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: Wrong Answer)

N = gets.to_i
A = N.times.map { gets.to_i }.sort
B = [A.shift]
(N - 1).times do |i|
  x = i.even? ? A.pop : A.shift
  if (B.last - x).abs < (B.first - x).abs
    B.unshift x
  else
    B.push x
  end
end
ans1 = 0
(N - 1).times  do |i|
  ans1 += (B[i] - B[i + 1]).abs
end
C = B.sort
D = [C.pop]
(N - 1).times do |i|
  x = i.even? ? C.shift : C.pop
  if (D.last - x).abs < (D.first - x).abs
    D.unshift x
  else
    D.push x
  end
end
ans2 = 0
(N - 1).times do |i|
  ans2 += (D[i] - D[i + 1]).abs
end
puts [ans1, ans2].max