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.chop.to_i
as = []
n.times do
  as << gets.chop.to_i
end
as.sort!
ans = 0

# 別解
if n.even?
  arr = Array.new((n-2)/2, -2) + [-1, 1] + Array.new((n-2)/2, 2)
  n.times do |i|
    ans += as[i] * arr[i]
  end
  puts ans
else
  arr_1 = Array.new(1 + (n-2)/2, -2) + [1, 1] + Array.new((n-2)/2, 2)
  arr_2 = Array.new((n-2)/2, -2) + [-1, -1] + Array.new(1 + (n-2)/2, 2)
  ans_1, ans_2 = 0, 0
  n.times do |i|
    ans_1 += as[i] * arr_1[i]
  end
  n.times do |i|
    ans_2 += as[i] * arr_2[i]
  end
  puts [ans_1, ans_2].max
end