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# (.NET Core 3.1.201) (judge verdict: Time Limit Exceeded)

using System;
class Program
{
    static void Main(string[] args)
    {
        int n = int.Parse(Console.ReadLine());

        for (int i = 1; i <= n; i++)
        {
            int count = 0;

            for (int x = 1; x < i - 2; x++)
            {
                if (i < x * x + 4)
                {
                    continue;
                }

                for (int y = 1; y < i - 1 - x; y++)
                {
                    if (i < x * x + y * y + x * y + 2)
                    {
                        continue;
                    }

                    for (int z = 1; z < i - x - y; z++)
                    {
                        //Console.WriteLine(x + ", " + y + ", " + z);
                        if (x * x + y * y + z * z + x * y + y * z + z * x == i)
                        {
                            count++;
                        }
                    }
                }
            }

            Console.WriteLine(count);
        }
    }
}