#include <iostream>
using namespace std;
typedef long long ll;

int main(){
  ll n;
  cin>>n;
  int m[n];fill(m,m+n,0);
  for(int i=1;i*i<=n;i++){
    for(int j=1;j*j<=n;j++){
      for(int k=1;k*k<=n;k++){
        if((i+j+k)*(i+j+k)-j*k-(j+k)*i-1<n)m[(i+j+k)*(i+j+k)-j*k-(j+k)*i-1]++;
      }
    }
  }
  for(int i=0;i<n;i++){
    cout << m[i]<<endl;
  }
}
### Prompt

Please formulate a CPP solution 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 <iostream>
using namespace std;
typedef long long ll;

int main(){
  ll n;
  cin>>n;
  int m[n];fill(m,m+n,0);
  for(int i=1;i*i<=n;i++){
    for(int j=1;j*j<=n;j++){
      for(int k=1;k*k<=n;k++){
        if((i+j+k)*(i+j+k)-j*k-(j+k)*i-1<n)m[(i+j+k)*(i+j+k)-j*k-(j+k)*i-1]++;
      }
    }
  }
  for(int i=0;i<n;i++){
    cout << m[i]<<endl;
  }
}
```