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.Text;
using System.Text.RegularExpressions;
using System.Diagnostics;
using System.Linq;
using System.Collections.Generic;
using System.IO;
using System.Numerics;

namespace competitive
{
    class Program
    {
        static void Main(string[] args)
        {
            var scanner = new Scanner();
            var n = scanner.NextInt();
            var an = scanner.NextLineToIntList();
            var ans = int.MaxValue;
            for (int i = -100; i <= 100; i++)
            {
                var sum = 0;
                var target = an[i];
                foreach (var item in an)
                {
                    sum += (item - target) * (item - target);
                }
                if (ans > sum)
                {
                    ans = sum;
                }
            }
            Console.WriteLine(ans);
        }
    }


    #region
    public static class Extensions
    {
        public static int ToInt(this string str) => int.Parse(str);
        public static double ToDouble(this string str) => double.Parse(str);
        public static long ToLong(this string str) => long.Parse(str);
        public static BigInteger ToBigInteger(this string str) => BigInteger.Parse(str);
    }

    public class Scanner
    {
        private TextReader reader;
        public Scanner()
        {
            reader = Console.In;
        }
        public Scanner(TextReader reader)
        {
            this.reader = reader;
        }
        private string NextWord()
        {
            var sb = new StringBuilder();
            while (true)
            {
                var c = reader.Read();
                if ((c == 13 || c == 10 || c == 32) && sb.Length > 0 || c == -1)
                {
                    break;
                }
                sb.Append((char)c);
            }
            return sb.ToString();
        }
        public int NextInt() => NextWord().ToInt();
        public string Next() => NextWord();
        public double NextDouble() => NextWord().ToDouble();
        public long NextLong() => NextWord().ToLong();
        public BigInteger NextBigInteger() => NextWord().ToBigInteger();
        public string NextLine()
        {
            var str = reader.ReadLine();
            if (string.IsNullOrWhiteSpace(str))
            {
                return reader.ReadLine();
            }
            else
            {
                return str;
            }
        }
        private List<string> NextLineToList() => NextLine().Split(new char[] { ' ' },
                                                                  StringSplitOptions.RemoveEmptyEntries)
                                                           .ToList();
        public List<int> NextLineToIntList() => NextLineToList().Select(x => int.Parse(x))
                                                                .ToList();
    }
    #endregion
}