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;
import java.util.Arrays;

class Main{
    public static void main(String[] args){
	Scanner scan = new Scanner(System.in);
	int N = scan.nextInt();
        int[] array = new int[N];
	int cost=0;
	int lowCost = 1000000;
        for(int i=0;i<N;i++){
            array[i] = scan.nextInt();
        }
	Arrays.sort(array);
        for(int i=-100;i<=100;i++){
            for(int j=0;j<array.length;j++){
                cost += Math.pow((array[j]-i),2);
	    }
            if(lowCost > cost){
                lowCost = cost;
	    }   
            cost = 0;
        }
        System.out.println(lowCost);
    }
}
