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.Linq;

class C
{
	static void Main()
	{
        int  N = int.Parse(Console.ReadLine());
        /*int[] a  = Console.ReadLine()
                            .Split(' ')
                            .Select(a => int.Parse(a))
                            .ToArray();*/
		
        for(int i = 1; i<=N; i++){
            int Count=0;
            double dMax = Math.Pow((double) i -2.0, 0.5) - 1.0;
            int iMax = (int)Math.Floor(dMax);
            for(int x=1;x<=iMax;x++)
            {
            for(int y=1;y<=iMax;y++)
            {
            for(int z=1;z<=iMax;z++)
            {
                if((x+y+z)*(x+y+z) -x*y-x*z-y*z == i)
                {
                    Count++;
                }
            }
            }
            }
            Console.WriteLine(Count.ToString());
        }


        
        
	}
}