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)

num = []
ans = 0

n = gets.to_i
n.times do
  num << gets.to_i
end

num.sort!
smaller = num[0..(n/2.to_f).ceil-1]
larger = num[(n/2.to_f).ceil..n].reverse

if center = (n % 4 == 3) && (num[n/2] - num[0] < num[-1] - num[n/2])

  num.clear
  num[0] = larger.shift

  while smaller.size != 0 || larger.size != 0

    if smaller.size == 1 && larger.size == 1

      larger<<smaller[0]
      smaller.clear

    end

    a = larger.shift
    b = smaller.shift
    c = larger.shift
    d = smaller.shift

    b != nil && num << b
    d != nil && num.unshift(d)
    a != nil && num << a
    c != nil && num.unshift(c)

  end

else

  num.clear
  num[0] = smaller.shift

  while smaller.size != 0 || larger.size != 0

    if smaller.size == 1 && larger.size == 1

      larger<<smaller[0]
      smaller.clear

    end

    a = larger.shift
    b = smaller.shift
    c = larger.shift
    d = smaller.shift

    a != nil && num << a
    c != nil && num.unshift(c)
    b != nil && num << b
    d != nil && num.unshift(d)

  end

end

for i in 0..n-2
  ans += (num[i+1]-num[i]).abs
end

p ans