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: Wrong Answer)

import Data.List

main = do
    (n:as) <- map read . words <$> getContents :: IO [Int]
    let (small,large) = splitAt ((n+1) `div` 2) $ sort as
    let ss = sorting True [] [] (reverse small)
        ls = sorting True [] [] large
        ans1 = ds $ marge ss ls
        ans2 = ds $ marge ss (reverse ls)
        ans3 = ds $ marge ls ss
        ans4 = ds $ marge ls (reverse ss)
    print $ maximum [ans1, ans2, ans3, ans4]

sorting b ls rs (s:[]) = ls ++ [s] ++ (reverse rs)
sorting b ls rs (s:ss) | b = sorting False (s:ls) rs ss
                       | otherwise = sorting True ls (s:rs) ss

marge ls rs = concat $ transpose [ls,rs]

ds xs = sum $ zipWith (\a b -> abs (a - b)) xs (tail xs)