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.ArrayList;
import java.util.List;
import java.util.Scanner;
import static java.lang.Math.round;

public class Main{

	public static void main(String[] args) {

		Scanner sc = new Scanner(System.in);
		int inputCount = sc.nextInt();
		List<Integer> inputList = new ArrayList<Integer>();
		for(int i=0;i<inputCount;i++){
			inputList.add(sc.nextInt());
		}
		
		//平均値を求める
		int sum = 0;
		for(Integer input : inputList){
			sum += input;
		}
		int ave = (int)round((double)sum/(double)inputCount);
		
		//コスト計算
		int cost = 0;
		for(Integer input : inputList){
			cost += (ave - input)*(ave - input);
		}
		sc.close();
		System.out.print(cost);
	}
}
