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 scn = new Scanner(System.in);
		ArrayList<Integer> caca = new ArrayList<Integer>();
		int suma = 0;
		for(int i = scn.nextInt();i>0;i--) {
			int n1 = scn.nextInt();
			caca.add(n1);
		}
		long tot = 0;
		long min = Long.MAX_VALUE;
		for(int i2 = -100;i2<=100;i2++) {
			for(int i = 0;i<caca.size();i++) {
				tot+=Math.pow(i2-caca.get(i), 2);
				if(tot>min) {
					break;
				}
			}
			if(tot<min)min = tot;
			tot = 0;
		}
		System.out.println(min);
		scn.close();
	}
}