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;
using System.Collections.Generic;
using System.Configuration;
using System.Linq;

static class Program
{
    static void Main(string[] args)
    {
        var n = int.Parse(Console.ReadLine());
        for (var i = 1; i <= n; i++) Console.WriteLine(f(i));
    }

    static int f(int n) {
        var res = 0;
        for (int x = 1; x < 100; x++) for (int y = 1; y < 100; y++)
        for (int z = 1; z < 100; z++) if (x*x+y*y+z*z+x*y+y*z+z*x == n) res++;
        //else if (x*x+y*y+z*z+x*y+y*z+z*x > n) break;
        return res;
    }
}