Problem:
Score : 200 points

Problem Statement

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.

Sample Input 1

2
4 8

Sample Output 1

8

Transforming the both into 6s will cost (4-6)^2+(8-6)^2=8 dollars, which is the minimum.

Sample Input 2

3
1 1 3

Sample Output 2

3

Transforming the all into 2s will cost (1-2)^2+(1-2)^2+(3-2)^2=3 dollars. Note that Evi has to pay (1-2)^2 dollar separately for transforming each of the two 1s.

Sample Input 3

3
4 2 5

Sample Output 3

5

Leaving the 4 as it is and transforming the 2 and the 5 into 4s will achieve the total cost of (2-4)^2+(5-4)^2=5 dollars, which is the minimum.

Sample Input 4

4
-100 -100 -100 -100

Sample Output 4

0

Without transforming anything, Evi's objective is already achieved. Thus, the necessary cost is 0.

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.Arrays;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        int n = sc.nextInt();

        int num[] = new int[n];
        int total = 0;
        for (int i = 0; i < n; i++) {
            int m = sc.nextInt();
            num[i] = m;
            total += m;
        }

        float avg = (float)total / (float)n;

        Arrays.sort(num);

        int average;
        if (avg % 1 == 0) {
            average = (int)avg;
        } else {
            average = (int)avg + 1;
        }

        int median =
                n > 2 ? num[(n%2==0 ? n/2 + 1 : n/2)]
                        : (n > 1 ? Math.min(num[0], num[1])
                                    :num[0]);

        int criteria = average;
        if(average < median) {
            criteria = median;
        }
        
        int cost = 0;
        for (int i = 0; i < n; i++) {
            if(num[i] != criteria) {
                cost += Math.pow((num[i] - criteria), 2);
            }
        }

        System.out.println(cost);
    }
}