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.chomp.to_i
x=[]
for a in 1..n
  x<<gets.chomp.to_i
end
x.sort!
y=[]
for b in 1..n
  if b.odd?
    y<<x.pop
  else
    y<<x.shift
  end
end
z=[]
z<<y.pop
for c in 1..n-1
  z<<y.shift
end
puts "#{z}"
result=0
for d in 1..n-1
  diff=z[d]-z[d-1]
  puts diff.abs
  result=result+diff.abs
end
puts "#{result}"