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 |i|
  a[i] = gets.chomp.to_i
end

def abs(n)
  return -n if n<0
  return n
end

a = a.sort
left = []
right = []

left[0] = a[0]
right[0] = a[0]
tmp = 2
(n-1).downto(1) do |i|
  if tmp%2 == 0
    left[tmp/2] = a[i]
  else
    right[tmp/2] = a[i]
  end
  tmp += 1
end


tmp = left[0]
sum = 0
for i in left do
  sum += abs(tmp-i)
  tmp = i
end

tmp = left[0]

for i in right do
  sum += abs(tmp-i)
  tmp = i
end

puts sum