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 {

    private static Scanner scan = new Scanner(System.in);

    public static void main(String[] args) {
	int N = Integer.parseInt(scan.next());
	int[] a = new int[N];
	int total = 0;
	for (int i = 0; i < N; i++) {
	    a[i] = Integer.parseInt(scan.next());
	    total += a[i];
	}

	int A1 = total / N;
	int A2 = A1 + 1;
	int score1 = 0;
	int score2 = 0;
	for (int i = 0; i < N; i++) {
	    score1 += (a[i] - A1)*(a[i] - A1);
	    score2 += (a[i] - A2)*(a[i] - A2);
	}

	System.out.println(Integer.min(score1, score2));
	scan.close();
    }
}
