#include <bits/stdc++.h>
using namespace std;
int ans[30000];
int main()
{
	int n;
	scanf("%d",&n);
	int t=(int)sqrt(n)+1;
	for(int i=1;i<=t;i++)
	{
		for(int j=1;j<=t;j++)
		{
			for(int z=1;z<=t;z++)
			{
				if(i*i+j*j+z*z+i*j+j*z+i*z<=n) ans[i*i+j*j+z*z+i*j+j*z+i*z]++;
			}
		}
	}
	for(int i=1;i<=n;i++) printf("%d\n",ans[i]);
 } 
### Prompt

Please formulate a cpp solution to the following problem:

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 ans[30000];
int main()
{
	int n;
	scanf("%d",&n);
	int t=(int)sqrt(n)+1;
	for(int i=1;i<=t;i++)
	{
		for(int j=1;j<=t;j++)
		{
			for(int z=1;z<=t;z++)
			{
				if(i*i+j*j+z*z+i*j+j*z+i*z<=n) ans[i*i+j*j+z*z+i*j+j*z+i*z]++;
			}
		}
	}
	for(int i=1;i<=n;i++) printf("%d\n",ans[i]);
 } 
```