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 do
    a << gets.to_i
end
a.sort!

ans = 0
if n % 2 == 0
    (n/2+1).upto(n-1) do |i|
        ans += a[i] * 2    
    end

    ans += a[n/2]
    (0).upto(n/2-2) do |i|
        ans -= a[i] * 2    
    end
    ans -= a[n/2-1]
else
    (n/2+1).upto(n-1) do |i|
        ans += a[i] * 2    
    end

    (0).upto(n/2-2) do |i|
        ans -= a[i] * 2    
    end
    ans -= a[n/2]
    ans -= a[n/2-1]

    tmp = ans
    ans = 0

    (n/2+2).upto(n-1) do |i|
        ans += a[i] * 2    
    end
    ans += a[n/2]
    ans += a[n/2+1]

    (0).upto(n/2-1) do |i|
        ans -= a[i] * 2    
    end

    ans = tmp if tmp > ans

end
puts ans