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 (2.7.1) (judge verdict: Wrong Answer)

N,*as=$<.read.split.map(&:to_i)
as = as.sort!
bs = as.dup

a = [as.shift]
loop do
    x = as.pop
    break unless x
    a.unshift x

    x = as.pop
    break unless x
    a.push x

    x = as.shift
    break unless x
    a.unshift x

    x = as.shift
    break unless x
    a.push x
end

ret = 0
a.each_cons(2) do |m,n|
    ret += (m-n).abs
end
ret_a = ret

as = bs
a = [as.pop]
loop do
    x = as.pop
    break unless x
    a.unshift x

    x = as.pop
    break unless x
    a.push x

    x = as.shift
    break unless x
    a.unshift x

    x = as.shift
    break unless x
    a.push x
end

ret = 0
a.each_cons(2) do |m,n|
    ret += (m-n).abs
end

puts [ret_a,ret].max