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

int main(){
  
  int N, i, j, k;
  cin>>N;
  map<int, int> data;
  for(i=1; i<=100; i++){
    for(j=1; j<=100; j++){
      for(k=1; k<=100; k++){
        
        data[i*i+j*j+k*k+i*j+j*k+k*i]++;
      }
    }
  }
  
  for(i=1; i<=N; i++){
    cout<<data[i]<<endl;
  }
  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;

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