#include<bits/stdc++.h>
using namespace std;
int main(){
  int n;
  cin>>n;
  vector<int> c(n,0);
  for(int x=1;x*x<=n*2;x++)
    for(int y=1;(x+y)*(x+y)<=n*2;y++)
      for(int z=1;(x+y+z)*(x+y+z)<=n*2;z++)
        if(x*x+y*y+z*z+x*y+y*z+z*x<=n)
          c.at(x*x+y*y+z*z+x*y+y*z+z*x-1)++;
  for(int i=0;i<n;i++)
    cout<<c.at(i)<<endl;
}
### Prompt

Please provide a Cpp coded solution to the problem described below:

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> c(n,0);
  for(int x=1;x*x<=n*2;x++)
    for(int y=1;(x+y)*(x+y)<=n*2;y++)
      for(int z=1;(x+y+z)*(x+y+z)<=n*2;z++)
        if(x*x+y*y+z*z+x*y+y*z+z*x<=n)
          c.at(x*x+y*y+z*z+x*y+y*z+z*x-1)++;
  for(int i=0;i<n;i++)
    cout<<c.at(i)<<endl;
}
```