#include<bits/stdc++.h>
using namespace  std;
int n;
int a[100100100];
int main ()
{
	cin>>n;
	for(int x=1;x<=100;x++)
	{
		for(int y=1;y<=100;y++)
		{
			for(int z=1;z<=100;z++)
			{
				int q=x*x+y*y+z*z+x*y+x*z+y*z;
				a[q]++;
			}
		}
	}
	for(int i=1;i<=n;i++)
	{
		cout<<a[i]<<endl;
	}
	return 0;
} 
### 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 n;
int a[100100100];
int main ()
{
	cin>>n;
	for(int x=1;x<=100;x++)
	{
		for(int y=1;y<=100;y++)
		{
			for(int z=1;z<=100;z++)
			{
				int q=x*x+y*y+z*z+x*y+x*z+y*z;
				a[q]++;
			}
		}
	}
	for(int i=1;i<=n;i++)
	{
		cout<<a[i]<<endl;
	}
	return 0;
} 
```