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 Common Lisp (SBCL 1.1.14) (judge verdict: Accepted)

(defun split (string &key (delimiterp #'delimiterp))
  (loop :for beg = (position-if-not delimiterp string)
    :then (position-if-not delimiterp string :start (1+ end))
    :for end = (and beg (position-if delimiterp string :start beg))
    :when beg :collect (subseq string beg end)
    :while end))
(defun delimiterp (c) (position c " ,.;/"))

(defun main ()
  (let ((n (read))
        (a_list (map 'list #'parse-integer (split (read-line))))
        (x nil))
    (setq x (/ (reduce #'+ a_list) n))
    (if (>= (- x (floor x)) (- (ceiling x) x))
      (setq x (ceiling x))
      (setq x (floor x)))

    (princ
      (reduce
        #'+
        (map 'list #'(lambda (l) (* (- l x) (- l x))) a_list)))
    (princ #\newline)

    ))
(main)