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) {
        new Main().solve();
    }

    void solve() {
        Scanner sc = new Scanner(System.in);
        int N=sc.nextInt();
        int[] a=new int[N];
        int ab=0;
        for(int i=0;i<N;i++){
            a[i]=sc.nextInt();
            ab+=a[i];
        }
        if(ab%N==0){
        ab=ab/N;
        }else{
            ab=ab/N+1;
        }
        long ans=0;
        for(int i=0;i<N;i++){
            ans+=(long)Math.pow(a[i]-ab,2);
        }
        long an1=0;
        ab--;
        for(int i=0;i<N;i++){
            an1+=(long)Math.pow(a[i]-ab,2);
        }
        System.out.println(Math.min(an1,ans));
    }
}
