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[] arg){
    Scanner sc = new Scanner(System.in);
    int N = sc.nextInt();
    int a[] = new int[N];
    double sum = 0;
    double ans = 0;
    double totalAns = 0;
    for(int i = 0 ;i < N;i++){
      a[i] = sc.nextInt();
    }
    for(int i = 0 ;i < N;i++){
      sum += a[i];
    }
    sum = Math.round(sum/N);
    for(int j = 0;j < N; j++){
      if(a[j] != sum){
        ans = Math.pow((sum - a[j]),2);
        totalAns += ans;
      }
    }
    System.out.println((int)totalAns);
  }

}
