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.ArrayList;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		int N = 0;
		int Cost1 = 0;
		int Cost2 = 0;
		int mid = 0;
		int mid2 = 0;
		int sum = 0;
		ArrayList <Integer> Array = new ArrayList<>();
		Scanner scan = new Scanner(System.in);

		N = scan.nextInt();
		for(int i = 0;i < N; i++) {
			Array.add(scan.nextInt());
			sum += Array.get(i);
		}

		mid = sum / N;

		mid2 = mid + 1;
		
		for(int j = 0; j < Array.size(); j++){
			Cost1 += (Array.get(j) -mid) * (Array.get(j) - mid);
			Cost2 += (Array.get(j) -mid2) * (Array.get(j) - mid2);
		}
		System.out.println(Math.min(Cost1, Cost2));

	}
}