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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) throws IOException {
        Scanner sc = new Scanner(System.in);
        //BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        int N = sc.nextInt();
        int[] arr = new int[N];
        int sum = 0;

        for(int i = 0; i<N; i++){
            arr[i] = sc.nextInt();
            sum += arr[i];
        }

        double mean = sum;
        mean /= N;

        int avg = (int) Math.round(mean);

        int price = 0;
        for(int i : arr){
            price += (avg - i) * (avg - i);
        }

        System.out.println(price);

    }
}
