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.io.*;
        import java.util.*;
        public class Main{
          public static void main(String[] args) throws IOException{
            BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
            int a = Integer.parseInt(reader.readLine());
            int[] list = new int[a];
            String[] inp = reader.readLine().split(" ");
            int i = 0;
            for(String s: inp){
                list[i] =Integer.parseInt(s);
                i++;
            }
            Arrays.sort(list);
            int fr = Integer.MAX_VALUE;
            for(int j = list[0];j<=list[list.length-1];j++){
                int res = 0;
                for(int h=0;h<list.length;h++){
                    res=res+(list[h]-j)*(list[h]-j);
                }
                
                fr = Math.min(res,fr);
                
            }
            System.out.println(fr);
              
          }}