#include <bits/stdc++.h>
using namespace std;
int f(int a,int b,int n){
	return a*a+b*b+n*n+a*b+a*n+b*n;
}
int main() {
	int n,x[10002];
	cin>>n;
	for(int i=1;i<=n;i++)x[i]=0;
	for(int a=1;a<=100;a++){
		for(int i=1;i<=100;i++)
			for(int j=1;j<=100;j++)
				if(f(i,j,a)<=n)x[f(i,j,a)]++;
	}
	for(int i=1;i<=n;i++)cout<<x[i]<<'\n';
	return 0;
}
### Prompt

In Cpp, your task is to solve 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 f(int a,int b,int n){
	return a*a+b*b+n*n+a*b+a*n+b*n;
}
int main() {
	int n,x[10002];
	cin>>n;
	for(int i=1;i<=n;i++)x[i]=0;
	for(int a=1;a<=100;a++){
		for(int i=1;i<=100;i++)
			for(int j=1;j<=100;j++)
				if(f(i,j,a)<=n)x[f(i,j,a)]++;
	}
	for(int i=1;i<=n;i++)cout<<x[i]<<'\n';
	return 0;
}
```