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: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using static System.Console;
using static System.Math;
using static AtCoderTemplate.MyLibrary;

namespace AtCoderTemplate
{
    class Program
    {
        static void Main (string[] args)
        {
            int N = int.Parse (Console.ReadLine ());

            int[] count = new int[100000];

            for (int x = 1; x < 100; x++)
            {
                for (int y = 1; y < 100; y++)
                {
                    for (int z = 1; z < 100; z++)
                    {
                        int k = x * x + y * y + z * z + x * y + y * z + z * x;
                        count[k] += 1;
                    }
                }
            }

            for (int i = 1; i <= N; i++)
            {
                Console.WriteLine (count[i]);
            }
        }
    }

    class MyLibrary
    {
        public static int GCD (int a, int b)
        {
            if (a % b == 0) return b;
            return GCD (b, a % b);
        }
    }
}