#include <stdio.h>

int main(void)
{
	int N,x,y,z,answer[10001],i;
	scanf("%d",&N);
	for(i=1;i<=N;i++){
		answer[i]=0;
	}
	for(x=1;x*x<N;x++){
		for(y=1;x*x+y*y<N;y++){
			for(z=1;x*x+y*y+z*z<N;z++){
				if(x*x+y*y+z*z+x*y+y*z+z*x<=N)answer[x*x+y*y+z*z+x*y+y*z+z*x]++;
			}
		}
	}
	for(i=1;i<=N;i++)printf("%d\n",answer[i]);
	return 0;
}
### 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 <stdio.h>

int main(void)
{
	int N,x,y,z,answer[10001],i;
	scanf("%d",&N);
	for(i=1;i<=N;i++){
		answer[i]=0;
	}
	for(x=1;x*x<N;x++){
		for(y=1;x*x+y*y<N;y++){
			for(z=1;x*x+y*y+z*z<N;z++){
				if(x*x+y*y+z*z+x*y+y*z+z*x<=N)answer[x*x+y*y+z*z+x*y+y*z+z*x]++;
			}
		}
	}
	for(i=1;i<=N;i++)printf("%d\n",answer[i]);
	return 0;
}
```