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: Accepted)

N=gets.to_i
array=[]
N.times do
    a=gets.to_i
    array.push(a)
end
array=array.sort
ret1=0
array.each_with_index do |a, i|
    if (i+1)*2 < N
        ret1-=2*a
    elsif (i+1)*2 == N
        ret1-=a
    elsif i*2-1<=N
        ret1+=a
    else
        ret1+=2*a
    end
end
ret2=0
array.reverse.each_with_index do |a, i|
    if (i+1)*2 < N
        ret2+=2*a
    elsif (i+1)*2 == N
        ret2+=a
    elsif i*2-1<=N
        ret2-=a
    else
        ret2-=2*a
    end
end
puts ret1 > ret2 ? ret1 : ret2