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.Arrays;
import java.util.Scanner;

public class Main {
public static void main(String[] args) {
		
		Scanner keyboard = new Scanner(System.in); 
		
		int N = keyboard.nextInt();
		int[] ebi = new int[N];
		for(int i=0; i<N; i++) {
			ebi[i] = keyboard.nextInt();
		}
		Arrays.sort(ebi);
		
		int min = ebi[0];
		int Max = ebi[N-1];
		
		int kotae = 100000000;
		
		for(int j = min; j < Max + 1; j++) {
			int sum = 0;
			for(int k = 0; k < N; k++) {
			sum += Math.pow(ebi[k] - j , 2);
			}
			kotae = sum < kotae ? sum : kotae;
		}
		
		System.out.println(kotae);
		keyboard.close();
	}
}