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.*;
import java.lang.Math;
public class Main{
public static void main(String[] args){
Scanner x= new Scanner(System.in);

int c= x.nextInt();
int[] arr = new int[c];
double a =0;
for(int i =0;i<c;i++){
	arr[i]=x.nextInt();
	a += arr[i];
}

int a1 = (int)(a/c);
int a2 = a1 +1;


int r1=0;
int r2=0;
for(int i =0;i<c;i++){
	r1 += Math.pow(arr[i]-a1 , 2);
}


for(int i =0;i<c;i++){
	r2 += Math.pow(arr[i]-a2 , 2);
}

System.out.println(Math.min(r1,r2));



}
}
