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 static System.Console;

class Program
{
    static void Main()
    {
        var n = NextInt();
        var a = new int[n];
        for (var i = 0; i < n; i++)
        {
            a[i] = NextInt();
        }
        var ans = int.MaxValue;
        for (var k = a.Min(); k <= a.Max(); k++)
        {
            var cnt = 0;
            foreach (var ai in a)
            {
                cnt += (int)Math.Pow(ai - k, 2);
            }
            ans = Math.Min(ans, cnt);
        }
        WriteLine(ans);
    }

    static int NextInt()
    {
        return int.Parse(NextString());
    }

    static string NextString()
    {
        var result = new List<char>();
        while (true)
        {
            int next = Read();
            if (next < 0)
            {
                break;
            }
            var nextChar = (char)next;
            if (!char.IsWhiteSpace(nextChar))
            {
                result.Add(nextChar);
            }
            else if (nextChar != '\r')
            {
                break;
            }
        }
        return string.Join("", result);
    }
}