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

int main(){
  int N; cin >> N;
  vector<int> a(N+1);
  
  for (int i=1; i<=100; i++){
    for (int j=1; j<=100; j++){
      for (int k=1; k<=100; k++){
        int b = i*i+j*j+k*k+i*j+j*k+k*i;
        if (b<=N){a.at(b)++;}
      }
    }
  }
  
  for (int i=1; i<=N;i++){
  cout << a.at(i) << endl;
  }
}
### Prompt

Construct a CPP code solution to the problem outlined:

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> a(N+1);
  
  for (int i=1; i<=100; i++){
    for (int j=1; j<=100; j++){
      for (int k=1; k<=100; k++){
        int b = i*i+j*j+k*k+i*j+j*k+k*i;
        if (b<=N){a.at(b)++;}
      }
    }
  }
  
  for (int i=1; i<=N;i++){
  cout << a.at(i) << endl;
  }
}
```