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) {
        Scanner sc = new Scanner(System.in);
        int n = Integer.parseInt(sc.next());
        List<Integer> list = new ArrayList<>(n);
        int m = 200, M = -200;
        for(int i = 0; i < n; ++i) {
            int t = Integer.parseInt(sc.next());
            list.add(t);
            m = Math.min(m, t);
            M = Math.max(M, t);
        }
        
        int ans = Integer.MAX_VALUE;
        for(int num = m; num <= M; ++num) {
            int cost = 0;
            for(int i = 0; i < n; ++i) {
                int changed = list.get(i);
                cost += (changed - num) * (changed - num);
            }
            ans = Math.min(ans, cost);
        }
        System.out.println(ans);
    }
}
