#include <bits/stdc++.h>
using namespace std;

int main() {
  int N;
  cin >> N;
  vector<int> f(N);
  for (int x=1; x*x<N; x++){
    for (int y=1; y*y<N; y++){
      for (int z=1; z*z<N; z++){
        int n;
        n=x*x+y*y+z*z+x*y+y*z+z*x;
        if (n<=N) f.at(n-1)++;
      }
    }
  }
  for (int i=0; i<N; i++)
    cout << f.at(i) << endl;
  return 0;
}
### Prompt

Construct a cpp code solution to the problem outlined:

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() {
  int N;
  cin >> N;
  vector<int> f(N);
  for (int x=1; x*x<N; x++){
    for (int y=1; y*y<N; y++){
      for (int z=1; z*z<N; z++){
        int n;
        n=x*x+y*y+z*z+x*y+y*z+z*x;
        if (n<=N) f.at(n-1)++;
      }
    }
  }
  for (int i=0; i<N; i++)
    cout << f.at(i) << endl;
  return 0;
}
```