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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;



public class Main {
	public static void main( String[] args ) throws IOException
    {
        BufferedReader br = new BufferedReader(
                                new InputStreamReader( System.in ) );
        double N = Integer.parseInt(br.readLine());
        String s = br.readLine();
        int result = 0;
        double sum = 0;
        String d[] = s.split(" ",0);
        int a[] = new int[d.length];
        for(int i = 0; i < d.length; i++){
        	a[i] = Integer.parseInt(d[i]);
        	sum += a[i];
        }
        int x = (int)Math.round(sum/N);
        for(int i = 0; i < a.length; i++){
        	result += (x-a[i])*(x-a[i]);
        }
        System.out.println(result);
	}
}
