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)

ary1 = []
ary2 = []
ans1 = 0
ans2 = 0

n, *ary0 = $<.map &:to_i

ary0.sort!
ary1[0] = ary0[0]
ary2[0] = ary0[-1]

for i in 0 .. n-2

  case i%4
  when 0
    ary1.unshift( ary0[-(i/4*2+1)] )
    ary2.unshift( ary0[i/4*2] )
  when 1
    ary1 << ary0[-(i/4*2+2)]
    ary2 << ary0[i/4*2+1]
  when 2
    ary1.unshift( ary0[i/4*2+1] )
    ary2.unshift( ary0[-(i/4*2+2)] )
  when 3
    ary1 << ary0[i/4*2+2]
    ary2 << ary0[-(i/4*2+3)]
  end

end

for i in 0 .. n-2
  ans1 += ( ary1[i+1] - ary1[i] ).abs
  ans2 += ( ary2[i+1] - ary2[i] ).abs
end

puts ans1 > ans2 ? ans1 : ans2