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;

class Main {

	public static void main(String[] args) {

		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		int[] a = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = in.nextInt();
		}

		int min = 100;
		int max = -100;
		for (int i = 0; i < n; i++) {
			if (a[i] < min) {
				min = a[i];
			}
			if (a[i] > max) {
				max = a[i];
			}
		}

		int mincost = 1999999999;
		int cost = 0;

		for (int i = min; i <= max; i++) {
			cost = 0;
			for (int j = 0; j < n; j++) {
				int sa = i - a[j];
				cost += sa * sa;
			}
			if(cost < mincost){
				mincost = cost;
			}
		}

		System.out.println(mincost);
		in.close();

	}

}