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.IOException;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) throws IOException {
		Scanner cin = new Scanner(System.in);
		String line;
		for (; cin.hasNext();) {
			line = cin.nextLine();
			int N = Integer.valueOf(line); // 整数値の個数
			line = cin.nextLine();
			String[] inputGroup = line.split(" ");  //2行目の文字列を配列に分割

			int targetNum = 0;
			for(String a : inputGroup){
				targetNum += Integer.valueOf(a);
			}
			float targetNum2 = (float)targetNum / inputGroup.length;
			targetNum = Math.round(targetNum2);

			int cost = 0;
			for(String a : inputGroup){
				cost += (Integer.valueOf(a) - targetNum) * (Integer.valueOf(a) - targetNum);
			}

			System.out.println(cost);
		}
	}
}