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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace paiza2
{
    class Program
    {
        static void Main(string[] args)
        {
            int N = Int32.Parse(Console.ReadLine());
            string read = Console.ReadLine();
            string[] split = read.Split(' ');
            int[] a = new int[N];
            for (int c = 0; c < N; c++)
            {
                a[c] = Int32.Parse(split[c]);
            }
            int n = bibunshite0(a);
            int a2 = 0;
            for (int c = 0; c < a.Length; c++)
                a2 += a[c] * a[c];
            int a1 = 2 * a.Sum() * n;
            int a0 = a.Length*n * n;
            Console.WriteLine(a2-a1+a0);
        }

        static int bibunshite0(int[] a)
        {
            double d_output = a.Average();
            int output = (int)Math.Round(d_output);
            return output;
        }

    }
}