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 {
    public static void main(String[] args) throws Exception {
        // Your code here!
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[] nums = new int[n];
        for (int i = 0; i < n; i++) {
            nums[i] = sc.nextInt();
        }
        
        Arrays.sort(nums);
        
        int min = nums[0];
        int max = nums[n - 1];
        if (min == max) {
            System.out.println("0");
            return;
        }
        
        int answer = Integer.MAX_VALUE;
        for (int i = min; i <= max; i++) {
            int sum = 0;
            for (int num : nums) {
                sum += (int)Math.pow(num - i, 2);
            }
            
            answer = Math.min(answer, sum);
        }
        
        System.out.println(answer);
    }
}
