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)

#!/usr/bin/ruby
# encoding: utf-8

# youtube解説動画による解法を実装する。

n = gets.to_i
$a = Array.new
for i in 0..n-1
  $a[i] = gets.to_i
end

# ascending order
$a.sort!

weight = Array.new(n)
signal1 = Array.new(n)
signal2 = Array.new(n)

# weight を作る
(0..n-1).each do |i|
  if i == 0 || i == n-1 then
    weight[i] = 1
  else
    weight[i] = 2
  end
end

# signal1 を作る
(0..n-1).each do |i|
  if i.odd? then
    signal1[i] = 1
  else
    signal1[i] = -1
  end
end

# signal2 を作る
(0..n-1).each do |i|
  if i.even? then
    signal2[i] = 1
  else
    signal2[i] = -1
  end
end

ws1 = Array.new(n)
ws2 = Array.new(n)

(0..n-1).each do |i|
  ws1[i] = weight[i] * signal1[i]
  ws2[i] = weight[i] * signal2[i]
end

ws1.sort!
ws2.sort!

ans1 = 0
ans2 = 0
for i in 0..n-1
  ans1 += ws1[i] * $a[i]
  ans2 += ws2[i] * $a[i]
end 

if ans1 >= ans2 then
  puts ans1
else
  puts ans2
end