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)

nu = gets.to_i
ar = Array.new(nu, 0)
for i in 0..nu - 1
  ar[i] = gets.to_i
end
nu1 = ar.sort

ans = 0
inst1 = nu1[0]
inst2 = nu1[0]
nu1.delete_at(0)
nu -= 1
count = 0
while count < nu - 1
  count += 1
  if count % 4 == 1
    ans += nu1[-1] - inst1
    inst1 = nu1[-1]
    nu1.delete_at(-1)
  elsif count % 4 == 2
    ans += nu1[-1] - inst2
    inst2 = nu1[-1]
    nu1.delete_at(-1)
  elsif count % 4 == 3
    ans += inst1 - nu1[0]
    inst1 = nu1[0]
    nu1.delete_at(0)
  elsif count % 4 == 0
    ans += inst2 - nu1[0]
    inst2 = nu1[0]
    nu1.delete_at(0)
  end
end

if (nu1[0] - inst1).abs >= (nu1[0] - inst2).abs
  ans += (nu1[0] - inst1).abs
else
  ans += (nu1[0] - inst2).abs
end


puts ans