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;


public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
			int N = sc.nextInt();
			long[] A = new long[N];
			int sum = 0;
			for(int i = 0 ; i < N ; i++){
				A[i] = sc.nextLong();
				sum+= A[i];
			}
			sc.close();


			int p1 = 0;
			int p2 = 0;

			int ans = 0;
			int ans2 = 0;
			if(sum%N == 0){
				p1 = sum/N;

				for(int i = 0 ; i < N ; i++){
					ans += Math.pow(Math.abs(A[i]-p1), 2);
				}
				System.out.println(ans);
			}
			else{
				p1 = sum/N;
				p2 = p1+1;

				for(int i = 0 ; i < N ; i++){
					ans += Math.pow(Math.abs(A[i]-p1), 2);
					ans2 += Math.pow(Math.abs(A[i]-p2), 2);
				}
				System.out.println(Math.min(ans, ans2));
			}

	}
}
