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 Julia (0.5.0) (judge verdict: Accepted)

function parseInt(x) parse(Int, x) end
function conInt(x) convert(Int, x) end

function main()
	n = parseInt(readline())
	x = Int[]
	sum = 0
	for i in 1:n
		push!(x, parseInt(readline()))
	end
	y = sort(x)
	if length(x) == 2
		println(y[2]-y[1])
	else
		sum += y[n]-y[1]
		if n%2 == 1
			for i in 1:conInt((n-3)/2)
				sum += y[n-i]-y[i]
				sum += y[n+1-i]-y[i+1]
			end
			sum += max(y[conInt((n+1)/2)]-y[conInt((n-1)/2)], y[conInt((n+3)/2)]-y[conInt((n+1)/2)])
		else
			for i in 1:conInt((n-4)/2)
				sum += y[n-i]-y[i]
				sum += y[n+1-i]-y[i+1]
			end
			sum += max(y[conInt(n/2)]-y[conInt((n-2)/2)]+y[conInt((n+4)/2)]-y[conInt((n+2)/2)], y[conInt((n+2)/2)]-y[conInt((n-2)/2)]+y[conInt((n+4)/2)]-y[conInt(n/2)])
		end
		println(sum)
	end
end
main()