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;

public class Program
{
    public static long loop;

    static long n;

    static long[] a;

    static string output;

    public static void Main(string[] args)
    {
        loop = 0;

        Input();
        Proc();
        Output();
    }

    static void Input()
    {
        string[] input = null;

        // スペース区切りの整数の入力(横、個別)
        input = Console.ReadLine().Split(' ');

        n = long.Parse(input[0]);

        // スペース区切りの整数の入力(横、配列)
        input = Console.ReadLine().Split(' ');

        a = new long[n];
        for (long idx = 0; idx < n; idx++)
        {
            a[idx] = long.Parse(input[idx]);
        }
    }

    static void Proc()
    {
        long ans;
        long cost;

        long min_cost = GetCost(-100);

        for (ans = -99; ans <= 100; ans++)
        {
            cost = GetCost(ans);

            if (min_cost > cost)
            {
                min_cost = cost;
            }
        }

        output = min_cost.ToString();
    }

    static long GetCost(long ans)
    {
        long cost = 0;

        for (long idx = 0; idx < a.Length; idx++)
        {
            cost += (a[idx] - ans) * (a[idx] - ans);
        }

        return cost;
    }

    static void Output()
    {
        // 出力
        Console.WriteLine(output);
        output = string.Empty;
    }
}