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 OCaml (4.02.3) (judge verdict: Wrong Answer)

let cost_to_n list n =
  List.fold_left (fun x y -> x + y) 0 (List.map (fun x -> (n-x)*(n-x)) list)

let solve list =
  let rec aux list min_cost cto cfrom cnow =
    if cnow = cto then min_cost else
      let cur_cost = cost_to_n list cnow in
      aux list (min min_cost cur_cost) cto cfrom (cnow+1)
  in
  aux list max_int
      (List.fold_left (fun x y -> max x y) min_int list)
      (List.fold_left (fun x y -> min x y) max_int list)
      (List.fold_left (fun x y -> min x y) max_int list)
    

let read_list_of_int () =
  let rec read_list_of_int_inner lst =
    try let ans = (Scanf.scanf "%d " (fun x->x)) in
        read_list_of_int_inner (ans::lst)
    with End_of_file ->
      List.rev lst
  in
  read_list_of_int_inner []

let () =
  let _ = read_int() in
  let list = read_list_of_int () in
  let ans = solve list in
  Printf.printf "%d\n" ans
;;