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;

public class Main {

	public static void main(String[] args) throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String line = br.readLine();
		int n = Integer.parseInt(line);
		line = br.readLine();
		String[] sp = line.split(" ");
		int[] a = new int[n];
		int min = Integer.MAX_VALUE;
		int max = Integer.MIN_VALUE;
		for (int i = 0; i < n; i++) {
			a[i] = Integer.parseInt(sp[i]);
			min = Math.min(a[i] , min);
			max = Math.max(a[i] , max);
		}
		int minCost = Integer.MAX_VALUE;
		for (int i = min; i <= max; i++) {
			int cost = 0;
			for (int j = 0; j < n; j++) {
				cost += Math.pow(a[j] - i, 2);
			}
			minCost = Math.min(cost, minCost);
		}
		System.out.println(minCost);
	}

}
