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.math.BigDecimal;
import java.util.*;

public class Main {
    
    public static void main(String[] args) {
        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();
        }
        
        boolean isSame = false;
        for (int i=0; i<a.length-1; i++){
            if (!(a[i] == a[i+1])){
                break;
            }
            if (i == a.length-2){
                isSame = true;
            }
        }
        
        int c = 0;
        if (!(isSame)){
            Arrays.sort(a);
            int minC = 10000000;
            for (int i=a[0]; i<a[n-1]; i++){
                int temp = 0;
               for (int j=0; j<n; j++){
                   if (!(i==a[j])){
                       temp += (int)Math.pow(a[j]-i,2);
                   }
               }
               if (temp < minC){
                   minC = temp;
               }
            }
            c = minC;
        }
        System.out.println(c);
    }
}