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
/* Filename: ABC043C.java
 * Author: Mushiyo
 */

import java.util.Scanner;

public class Main{

	public static void main(String[] args) {
		Scanner input = new Scanner(System.in);

		while (input.hasNext()) {
			int N = input.nextInt();
			int[] a = new int[N];
			
			int sumA = 0;
			for(int i = 0; i < a.length; ++i){
				a[i] = input.nextInt();
				sumA += a[i];
			}
			
			int avgA = (int)Math.round(sumA / (double)N);
			int cost = 0;
			
			for(int i = 0; i < a.length; ++i){
				cost += (avgA - a[i]) * (avgA - a[i]);
			}
			
			System.out.println(cost);
		}
	}

}
