#include<bits/stdc++.h>
using namespace std;
int main()
{
  int n;
  int ans[60001];
  scanf("%d",&n);
  memset(ans,0,sizeof(ans));
  for(int x=1;x<=100;x++)
  {
    for(int y=1;y<=100;y++)
    {
      for(int z=1;z<=100;z++)
        ans[x*x+y*y+z*z+x*z+y*z+x*y]++;
    }
  }
  for(int i=1;i<=n;i++)
    printf("%d\n",ans[i]);
}
### Prompt

Please create a solution in Cpp to 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 main()
{
  int n;
  int ans[60001];
  scanf("%d",&n);
  memset(ans,0,sizeof(ans));
  for(int x=1;x<=100;x++)
  {
    for(int y=1;y<=100;y++)
    {
      for(int z=1;z<=100;z++)
        ans[x*x+y*y+z*z+x*z+y*z+x*y]++;
    }
  }
  for(int i=1;i<=n;i++)
    printf("%d\n",ans[i]);
}
```