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.io.*;
import java.util.*;
public class Main {
	
	public static void main(String[] args) {
		InputReader in = new InputReader();
		int n = in.nextInt();
		
		int[] arr = new int[n];
		for (int i=0; i<n; i++)
			arr[i] = in.nextInt();
		
		long res = Long.MAX_VALUE;
		for (int i=-100; i<=100; i++) {
			long cost = 0;
			for (int j=0; j<n; j++)
				cost += (arr[j]-i)*(arr[j]-i);
			res = Math.min(res, cost);
		}
		System.out.println(res);
	}

	static class InputReader {
		public BufferedReader br;
		public StringTokenizer st;
		
		public InputReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
			st = null;
		}
		
		public String next() {
			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				}
				catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return st.nextToken();
		}
		
		public int nextInt() {
			return Integer.parseInt(next());
		}
	}
}