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[] cost=new int[201];
 int[] a=new int[N];
 int temp=0;
 for(int k=0;k<N;k++){a[k]=sc.nextInt();}
for(int i=-100;i<=100;i++){
    temp=0;
    for(int j=0;j<N;j++){
        temp+=Math.pow((a[j]-i),2);
        }
    cost[i+100]=temp;
    }
Arrays.sort(cost);
System.out.println(cost[0]);
}
}