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.*;
public class Main {

	public static void main(String[] args) {
		Scanner seer = new Scanner(System.in);
		int n = seer.nextInt();
		int[] arr = new int[n];
		for(int i = 0; i < n; i++){
			arr[i] = seer.nextInt();
		}
		int mincost = Integer.MAX_VALUE;
		for(int val = -100; val <= 100; val++){
			int cost = 0;
			for(int k: arr){
				cost += (k - val)*(k - val);
			}
			mincost = Integer.min(mincost, cost);
		}
		System.out.println(mincost);
	}

}
