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 AtCoderSnippet
{
    class Program
    {
        static void Main(string[] args)
        {
            var N = int.Parse(Console.ReadLine());
            var arr = new int[N];
            Func3(N, arr);

            for (int i = 0; i < N; i++)
            {
                Console.WriteLine(arr[i]);
                
            }
        }

        static int Func2(int x, int y, int z)
        {
            var q1 = x * x;
            var q2 = y * y;
            var q3 = z * z;
            var q4 = x * y;
            var q5 = y * z;
            var q6 = z * x;
            return q1 + q2 + q3 + q4 + q5 + q6;
        }

        static void Func3(int N, int[] arr)
        {
            for (int x = 1; x <= N / 6; x++)
            {
                for (int y = 1; y <= N / 6; y++)
                {
                    for (int z = 1; z <= N / 6; z++)
                    {
                        if ((x+y+z) >= N) break;
                        var num = Func2(x, y, z);
                        if (num < N) arr[num - 1] += 1;
                    }
                }
            }
        }
    }
}