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 {a << gets.to_i}
a.sort!

m = n/2
if n.odd?
    x = -2 * a[0, m].inject(0, :+) + a[m] + a[m + 1] + 2 * a[m + 2, m - 1].inject(0, :+)
    y = -2 * a[0, m - 1].inject(0, :+) - a[m - 1] - a[m] + 2 * a[m + 1, m].inject(0, :+)
    puts x > y ? x : y
else
    puts -2 * a[0, m - 1].inject(0, :+) - a[m - 1] + a[n/2] + 2 * a[m + 1, m - 1].inject(0, :+)
end