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.BufferedInputStream;
import java.util.*;

public class Main {

    // 1处理全为负数的情况
    // 2处理相同的数
    // 3正数
    // 4正数负数混合
    // 暴力试探
    public static void main(String[] args) {

        Scanner s = new Scanner(new BufferedInputStream(System.in));
        int n = s.nextInt();
        int[] nums = new int[n];
        for (int i = 0; i < nums.length; i++) {
            nums[i] = s.nextInt();
        }
        int sum = Integer.MAX_VALUE;

        for (int i = -100; i <= 100; i++) {
            int cur = 0;
            for (int j : nums) {
                int o = Math.abs(j - i);
                o = o * o;
                cur += o;
            }
            sum = Math.min(sum, cur);
        }
        System.out.println(sum);

    }
}
