#include <bits/stdc++.h>
using namespace std;
#define LL long long
#define F(i,a,b) for(int i=a;i<=b;++i)
int n,f[10005];
int main()
{
	cin>>n;
	F(i,1,100) F(j,1,100) F(k,1,100)
	if(i*i+j*j+k*k+i*j+j*k+k*i<=n) ++f[i*i+j*j+k*k+i*j+j*k+k*i];
	F(i,1,n) printf("%d\n",f[i]);
	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;
#define LL long long
#define F(i,a,b) for(int i=a;i<=b;++i)
int n,f[10005];
int main()
{
	cin>>n;
	F(i,1,100) F(j,1,100) F(k,1,100)
	if(i*i+j*j+k*k+i*j+j*k+k*i<=n) ++f[i*i+j*j+k*k+i*j+j*k+k*i];
	F(i,1,n) printf("%d\n",f[i]);
	return 0;
}
```