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.math.BigDecimal;
import java.util.Scanner;

public class Main {

	void run() {
		Scanner sc = new Scanner(System.in);

		int n = sc.nextInt();
		int[] a = new int[n];
		float sum = 0;
		for (int i = 0; i < n; i++) {
			a[i] = sc.nextInt();
			sum += (float) a[i];
		}

		BigDecimal bd = new BigDecimal((float) sum / n);
		int ave = bd.ROUND_HALF_UP;

		System.out.println(sum);
		System.out.println(ave);

		int ans = 0;
		for (int i = 0; i < n; i++) {
			int tmp = ave - a[i];
			ans += tmp * tmp;
		}
		System.out.println(ans);

	}

	void run1() {
		Scanner sc = new Scanner(System.in);

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

		int min = Integer.MAX_VALUE / 2;
		for (int i = -100; i <= 100; i++) {
			int sum = 0;
			for (int j = 0; j < n; j++) {
				int tmp = i - a[j];
				sum += tmp * tmp;
			}
			min = Math.min(min, sum);
		}
		System.out.println(min);
	}

	public static void main(String[] args) {
		new Main().run1();
	}

}