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=[]
b=[]
n.times{a<<gets.to_i}
a.sort!
if a.size%2==0
  count=0
  while a.size!=0
    if count%2==0
      b.insert 0,a[0]
      a.delete_at 0
      b.insert -1,a[-1]
      a.delete_at -1
    else
      b.insert -1,a[0]
      a.delete_at 0
      b.insert 0,a[-1]
      a.delete_at -1
    end
    count+=1
  end
else
  count=0
  b.insert 0,a[0]
  a.delete_at 0
  while a.size!=0
    b.insert -1*(count+1),a[0]
    a.delete_at 0
    b.insert  count,a[0]
    a.delete_at 0
    count+=1
  end
end
puts b.join " "
ans=0
(n-1).times{|i|
  ans+=(b[i+1]-b[i]).abs
}
puts ans