#include<bits/stdc++.h>
using namespace std;

const int N=1e+4+1;
int f[N],n;
int main()
{
	cin>>n;
	for(int i=1;i<=min(n,100);i++)
		for(int j=1;j<=min(n,100);j++)
			for(int k=1;k<=min(n,100);k++)
			{
				int a=i*i+j*j+k*k+i*j+k*j+i*k;
				if(a<=n)
					f[a]++;
			}
	for(int i=1;i<=n;i++)
		cout<<f[i]<<"\n";
}


### Prompt

Construct a cpp code solution to the problem outlined:

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;

const int N=1e+4+1;
int f[N],n;
int main()
{
	cin>>n;
	for(int i=1;i<=min(n,100);i++)
		for(int j=1;j<=min(n,100);j++)
			for(int k=1;k<=min(n,100);k++)
			{
				int a=i*i+j*j+k*k+i*j+k*j+i*k;
				if(a<=n)
					f[a]++;
			}
	for(int i=1;i<=n;i++)
		cout<<f[i]<<"\n";
}


```