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

namespace ConsoleApplication1
{
    class Program
    {
        static void Main(string[] args)
        {
            Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });

            var n = Int32.Parse(Console.ReadLine());
            var a = Console.ReadLine().Split().Select(v => Int64.Parse(v)).ToList();

            var ret = Int64.MaxValue;

            for (int i = -100; i <= 100; i++)
            {
                ret = Math.Min(ret, a.Select(v => (v - i) * (v - i)).Sum());
            }

            Console.WriteLine(ret);
            Console.Out.Flush();
        }
    }
}