#include <iostream>

using namespace std;
int n,x,y,z,vfs[10050],rez;
int main()
{
    cin >> n;
    for(x=1; x<=105; x++)
      for(y=1; y<=105; y++)
        for(z=1; z<=105; z++) {
          rez=x*x+y*y+z*z+x*y+y*z+x*z;
          if(rez<10050)
            vfs[rez]++;
        }
    for(int i=1; i<=n; i++)
      cout << vfs[i] << "\n";
    return 0;
}

### Prompt

Generate 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 <iostream>

using namespace std;
int n,x,y,z,vfs[10050],rez;
int main()
{
    cin >> n;
    for(x=1; x<=105; x++)
      for(y=1; y<=105; y++)
        for(z=1; z<=105; z++) {
          rez=x*x+y*y+z*z+x*y+y*z+x*z;
          if(rez<10050)
            vfs[rez]++;
        }
    for(int i=1; i<=n; i++)
      cout << vfs[i] << "\n";
    return 0;
}

```