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.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        
        int n = sc.nextInt();
        int[] data = new int[n];
        double sum = 0.0;
        int ave = 0;
        
        for(int i=0; i<n; i++){
            data[i] = sc.nextInt();
            sum += data[i];
        }
        
        ave = (int)(Math.round(sum/n));
        sum = 0;
        
        for(int i=0; i<n; i++){
            if(data[i]!=ave){
                sum += (data[i]-ave) * (data[i]-ave); 
            }
        }
        
        System.out.println((int)(sum));
        
    }
}
