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


if n.even?
  u, v = a[0, a.size/2], a[a.size/2, a.size]
  puts (v.inject(0,&:+)*2 - v.min) - (u.inject(0,&:+)*2 - u.max)
else
  u1, v1 = a[0, a.size/2], a[a.size/2, a.size]
  u2, v2 = a[0, (a.size+1)/2], a[(a.size+1)/2, a.size]
  puts [
    (v1.inject(0,&:+)*2 - v1[0,2].inject(0,&:+)) - (u1.inject(0,&:+)*2),
    (v2.inject(0,&:+)*2) - (u2.inject(0,&:+)*2 - u2.reverse[0,2].inject(0,&:+))
  ].max
end