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
import java.util.*;
import java.util.Arrays;


public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        int[] a = new int[N];
        int min = 0;
        int max = 0;
        int sum = 0;
        int ans = 0;

        for(int i = 0 ; i < N ; i++){
            a[i] = sc.nextInt();
            min = a[0];
            max = a[0];

            if(min > a[i]){
                min = a[i];
            }

            if(max < a[i]){
                max = a[i];
            }
        }

        for(int j = -100 ; j <= 100 ; j ++){
            sum = 0;
            
            for (int i = 0 ; i < N ; i++){
                sum = sum + (a[i] - j) * (a[i] - j) ;
            }

            if(j == -100){
                ans = sum;
            }

            if(ans > sum){
                ans = sum;
            }
        }

        System.out.println(ans);
    }
}