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
c = Array.new(n){|i|
  if i < n/2
    -2
  else
    2
  end
}
ans = 0

if n%2 == 0
  c[n/2-1] = -1
  c[n/2] = 1
  for i in 0..n-1
    ans += a[i]*c[i]
  end
  puts ans
else
  temp = 0
  c[n/2] = c[n/2+1] = 1
  for i in 0..n-1
    temp += a[i]*c[i]
  end
  c[n/2-1] = c[n/2] = -1
  c[n/2+1] = 2
  for i in 0..n-1
    ans += a[i]*c[i]
  end
  puts [ans,temp].max
end