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 scanner = new Scanner(System.in);
      
      	int N = scanner.nextInt();
      
      	int[] array = new int[N];

      	for(int i = 0; i < N; i++) {
          	array[i] = scanner.nextInt();
            //System.out.println(array[i]);
        }
      	int plus = 0;
      	double sum = 0;
      	for(int j = 0; j < N; j++) {
        	plus = plus + (int) Math.pow(array[j], 2);
          	sum = sum + array[j] * 2;
        }
      	sum = Math.round(sum / (2 * N));
      
      	int ans = 0;
      	for(int k = 0; k < N; k++) {
        	ans = ans + (int) Math.pow((array[k] - (int) sum), 2);
        }
      
     	System.out.println(ans);
      	
	}
}
 

 

