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();
    }
    sc.close();
    Arrays.sort(a);
    int cost[]=new int[a[n-1]-a[0]+1];
    for(int i=0;i<cost.length;i++){
      for(int j=0;j<n;j++){
        cost[i]+=Math.pow((a[0]+i-a[j]),2);
      }
    }
    Arrays.sort(cost);
    System.out.println(cost[0]);
  }
}