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.InputStreamReader;
import java.io.IOException;
import java.lang.Math;
import java.util.Arrays;

public class Main {
  public static void main(String[] args) throws IOException {
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    int len = Integer.parseInt(br.readLine());
    String[] strs = br.readLine().split(" ");
    int[] numbers = new int[len];
    for (int i = 0; i < len; i++) {
      numbers[i] = Integer.parseInt(strs[i]);
    }
    Arrays.sort(numbers);
    int left = numbers[0], right = numbers[len-1];
    int sum = 0, min = 0;
    for (int i = left; i <= right; i++) {
      for (int j = 0; j < len; j++) {
        sum += Math.pow(numbers[j] - i, 2);
      }
      if (min == 0) {
        min = sum;
      } else {
        min = Math.min(min, sum);
      }
      sum = 0;
    }
    System.out.println(min);
  }
}