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) {
        // 自分の得意な言語で
        // Let's チャレンジ！！
        Scanner sc = new Scanner(System.in);
        String line = sc.nextLine(); line = sc.nextLine();
String s[]=line.split(" ",0);
int num=s.length;
int m[]=new int[num];
double ans=0.0;
for(int i=0;i<num;i++){
m[i]=Integer.parseInt(s[i]);
ans+=m[i];
}
ans/=num;
int ans2=(int)ans;
if(ans%1>0.5){
ans2=(int)ans+1;
}
int an=0;
for(int i=0;i<num;i++){
an+=(m[i]-ans2)*(m[i]-ans2);
}
System.out.println(an);
}
}