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.Scanner;

public class Main{
	public static void main(String[]args) {
		try(Scanner scan = new Scanner(System.in)){
			
			
			int N = scan.nextInt();
			
			int[]a = new int[N];
			for(int i = 0;i<N;i++)a[i] = scan.nextInt();
			
			
			Arrays.sort(a);
			
			int min = a[0];
			int max = a[N-1];
			
			long mincost = Integer.MAX_VALUE;
			
			for(int i = min;i<=max;i++) {
				long cost = 0;
				
				for(int j = 0;j<N;j++) {
					cost+=(a[j]-i)*(a[j]-i);
				}
				
				if(mincost>cost)mincost = cost;
				
				
			}
			
			
			System.out.println(mincost);
			
			
			
			
			
			
			
			
			
		}
		
		
	}
		

}
