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];
    int X = 0;
    int T = 0;
    for(int i = 0; i < N; i++) {
      a[i] = sc.nextInt();
      T += a[i];
    }
    double average = (double)T / (double)N;
    if((Math.ceil(average) - average) >= (average - Math.floor(average))) {
      X = (int)Math.floor(average);
    } else {
      X = (int)Math.ceil(average);
    }
    int cost = 0;
    for(int i = 0; i < N; i++) {
      cost += (int)(Math.pow(a[i] - X, 2));
    }
    System.out.println(cost);
  }
}