#include<bits/stdc++.h>
using namespace std;
int n,ans[10100];
int main()
{
	cin>>n;
	int x=1e2;
	for(int a=1;a<=x;a++)
		for(int b=1;b<=x;b++)
			for(int c=1;c<=x;c++)
			{
				int f=a*a+b*b+c*c+a*b+a*c+b*c;
				if(1<=f&&f<=x*x)
					ans[f]++;
			}
	for(int i=1;i<=n;i++)
		cout<<ans[i]<<endl;
	return 0;
}
### Prompt

Your challenge is to write 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 n,ans[10100];
int main()
{
	cin>>n;
	int x=1e2;
	for(int a=1;a<=x;a++)
		for(int b=1;b<=x;b++)
			for(int c=1;c<=x;c++)
			{
				int f=a*a+b*b+c*c+a*b+a*c+b*c;
				if(1<=f&&f<=x*x)
					ans[f]++;
			}
	for(int i=1;i<=n;i++)
		cout<<ans[i]<<endl;
	return 0;
}
```