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

int main() {
	//cout<<"GfG!";
	int j,k,n,i,c=0;
	cin>>n;
	map<int,int>mp;
	for(i=1;i<105;i++)
	{
	for(j=1;j<105;j++)
	{
	for(k=1;k<105;k++){
	    mp[i*i+j*j+k*k+i*j+j*k+k*i]++;
	}}}
	for(i=1;i<=n;i++)
	cout<<mp[i]<<endl;
//	return 0;
}

### Prompt

Please provide a CPP coded solution 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 <bits/stdc++.h>
using namespace std;

int main() {
	//cout<<"GfG!";
	int j,k,n,i,c=0;
	cin>>n;
	map<int,int>mp;
	for(i=1;i<105;i++)
	{
	for(j=1;j<105;j++)
	{
	for(k=1;k<105;k++){
	    mp[i*i+j*j+k*k+i*j+j*k+k*i]++;
	}}}
	for(i=1;i<=n;i++)
	cout<<mp[i]<<endl;
//	return 0;
}

```