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 System;
using System.Linq; 

namespace Sample
{
  class Sample
  {
    static void Main(string[] args)
    {
      int N=int.Parse(Console.ReadLine());
      int[] ans=new int[N];
      int sqrtN=(int)Math.Sqrt(N);
	for(int x=1;x<sqrtN;x++){
      for(int y=1;y<sqrtN;y++){
        for(int z=1;z<sqrtN;z++){
         
         int n=x*x+y*y+z*z+x*y+y*z+z*x;
         if(n<=N){
           ans[n-1]++;
          
         }
        }
      }
    }
        for(int i=0;i<N;i++){
          Console.WriteLine(ans[i]);
        }
      
    }
    
  }

}