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

int main() {
  long n;
  cin >> n;
  vector<long> ans(n);
  for(long x=1;x*x+1+1+x+1+x<=n;x++) {
    for(long y=1;x*x+y*y+1+x*y+y+x<=n;y++) {
      for(long z=1;x*x+y*y+z*z+x*y+y*z+z*x<=n;z++) {
        ans[x*x+y*y+z*z+x*y+y*z+z*x-1]++;
      }
    }
  }
  for(long i=0;i<n;i++) cout << ans[i] << endl;
}
### 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() {
  long n;
  cin >> n;
  vector<long> ans(n);
  for(long x=1;x*x+1+1+x+1+x<=n;x++) {
    for(long y=1;x*x+y*y+1+x*y+y+x<=n;y++) {
      for(long z=1;x*x+y*y+z*z+x*y+y*z+z*x<=n;z++) {
        ans[x*x+y*y+z*z+x*y+y*z+z*x-1]++;
      }
    }
  }
  for(long i=0;i<n;i++) cout << ans[i] << endl;
}
```