#include<bits/stdc++.h>
using namespace std;
int main()
{
  vector<int>v(100000,0);
  for(int i=1;i<=100;i++)
  {
    for(int j=1;j<=100;j++)
    {
      for(int k=1;k<=100;k++)
      {
        int res=(i*i)+(j*j)+(k*k)+(i*j)+(j*k)+(k*i);
        v[res]++;
      }
    }
  }
  int n;
  cin>>n;
  for(int i=1;i<=n;i++)
    cout<<v[i]<<endl;
}
### Prompt

Your task is to create a CPP solution to the following problem:

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).

Example

Input

20


Output

0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
3
3
0
0

### Response

```cpp
#include<bits/stdc++.h>
using namespace std;
int main()
{
  vector<int>v(100000,0);
  for(int i=1;i<=100;i++)
  {
    for(int j=1;j<=100;j++)
    {
      for(int k=1;k<=100;k++)
      {
        int res=(i*i)+(j*j)+(k*k)+(i*j)+(j*k)+(k*i);
        v[res]++;
      }
    }
  }
  int n;
  cin>>n;
  for(int i=1;i<=n;i++)
    cout<<v[i]<<endl;
}
```