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 {

	private void doit(){
		Scanner sc = new Scanner(System.in);
		long mod = 1000000007;
		while(sc.hasNext()){
			int n = sc.nextInt();
			int [] data = new int[n];
			int sum = 0;
			for(int i = 0; i < data.length; i++){
				data[i] = sc.nextInt();
				sum += data[i];
			}
			
			double ave = (double)sum / n;
			
			int ans = Integer.MAX_VALUE;
			int [] comp = {(int) Math.ceil(ave), (int) Math.floor(ave)};
			
			for(int i =0 ;i < comp.length; i++){
				int now = 0;
				for(int j = 0; j < data.length; j++){
					now += (data[j] - comp[i]) * (data[j] - comp[i]);
				}
				ans = Math.min(now, ans);
			}
			
			System.out.println(ans);
		}

	}

	private void debug(Object... o) {
		System.out.println("debug = " + Arrays.deepToString(o));
	}

	public static void main(String[] args) {
		new Main().doit();
	}

}
