Problem:
Score : 200 points

Problem Statement

Evi has N integers a_1,a_2,..,a_N. His objective is to have N equal integers by transforming some of them.

He may transform each integer at most once. Transforming an integer x into another integer y costs him (x-y)^2 dollars. Even if a_i=a_j (i≠j), he has to pay the cost separately for transforming each of them (See Sample 2).

Find the minimum total cost to achieve his objective.

Constraints

1≦N≦100

-100≦a_i≦100

Input

The input is given from Standard Input in the following format:

N
a_1 a_2 ... a_N

Output

Print the minimum total cost to achieve Evi's objective.

Sample Input 1

2
4 8

Sample Output 1

8

Transforming the both into 6s will cost (4-6)^2+(8-6)^2=8 dollars, which is the minimum.

Sample Input 2

3
1 1 3

Sample Output 2

3

Transforming the all into 2s will cost (1-2)^2+(1-2)^2+(3-2)^2=3 dollars. Note that Evi has to pay (1-2)^2 dollar separately for transforming each of the two 1s.

Sample Input 3

3
4 2 5

Sample Output 3

5

Leaving the 4 as it is and transforming the 2 and the 5 into 4s will achieve the total cost of (2-4)^2+(5-4)^2=5 dollars, which is the minimum.

Sample Input 4

4
-100 -100 -100 -100

Sample Output 4

0

Without transforming anything, Evi's objective is already achieved. Thus, the necessary cost is 0.

Solution in Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

import Data.Foldable (and, or, product, sum)
import Data.Function

import qualified Data.List as L

main :: IO ()
main = do
    n  <- read <$> getLine
    as <- getSeq
    print $ solve n as

getSeq  = map read . words <$> getLine   :: Read a => IO [a]

solve :: Int -> [Int] -> Int
solve n as =
  let
    mean = ceiling $ ((/) `on` fromIntegral) (sum as) n
    mode = L.head . L.maximumBy (compare `on` length) $ L.group as
    replaceTo :: Int -> Int
    replaceTo y = sum $ L.map (`cost` y) as
  in
    min (replaceTo mean) (replaceTo mode)

cost :: Int -> Int -> Int
cost x y = (x - y) ^ 2