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.IO;
using System.Text;
using static System.Math;
using static System.Array;

namespace AtCoderSolve
{
    class Solve
    {
        const int mod = 1000000007;
        const int INF = 2147483647;
        const long SINF = 9223372036854775807;

        static int N;
        static int[] a;
        //static string S;


        public static void Input()
        {
            var cin = new Scanner();
            N = int.Parse(Console.ReadLine());
            a = cin.SplitReader();
        }

        static void Main(string[] args)
        {
            Input();
            //var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            //Console.SetOut(sw);

            long ans = INF;
            for(var i = -100; i <= 100; i++)
            {
                long cost = 0;
                for(var j = 0; j < N; j++)
                {
                    cost += Abs(a[j] - i) * Abs(a[j] - i);
                }

                ans = Min(ans, cost);
            }

            Console.WriteLine(ans);
            //Console.Out.Flush();
        }

        
    }

    

    public class Scanner
    {
        public int[] SplitReader()
        {
            int[] array = Console.ReadLine().Split().Select(int.Parse).ToArray();
            return array;
        }
        public long[] SplitReaderL()
        {
            long[] array = Console.ReadLine().Split().Select(long.Parse).ToArray();
            return array;
        }

        public int[] MultiLineReader(int N)
        {
            int[] ret = new int[N];
            for(var i = 0; i < N; i++)
            {
                ret[i] = int.Parse(Console.ReadLine());
            }

            return ret;
        }
        public long[] MultiLineReaderL(int N)
        {
            long[] ret = new long[N];
            for (var i = 0; i < N; i++)
            {
                ret[i] = long.Parse(Console.ReadLine());
            }

            return ret;
        }

    }

    public class Graph
    {
        
    }
}