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.Scanner;
    
    public class Main{
    public static void main(String args[]){
    int N;
    int[] a=new int[101];
    int sum=0;
    int av;
    int cost=10000000;
    int ncost=0;
    Scanner scan = new Scanner(System.in);

    N=scan.nextInt();
    for(int i=0;i<N;i++){
    	a[i]=scan.nextInt();
    	sum=sum+a[i];
    }
    av=sum/N;
    
    for(int i=0;i<N;i++){
    	ncost=ncost+(a[i]-(av-1))*(a[i]-(av-1));
    }
    if(cost>ncost)cost=ncost;
    ncost=0;
    for(int i=0;i<N;i++){
    	ncost=ncost+(a[i]-(av))*(a[i]-(av));
    }
    if(cost>ncost)cost=ncost;
    ncost=0;
    for(int i=0;i<N;i++){
    	ncost=ncost+(a[i]-(av+1))*(a[i]-(av+1));
    }
    if(cost>ncost)cost=ncost;
    ncost=0;
    
    System.out.println(cost);
    }
}