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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

    import java.util.*;
    import java.io.*;
     
     
    public class Main{
     
         public static void main(String []args){
            Scanner scanner = new Scanner(System.in);
           int n = scanner.nextInt();
           int [] arr = new int[n];
           
           List<Integer> list = new ArrayList<>();
           
         
           
           for(int i=0;i<n;i++)
           arr[i] = scanner.nextInt();
           
           Arrays.sort(arr);
           
           long min =101;
           long index=0;
          
            for(int i=arr[0];i<=arr[n-1];i++)
            {
                long sum=0;
                for(int j=0;j<n;j++)
                {
                    sum=sum+(long) Math.pow((arr[j]-i),2);
                   
                }
                 if(sum<min){
                    min=sum;
                    index=sum;
                 }
                
            }
            
            System.out.println(index);
            
            
        
            
            //System.out.println()
            //for(int i=0;i<n;i++)
         }
    }