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: Time Limit Exceeded)


n = gets.to_i
a = []
for i in 1..n
  a << gets.to_i
end

a = a.sort
ls = [a[0], a[-1]]
lmin = true
rmin = false
a = a[1..(a.size-2)]

while a.size > 0
  if lmin
    ldif = a[-1] - ls[0]
  else
    ldif = ls[-1] - a[0]
  end
  if rmin
    rdif = a[-1] - ls[0]
  else
    rdif = ls[-1] - a[0]
  end

  if rdif > ldif
    if rmin
      ls << a[-1]
      a = a[0,a.size-1]
      rmin = false
    else
      ls << a[0]
      a = a[1,a.size-1]
      rmin = true
    end
  else
    if lmin
      ls = [ a[-1] ].concat(ls)
      a = a[0,a.size-1]
      lmin = false
    else
      ls = [ a[0] ].concat(ls)
      a = a[1,a.size-1]
      lmin = true
    end
  end
end

sum = 0
for i in 0..(ls.size-2)
  sum += (ls[i+1]-ls[i]).abs
end
print sum