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.PrintWriter;
import java.util.Arrays;
import java.util.Scanner;
import java.util.stream.IntStream;

public class Main {
	static PrintWriter out = new PrintWriter(System.out);
	public static void main(String[] args) {
		// 入力
		final int n;	// 1≦N≦100
		final int[] a;	// −100≦ai≦100
		try(Scanner scan = new Scanner(System.in)) {
			n = scan.nextInt();
			a = new int[n];
			for (int i = 0; i < n; i++) {
				a[i] = scan.nextInt();
			}
		}
		
		// 数値が小さいのでそのまま全列挙計算したほうが速い。
		
		int result = IntStream.rangeClosed(-100, 100)
				.map(y -> Arrays.stream(a).map(e -> (e-y)*(e-y)).sum())
				.min().getAsInt();
		
		// 出力
		out.println(result);
		out.close();
	}

}