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;

namespace C
{
    class Program
    {
        static void Main(string[] args)
        {
            int n = int.Parse(Console.ReadLine());
            int[] ans = new int[n];
            for(int i = 1; i <= n; i++)
            {
                int count = 0;
                for (int x = 1; x <= n; x++)
                {
                    for (int y = 1; y <= n; y++)
                    {
                        for (int z = 1; z <= n; z++)
                        {
                            if (Math.Pow(x, 2) + Math.Pow(y, 2) + Math.Pow(z, 2) + x * y + y * z + z * x == i)
                            {
                                count++;
                            }
                        }
                    }
                }
                ans[i - 1] = count;
            }
            foreach(int i in ans)
            {
                Console.WriteLine(i);
            }
            
        }
    }
}