#include<bits/stdc++.h>
int main()
{
	int x;
	scanf("%d",&x);
	for(int i=1;i<=x;i++)
	{
		int c=0;
		for(int m=1;m<sqrt(i);m++)
		{
			for(int n=1;n<sqrt(i);n++)
			{
				int b=(sqrt(4*i-3*m*m-3*n*n-2*m*n)-(m+n))/2;
				if(b<=0)break;
				if((m*m+n*n+b*b+m*n+m*b+n*b)==i)c++;
			}
		}
		if(c==0)printf("0\n");
		else printf("%d\n",c);
	}
}
### Prompt

Please create a solution in Cpp 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>
int main()
{
	int x;
	scanf("%d",&x);
	for(int i=1;i<=x;i++)
	{
		int c=0;
		for(int m=1;m<sqrt(i);m++)
		{
			for(int n=1;n<sqrt(i);n++)
			{
				int b=(sqrt(4*i-3*m*m-3*n*n-2*m*n)-(m+n))/2;
				if(b<=0)break;
				if((m*m+n*n+b*b+m*n+m*b+n*b)==i)c++;
			}
		}
		if(c==0)printf("0\n");
		else printf("%d\n",c);
	}
}
```