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,*a=$<.map(&:to_i)
a.sort!
s = 0
res = -1
if n&1 == 1
  med = a[n/2]

  a = a[0,n/2].zip(a[n/2+1,n/2].reverse).flatten

  [a,a.rotate,a.rotate(-1)].each{|x|
    s = 0
    x.each_cons(2){|x,y|s += (x-y).abs}
    res = [res,(med-x[0]).abs+s,(x[-1]-med).abs+s].max
  }

else
  a = a[0,n/2].zip(a[n/2,n/2].reverse).flatten
  [a,a.rotate,a.rotate(-1)].each{|x|

    s = 0
    x.each_cons(2){|x,y|s += (x-y).abs}
    res = [res,s].max
  }
end
p res