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.chomp.to_i
A = STDIN.readlines.map(&:to_i)


arr1 = A.sort
arr2 = arr1.dup
# puts arr.join(',')

result1 = [arr1.shift]
result2 = [arr2.pop]

i = 0

while arr1.length > 0
  case i % 4
  when 0
    result1.push(arr1.pop)
    result2.push(arr2.shift)
  when 1
    result1.unshift(arr1.pop)
    result2.unshift(arr2.shift)
  when 2
    result1.unshift(arr1.shift)
    result2.unshift(arr2.pop)
  when 3
    result1.push(arr1.shift)
    result2.push(arr2.pop)
  end
  i += 1
  # puts result.join(',')
end

# puts result1.join(',')
# puts result2.join(',')

diff1 = 0
diff2 = 0
result1.each_cons(2) do |arr|
  diff1 += (arr[0] - arr[1]).abs
end

result2.each_cons(2) do |arr|
  diff2 += (arr[0] - arr[1]).abs
end

puts diff1 > diff2 ? diff1 : diff2