Problem:
Score : 300 points

Problem Statement

Let f(n) be the number of triples of integers (x,y,z) that satisfy both of the following conditions:

1 \leq x,y,z

x^2 + y^2 + z^2 + xy + yz + zx = n

Given an integer N, find each of f(1),f(2),f(3),\ldots,f(N).

Constraints

All values in input are integers.

1 \leq N \leq 10^4

Input

Input is given from Standard Input in the following format:

N

Output

Print N lines. The i-th line should contain the value f(i).

Sample Input 1

20

Sample Output 1

0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
3
3
0
0

For n=6, only (1,1,1) satisfies both of the conditions. Thus, f(6) = 1.

For n=11, three triples, (1,1,2), (1,2,1), and (2,1,1), satisfy both of the conditions. Thus, f(6) = 3.

For n=17, three triples, (1,2,2), (2,1,2), and (2,2,1), satisfy both of the conditions. Thus, f(17) = 3.

For n=18, three triples, (1,1,3), (1,3,1), and (3,1,1), satisfy both of the conditions. Thus, f(18) = 3.

Solution in C# (Mono-mcs 6.8.0.105) (judge verdict: Time Limit Exceeded)

using System;
using System.Linq;

class Program
{
    static int count;

    static void Main()
    {
        int N = int.Parse(Console.ReadLine());
        for (int i = 0; i < N; i++)
        {
            Console.WriteLine(Solve(i+1));
        }
        
    }

    static int Solve(int x)
    {
        count = 0;
        int a,b;

        for (int i = 1; i < Math.Round(Math.Sqrt(x)); i++)
        {
            a = i;
            for (int j = 1; j < Math.Round(Math.Sqrt(x-Math.Pow(a,2))); j++)
            {
                b = j;
                for (int k = 1; k < Math.Round(Math.Sqrt(x - Math.Pow(a, 2) - Math.Pow(b, 2))); k++)
                {
                    if ((Math.Pow((i+j+k),2)-(i*j+j*k+k*i))==x)
                    {
                        count++;
                    }
                }
            }
        }
        return count;
    }
}