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
as = N.times.map{gets.to_i}.sort

if N%2 == 0
    ans = 0
    (0..(N/2-2)).each do |i|
        ans -= as[i]*2
    end
    ans += as[N/2] - as[N/2-1]
    ((N/2+1)...N).each do |i|
        ans += as[i]*2
    end
    puts ans
else
    ans1 = 0
    (0..(N/2-1)).each do |i|
        ans1 -= as[i]*2
    end
    ans1 += as[N/2] + as[N/2+1]
    ((N/2+2)...N).each do |i|
        ans1 += as[i]*2
    end

    ans2 = 0
    (0..(N/2-2)).each do |i|
        ans2 -= as[i]*2
    end
    ans2 -= as[N/2-1] + as[N/2]
    ((N/2+1)...N).each do |i|
        ans2 += as[i]*2
    end

    puts [ans1, ans2].max
end