#include <bits/stdc++.h>
using namespace std;

int main(){
  int N;
  cin >> N;
  vector<int> f(N+1,0);
  for(int i=1; i<100; i++){
    for(int j=1; j<100; j++){
      for(int k=1; k<100; k++){
        int p = i*i + j*j + k*k + i*j + i*k + j*k;
        if(p <= N) f[p]++;
      }
    }
  }
  for(int i=1; i<=N; i++){
    cout << f[i] << endl;
  }
  return 0;
}
### 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 <bits/stdc++.h>
using namespace std;

int main(){
  int N;
  cin >> N;
  vector<int> f(N+1,0);
  for(int i=1; i<100; i++){
    for(int j=1; j<100; j++){
      for(int k=1; k<100; k++){
        int p = i*i + j*j + k*k + i*j + i*k + j*k;
        if(p <= N) f[p]++;
      }
    }
  }
  for(int i=1; i<=N; i++){
    cout << f[i] << endl;
  }
  return 0;
}
```