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.Arrays;
import java.util.Collections;
import java.util.Scanner;

class Main {

    public static void main(String[] args) {
        int x;
        int mincost;
        int result =0;
        Scanner input =  new Scanner(System.in);
        x=input.nextInt();
        int[] arr = new int[x];
        for(int i =0 ;i<x;i++){
            arr[i]=input.nextInt();
        }

        Arrays.sort(arr);
        int min =Arrays.stream(arr).min().getAsInt();
        int max = Arrays.stream(arr).max().getAsInt();
        mincost = Integer.MAX_VALUE;
        for(int i=min;i<=max;i++){
            for(int j=0;j<arr.length;j++){
                result+=Math.pow(arr[j]-i,2);

            }
            if(result<mincost){
                mincost=result;
            }
            result=0;
        }

        System.out.println(mincost);

    }
}