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;
namespace AISing.Problems
{
    class C
    {
        static void Main()
        {
            var sw = new System.IO.StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
            long n = long.Parse(Console.ReadLine());
            for (int i = 1; i <= n; i++) {
                long res = 0;
                for (int x = 1; x*x <= i; x++)
                {
                    for (int y = x; y*y <= i; y++)
                    {
                        for (int z = y; z*z <= i; z++)
                        {
                            if (x*x + y*y + z*z + x*y + y*z + z*x == i)
                            {
                                if (x == y & y == z)
                                {
                                    res += 1;
                                }
                                else if (x == y | y == z)
                                {
                                    res += 3;
                                }
                                else
                                {
                                    res += 6;
                                }
                            }
                        }
                    }
                }
                Console.WriteLine(res);
            }
            Console.Out.Flush();
        }
    }
}