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.io.*;
import java.util.*;
public class Main{
	public static void main(String args[]){
    	Scanner in = new Scanner(System.in);
      	int n = in.nextInt();
      	int a[] = new int[n];
      	int ans = Integer.MAX_VALUE;
      	for(int i=0;i<n;i++){
        	a[i] = in.nextInt();
        }
      	for(int i=-100;i<=100;i++){
        	int ans1 =0;
          	for(int j =0; j < n ;j++){
            	ans1+=(i-a[j])*(i-a[j]);
            }
          	ans = Math.min(ans,ans1);
        }
   		System.out.println(ans);
    }

}