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.HashSet;
import java.util.LinkedList;
import java.util.Scanner;
import java.util.Set;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		
		final int N = sc.nextInt();
		long[] arr = new long[N];
		for(int i = 0; i < N; i++){
			arr[i] = sc.nextLong();
		}
		
		final long sum = Arrays.stream(arr).sum();
		final long lo_avg = sum / N;
		final long hi_avg = (sum + N - 1) / N;
		
		long lo_answer = 0, hi_answer = 0;
		for(int i = 0; i < N; i++){
			lo_answer += (arr[i] - lo_avg) * (arr[i] - lo_avg);
			hi_answer += (arr[i] - hi_avg) * (arr[i] - hi_avg);
		}
		
		System.out.println(Math.min(lo_answer, hi_answer));
		
		
	}

}