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.

Examples

Input

2
4 8


Output

8


Input

3
1 1 3


Output

3


Input

3
4 2 5


Output

5


Input

4
-100 -100 -100 -100


Output

0
/**
 * Created by abhishek on 8/12/2016.
 */
import java.util.*;
import java.io.*;
public class Main {
    public static void main(String[] args)throws Exception {
     BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
       int n = Integer.parseInt(br.readLine());
        StringTokenizer st = new StringTokenizer(br.readLine());
        int array[] = new int[n + 1];
        for(int i = 1;i <= n;i++)
            array[i] = Integer.parseInt(st.nextToken());
        int ans = (int)1E9;
        for(int i = -100;i <= 100;i++){
            int cost = 0;
            for(int j = 1;j <= n;j++){
                cost += (array[j] - i)*(array[j] - i);
            }
            ans = Math.min(cost,ans);
        }
        System.out.println(ans);

    }
}
