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.Scanner;
public class Main {
	public static void main(String[] args) {
		BeTogether together = new BeTogether();
		together.run();
	}
}

class BeTogether {
	
	int N;
	int[] nums;
	
	BeTogether() {
		Scanner cin = new Scanner(System.in);
		this.N = cin.nextInt();
		this.nums = new int[N];
		for (int i = 0; i < N; i++) {
			nums[i] = cin.nextInt();
		}
	}
	
	void run() {
		int avarage = calculateAvarage();
		int min = 0;
		for (int i = 0; i < N; i++) {
			min += (nums[i] - avarage) * (nums[i] - avarage);
		}
		System.out.println(min);
	}
	
	int calculateAvarage() {
		double sum = 0.0;
		for (int i = 0; i < N; i++) {
			sum += nums[i];
		}
		return (int)Math.round(sum / nums.length);
	}
}
