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

l = 0
r = N-1
ret = as[r]-as[l]
(N/2-1).times do
    ret += (as[l+1] - as[r]).abs
    ret += (as[l] - as[r-1]).abs
    l += 1
    r -= 1
end

if N.odd?
    center = N/2
    ret += [
        (as[center]-as[center-1]).abs,
        (as[center]-as[center+1]).abs,
    ].max
end

puts ret