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.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace AtCoder.Abc
{
    class QuestionC
    {
        public static void Main(string[] args)
        {
            var sw = new System.IO.StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);

            var n = int.Parse(Console.ReadLine());
            int[] cc = new int[10000+1];
            cnt(cc);
            for (int i = 1; i <= n; i++)
            {
                Console.WriteLine(cc[i]);
            }

            // 10000 1+1+z*z+1+z+z
            Console.Out.Flush();
        }

        public static int calc(int x, int y, int z)
        {
            return (x * x) + (y * y) + (z * z) + (x * y) + (y * z) + (x * z);
        }

        public static void cnt(int[] cc)
        {
            int m = 100;
            for (int x = 1; x < m; x++)
            {
                for (int y = 1; y < m; y++)
                {
                    for (int z = 1; z < m; z++)
                    {
                        var d = calc(x, y, z);
                        if (d<=10000)
                        {
                            cc[d]++;
                        }
                    }
                }
            }
        }
    }
}