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 = STDIN.gets.to_i
numbers = []

n.times do
  numbers << STDIN.gets.to_i
end

coefficients = []
if n % 2 == 0
  coefficients << -1
  coefficients << 1
else
  coefficients << -1
  coefficients << -1
end

(n - 2).times do |i|
  if i % 2 == 0
    coefficients << 2
  else
    coefficients << -2
  end
end

sum = coefficients.sort.zip(numbers.sort).reduce(0) do |accum, (coefficient, number)|
  accum + coefficient * number
end

puts sum