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[] a = new int[N];
        for(int i=0; i<N; i++){
          a[i] = sc.nextInt();
        }
        int min = 0;
        for(int i=0; i<N; i++){
          min += (a[i]-(-101)) * (a[i]-(-101));
        }
      
        for(int i=-100; i<=101; i++){
          int sum = 0;
          for(int j=0; j<N; j++){
            sum += (a[j]-i) * (a[j]-i);
          }
          if(sum < min){
            min = sum;
          }
        }

        System.out.println(min);
    }
}