// C - XYZ Triplets
#include <bits/stdc++.h>
using namespace std;

int main(){
	int n; cin>>n;
	vector<int> f(n);
	for(int x=1; x*x<n; ++x)
		for(int y=1; y*y<n; ++y)
			for(int z=1; z*z<n; ++z){
				int k = x*x + y*y + z*z + x*y + y*z + z*x;
				if(1<=k && k<=n) f[k]++;
			}
	for(int i=1; i<=n; ++i) cout<< f[i] <<endl;
}

### 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
// C - XYZ Triplets
#include <bits/stdc++.h>
using namespace std;

int main(){
	int n; cin>>n;
	vector<int> f(n);
	for(int x=1; x*x<n; ++x)
		for(int y=1; y*y<n; ++y)
			for(int z=1; z*z<n; ++z){
				int k = x*x + y*y + z*z + x*y + y*z + z*x;
				if(1<=k && k<=n) f[k]++;
			}
	for(int i=1; i<=n; ++i) cout<< f[i] <<endl;
}

```