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.map{gets.to_i}.sort

index = N/2
ans=0
if N == 2
    ans = A[1] - A[0]
elsif N == 3
    a = A[0] * (-2) + A[1] + A[2]
    b = A[2] * 2 - A[0] - A[1]
    ans = a > b ? a : b
elsif N % 2 == 0
    ans = A[0..index-2].inject(:+) * (-2) + A[index+1..-1].inject(:+) * 2 - A[index-1] + A[index]
else
    a = A[0..index-1].inject(:+) * (-2) + A[index+2..-1].inject(:+) * 2 + A[index] + A[index+1]
    b = A[0..index-2].inject(:+) * (-2) + A[index+1..-1].inject(:+) * 2 - A[index-1] - A[index]

    ans = a > b ? a : b
end

p ans