    flag = false
  else
    nl = a.pop
    nr = a.pop
    sum1 = (left - nl).abs + (right - nr).abs
    sum2 = (left - nr).abs + (right - nl).abs
    if sum1 >= sum2
      ans += sum1
    else
      ans += sum2
    end
    left = nl
    right = nr
    flag = true
  end
end
puts ans