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 = Integer.parseInt(sc.next());
		int max = 0;
		int min = 0;
		int ans = Integer.MAX_VALUE;
		ArrayList<Integer> ary = new ArrayList<Integer>();
		
		for(int i = 0; i < N; i ++) {
			ary.add(Integer.parseInt(sc.next()));
		}
		max = Collections.max(ary);
		min = Collections.min(ary);
		
		for(int i = min; i <= max; i++) {
			int x = 0;
			for(int y = 0;y < ary.size(); y++) {
				x += (ary.get(y) - i) * (ary.get(y) - i);
			}
			if(x <= ans) {
				ans = x;
			}
		}
		System.out.println(ans);
	}
}