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 = n.times.map{gets.to_i}.sort

if n==2
  p (a[0]-a[1]).abs
  exit
end

ans = 0
l = 1
r = n-2
#
x = [a[-1],a[0]]
ans += (a[-1]-a[0]).abs
#
(n-2).times.map{|i|
  x.sort!
  if (x[1]-a[l]).abs > (x[0]-a[r]).abs
    ans += (x[1]-a[l]).abs
    x[1] = a[l]
    l += 1
  else
    ans += (x[0]-a[r]).abs
    x[0] = a[r]
    r -= 1
  end
}
ans

p ans