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: Accepted)

N = gets.to_i
A = $<.map &:to_i
A.sort!

def f(_a)
  a = _a.dup
  res = [a.pop]
  while !a.empty?
    res.unshift a.shift
    res << a.shift

    res.unshift a.pop
    res << a.pop
  end
  res.compact
end

def f2(_a)
  a = _a.dup
  res = [a.pop]
  while !a.empty?
    res << a.shift
    res.unshift a.shift

    res << a.pop
    res.unshift a.pop
  end
  res.compact!
end

def g(a)
  a.each_cons(2).inject(0){|r, (a, b)|
    r + (a - b).abs
  }
end

p [g(f(A)), g(f(A.reverse))].max