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) {
		// TODO 自動生成されたメソッド・スタブ
		Scanner scan = new Scanner(System.in);
		int N = scan.nextInt();
		int[] a = new int[N];
		int min = 101;
		int max = -101;
		int sum = 1000000000;
		int tmp = 0;
		for(int i = 0; i < N; i++) {
			a[i] = scan.nextInt();
		}
		
		for(int i = 0; i < N; i++) {
			if(min > a[i]) {
				min = a[i];
			}
			if(max < a[i]) {
				max = a[i];
			}
		}
		
		for(int i = min; i <= max; i++) {
			for(int j = 0; j < N; j++) {
				tmp += (int)Math.pow(a[j] - i, 2);
			}
			if(tmp < sum) {
				sum = tmp;
			}
			tmp = 0;
		}
		
		System.out.println(sum);
		
		scan.close();
	}

}
