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 scan = new Scanner(System.in);
		int n = scan.nextInt();
		int x[] = new int[n];
		int low = 100,high = -100;
		for(int i =0 ; i < n; i++){
			x[i] =  scan.nextInt();
			if(x[i] >= high)high = x[i];
			if(x[i] <= low)low = x[i];
		}
		
		int cost, min = 10000000;
		for(int i = -100; i <= 100; i++){
			cost = 0;
			for(int j = 0; j < n; j++){
				cost += (x[j] - i)*(x[j] - i);
			}
			if(cost <= min )min = cost;
		}
		System.out.print(min);
	}

}