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

def calc(list)
	prev = list[0]
	sum = 0
	list[1..-1].each{|n|
		sum += (prev - n).abs
		prev = n
	}
	sum
end

list = []
N.times{
	list << gets.to_i
}

list.sort!

def arrange(list)
	first = 0
	last = N - 1
	result = [list[first]]
	first += 1
	while first <= last
		result << list[last]
		last -= 1
		break if first > last
		result.unshift(list[last])
		last -= 1
		break if first > last
		result << list[first]
		first += 1
		break if first > last
		result.unshift(list[first])
		first += 1
	end
	result
end

c1 = calc(arrange(list))
c2 = calc(arrange(list.reverse))

puts [c1, c2].max