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.*;
import java.lang.Math;

public class Main {

	public static void main(String[] args){
	
		Scanner sc = new Scanner(System.in);
		
		int a = sc.nextInt();
		
		int[] x = new int[a];

		int b = 0;
		
		for (int i = 0 ;i < a; i++){
			x[i] = sc.nextInt();
			b += x[i];
		}
		
		int c = (int)(b/a);
		int d = c + 1;
		
		int sum1 = 0;
		int sum2 = 0;
		
		for(int i = 0; i < a; i++){
			sum1 += Math.pow(x[i] - c, 2);
		}
		for(int i = 0; i < a; i++){
			sum2 += Math.pow(x[i] - d, 2);
		}
		
		System.out.println(Math.min(sum1, sum2));
	}
}
