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: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;

namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            //[summary]C - いっしょ / Be Together
            int n = int.Parse(Console.ReadLine());
            var a = GetNumbers();

            int min = int.MaxValue;
            int aMin = a[GetAMin(n)];
            int aMax = a[GetAMax(n)];
            //int aMin = a.Min();
            //int aMax = a.Max();

            for(int i = aMin; i <= aMax; i++)
            {
                int sum = 0;

                for(int j = 0; j < n; j++)
                {
                    sum += (int)Math.Pow(a[j] - i, 2);
                }

                if (sum < min)
                {
                    min = sum;
                }
            }

            Console.WriteLine(min);
        }
        
        static int GetAMin(int n)
        {
            return n / 2 - 1;  
        }
        
        static int GetAMax(int n)
        {
            if(n % 2 == 0)
            {
                return n / 2;    
            }
            else
            {
                return n /2 + 1;    
            }    
        }
        
        static List<int> GetNumbers()
        {
            var line = Console.ReadLine();
            var array = line.Split(' ');

            return array.Select(x => int.Parse(x)).OrderBy(x => x).ToList();
        }
    }
}