#include<bits/stdc++.h>

using namespace std;

int main()
{
	int n, m;
	cin>>n;
	vector<int>ans(n+1);
	for(int i=1; i<=100; i++)
	{
		for(int j=1; j<=100; j++)
		{
			for(int k=1; k<=100; k++)
			{
				m=(i*i)+(j*j)+(k*k)+(i*j)+(j*k)+(k*i);
				if(m<=n)
				ans[m]++;
				else
				break;
			}
		}
	}
	for(int i=0; i<n; i++)
	cout<<ans[i+1]<<"\n";
	return 0;
}

### 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 main()
{
	int n, m;
	cin>>n;
	vector<int>ans(n+1);
	for(int i=1; i<=100; i++)
	{
		for(int j=1; j<=100; j++)
		{
			for(int k=1; k<=100; k++)
			{
				m=(i*i)+(j*j)+(k*k)+(i*j)+(j*k)+(k*i);
				if(m<=n)
				ans[m]++;
				else
				break;
			}
		}
	}
	for(int i=0; i<n; i++)
	cout<<ans[i+1]<<"\n";
	return 0;
}

```