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.ArrayList;
import java.util.Collections;
import java.util.Comparator;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		int N = 0;
		int Cost1 = 0;
		int Cost2 = 0;
		int mid = 0;
		int count = 0;
		int mid2 = 0;
		ArrayList <Integer> Array = new ArrayList<>();
		Scanner scan = new Scanner(System.in);

		N = scan.nextInt();
		for(int i = 0;i < N; i++) {
			Array.add(scan.nextInt());
		}

		Collections.sort(Array, Comparator.naturalOrder());
		if(Array.size() % 2 != 0) {
			mid = Array.get(Array.size() / 2);
		}
		else {
			mid = (Array.get(Array.size() / 2) + Array.get((Array.size() / 2) - 1)) / 2;
		}
		mid2 = mid;
		for(int k : Array) {
			if(k == mid2) {
				count += 1;
				if(count > 1) {
					mid += 1;
					if(count == Array.size()) {
						mid = mid2; 
					}
				}
			}
		}
		for(int j = 0; j < Array.size(); j++){
			Cost1 += (Array.get(j) -mid) * (Array.get(j) - mid);
			Cost2 += (Array.get(j) -mid2) * (Array.get(j) - mid2);
		}
		System.out.println(Math.min(Cost1, Cost2));

	}
}