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.*;

class Main{
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        int N = sc.nextInt();
        int[] A = new int[N];
        for(int i=0;i<N;i++){
            A[i]=sc.nextInt();
        }
        Arrays.sort(A);
        int ans = Integer.MAX_VALUE;
        for(int i=A[0];i<=A[N-1];i++){
            ans = Math.min(ans,help(A,i));
        }
        System.out.println(ans);
    }
    static int help(int[] a, int tar){
        int ans=0;
        for(int i=0;i<a.length;i++){
            ans += (a[i]-tar)*(a[i]-tar);
        }
        return ans;
    }
}
