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: Wrong Answer)

N = gets.to_i
A = N.times.map{gets.to_i}.sort
B = []
B << A.shift
while !A.empty?
    if 1 < A.length then
        x = A.pop
        y = A.pop
        if (B.first - x).abs + (B.last - y).abs < (B.first - y).abs + (B.last - x).abs then
            B.push x
            B.unshift y
        else
            B.push y
            B.unshift x
        end
    else
        x = A.pop
        if (B.first - x).abs < (B.last - x).abs then
            B.push x
        else
            B.unshift x
        end
    end
    next if A.empty?
    if 1 < A.length then
        x = A.shift
        y = A.shift
        if (B.first - x).abs + (B.last - y).abs < (B.first - y).abs + (B.last - x).abs then
            B.push x
            B.unshift y
        else
            B.push y
            B.unshift x
        end
    else
        x = A.pop
        if (B.first - x).abs < (B.last - x).abs then
            B.push x
        else
            B.unshift x
        end
    end
end
ans = 0
(N - 1).times{|i|
    ans += (B[i] - B[i + 1]).abs
}
puts ans