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

int n,N;

int main()
{
	cin>>N;

	for(int n=1;n<=N;n++)
	{
		int ans=0;
		for(int x=1;x*x<=n;x++)
			for(int y=1;x*x+y*y+x*y<=n;y++)
				for(int z=1;x*x+y*y+z*z+x*y+y*z+z*x<=n;z++)
					if(x*x+y*y+z*z+x*y+y*z+z*x==n) ans++;
		cout<<ans<<"\n";
	}
}
### Prompt

Develop a solution in Cpp 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 n,N;

int main()
{
	cin>>N;

	for(int n=1;n<=N;n++)
	{
		int ans=0;
		for(int x=1;x*x<=n;x++)
			for(int y=1;x*x+y*y+x*y<=n;y++)
				for(int z=1;x*x+y*y+z*z+x*y+y*z+z*x<=n;z++)
					if(x*x+y*y+z*z+x*y+y*z+z*x==n) ans++;
		cout<<ans<<"\n";
	}
}
```