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 sc = new Scanner(System.in);
 
		int N = sc.nextInt();
		if (N<=1) {
			System.out.println(0);
			return;
		}
		
		int[] arr = new int[N];
		for (int i = 0; i < N; i++) {
			arr[i] = sc.nextInt();
		}
		Arrays.sort(arr);
		int min = arr[0];
		int max = arr[N - 1];
		
		int ans = Integer.MAX_VALUE;
        for (int i = min; i <= max; i++) {
			int part = 0;
			for (int j = 0; j < N; j++) {
				part += (int)Math.pow(arr[j]-i, 2);
			}
			if (part < ans) {
				ans = part;
			}
		}
		System.out.println(ans);
	}
}