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 static System.Console;
using System.Linq;

namespace AC
{
   public class shiokara
   {
      static void Main(string[] args)
      {
         int N = int.Parse(ReadLine());
         for(int i = 1; i <= N; i++){
             WriteLine(func(i));
         }
      }

      static int func(int n){
          int cnt = 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) cnt++;
                      else if(x*x+y*y+z*z+x*y+y*z+z*x > n) break;
                  }
              }
          }
          return cnt;
      }
   }
}