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 Haskell (GHC 7.10.3) (judge verdict: Accepted)

import Control.Monad
import Data.List

pattern :: Int -> [[Int]]
pattern n
  | even n = let h = div n 2 in [replicate (h-1) (-2) ++ [-1, 1] ++ replicate (h-1) 2]
  | odd n = let h = div n 2 in [replicate (h-1) (-2) ++ [-1, -1] ++ replicate h 2, replicate h (-2) ++ [1, 1] ++ replicate (h-1) 2]

f n cs = maximum $ map (sum . zipWith (*) cs) (pattern n)

main = readLn >>= \n -> replicateM n readLn >>= print . f n . sort