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 static System.Console;

public static class Program
{
    public static void Main()
    {
        var N = int.Parse(ReadLine());
        var fArray = new int[N];
        for (int n = 1; n <= N; ++n) {
            //xの探索
            for (int x = 1; n >= x * x; ++x)
            {
                int yMax = n - x * x;
                for (int y = 1; yMax >= (y * y + x * y); ++y)
                {
                    int precaluLated = yMax - y * y - x * y;
                    for (int z = 1; ; ++z)
                    {
                        int right = z * z + x * z + y * z;
                        if (precaluLated <= right) 
                        {
                            if (precaluLated == right) ++fArray[n - 1];
                            else break;
                        }
                    }
                }
            }
        }
        for (int i = 0; i < N; ++i)
            WriteLine(fArray[i]);
    }
}