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 {

	public static void main(String[] args) {

		Scanner s = new Scanner(System.in);
		int N = s.nextInt();
		int[] a = new int[N];
		for (int i = 0; i < N; i++) {
			a[i] = s.nextInt();
		}
		int min = a[0];
		int max = a[0];
		for (int i = 0; i < N; i++) {
			min = Math.min(min, a[i]);
			max = Math.max(max, a[i]);
		}

		long result=2147483647L;
		
		for(int i=min;i<=max;i++){
			int sum=0;
			for(int j=0;j<N;j++){
				sum+=(i-a[j])*(i-a[j]);
			}
			result=Math.min(sum, result);
		}
		System.out.println(result);
	}
}