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.Text;

namespace AtTest.C_Challenge
{
    class ABC_043
    {
        static void Main(string[] args)
        {
            Method(args);
            Console.ReadLine();
        }

        static void Method(string[] args)
        {
            int n = int.Parse(Console.ReadLine());
            var array = new int[n];
            string[] input = Console.ReadLine().Split(' ');
            int average = 0;
            for (int i = 0; i < n; i++)
            {
                array[i] = int.Parse(input[i]);
                average += array[i];
            }
            average /= n;
            int cost0 = 0, cost1 = 0, cost2 = 0;
            for (int i = 0; i < n; i++)
            {
                cost0 += (average - array[i])
                    * (average - array[i]);
                cost1 += (average + 1 - array[i])
                    * (average + 1 - array[i]);
                cost2 += (average - 1 - array[i])
                    * (average - 1 - array[i]);
            }
            if (cost0 < cost1 && cost0 < cost2)
            {
                Console.WriteLine(cost0);
            }
            else if (cost1 < cost0 && cost1 < cost2)
            {
                Console.WriteLine(cost1);
            }
            else
            {
                Console.WriteLine(cost1);
            }
        }
    }
}