#include <stdio.h>

int count[10010];
int main()
{
	int a;
	scanf("%d",&a);
	
	for(int i=1;i<=100;i++)
	{
		for(int j=1;j<=100;j++)
		{
			for(int k=1;k<=100;k++)
			{
				int C = i*i+j*j+k*k+i*j+j*k+k*i;
				if(C<=a) count[C]++;
			}
		}
	}
	for(int i=1;i<=a;i++) printf("%d\n",count[i]);
}
### 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 <stdio.h>

int count[10010];
int main()
{
	int a;
	scanf("%d",&a);
	
	for(int i=1;i<=100;i++)
	{
		for(int j=1;j<=100;j++)
		{
			for(int k=1;k<=100;k++)
			{
				int C = i*i+j*j+k*k+i*j+j*k+k*i;
				if(C<=a) count[C]++;
			}
		}
	}
	for(int i=1;i<=a;i++) printf("%d\n",count[i]);
}
```