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.*;

class Main{
public static void main(String[] args){
	Scanner sc = new Scanner(System.in);
	int n = sc.nextInt();
	int[] a = new int[n];
	int x = 40000000;
	int y = 0;
	for(int i = 0; i < n; i++) {
		a[i] = sc.nextInt();
	}
	for(int i = -100; i < 101; i++) {
		for(int j = 0; j < n; j++) {
			y += Math.pow((i - a[j]), 2);
		}
		if(x > y) {
			x = y;
		}
		y = 0;
	}
	System.out.println(x);
}
}