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.to_i
A = N.times.map { gets.to_i }.sort

a = A.dup
b = A.dup

listA = Array.new(N, -1)
listB = Array.new(N, -1)

1.step(N - 1, 2) do |i|
  listA[i] = a.pop
  listB[i] = b.shift
end

2.step(N - 1, 2) do |i|
  listA[i] = a.shift
  listB[i] = b.pop
end

listA[0] = a.pop
listB[0] = b.pop

sumA = listA.each_cons(2).map { |i, j| (i - j).abs }.inject(:+)
sumB = listB.each_cons(2).map { |i, j| (i - j).abs }.inject(:+)

puts [sumA, sumB].max