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: Accepted)

import Control.Applicative
import Control.Monad
import Data.List
import Data.Char
import Data.Maybe
strToInt s = (read :: String -> Int) s
strToInteger s = (read :: String -> Integer) s
strToDouble s = (read :: String -> Double) s

roundUpOn5 :: (RealFrac a, Integral b) => a -> b
roundUpOn5 x
  | n <= -0.5 = m - 1
  | n >= 0.5 = m + 1
  | otherwise = m
  where (m, n) = properFraction x

main :: IO ()
main = do
    -- 整数の入力
    _ <- getLine
    -- スペース区切り整数の入力
    as <- map strToInt . words <$> getLine
    let ave = roundUpOn5 $ (fromIntegral $ sum as) / (fromIntegral $ length as)
    -- 出力
    putStrLn . show $ foldl (\acc x -> acc + (x - ave) ^ 2) 0 as