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 = gets.to_i
a = n.times.map{gets.to_i}.sort
ans = 0
l,r = a[-1],a[0]
for i in 1..n/2-1
  if (l-a[i]).abs > (r-a[i]).abs
    ans += (l-a[i]).abs
    l = a[i]
  else
    ans += (r-a[i]).abs
    r = a[i]
  end
  if (l-a[-1-i]).abs > (r-a[-1-i]).abs
    ans += (l-a[-1-i]).abs
    l = a[-1-i]
  else
    ans += (r-a[-1-i]).abs
    r = a[-1-i]
  end
end
if n%2 == 1
  ans += [(l-a[n/2]).abs,(r-a[n/2]).abs].max
end
puts ans+a[-1]-a[0]