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: Accepted)

import java.util.Scanner;
import java.util.List;
import java.util.ArrayList;

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

        int N = scan.nextInt();
        if ( N<1 || N>100) {
            System.exit(-1);
        }
        int sum = 0;
        List<Integer> nums = new ArrayList<Integer>();
        for(int i=0; i<N; i++) {
            int num = scan.nextInt();
            if ( num < -100 || num > 100) {
                System.exit(-2);
            }
            nums.add(new Integer(num));
            sum += num;
        }
        int avg = Math.round((float)sum/N);
        int cost = 0;
        for (Integer num: nums) {
            cost += Math.pow(num.intValue() - avg, 2);
        }

        System.out.println(cost);
    }
}