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();
		
		int[] arr = new int[N];
		int sum = 0;
		
		for(int i = 0 ; i < N ; i++){
			arr[i] = sc.nextInt();
			sum += arr[i];
		}

		sc.close();
		
		int aver = sum / N;
		
		int value = calculateDiff(arr, aver);
	
		value = Math.min( calculateDiff(arr, aver + 1), value );
		
		System.out.println(value);
	}

	static int calculateDiff(int[] arr, int aver) {
		int diff = 0;
		
		for(int i = 0 ; i < arr.length ; i++){
			diff += ((arr[i] - aver) * (arr[i] - aver));
		}
		
		return diff;
	}
}
