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 ans=100*100*100;
   int tmp=0;
   for(int i=-100;i<=100;i++)
   {
     tmp=0;
     for(int k=0;k<N;k++)
     {
       tmp+= (a[k]-i)*(a[k]-i);
     }
     if(tmp<ans) ans=tmp;
   }
   System.out.println(ans);
 }
}