#include <bits/stdc++.h>
using namespace std;
 
int main() {
    
           int n;
           cin >>n;

    vector<int> vec(10005,0);
  int v=0;
  for(int i=1;i<=sqrt(n);i++){
  for(int j=1;j<=sqrt(n);j++){
  for(int k=1;k<=sqrt(n);k++){
    
v=j*(i+j+k)+k*(i+k)+i*i;
    if(v<=10000){vec[v]++;}
  
  }
  }
  }
 for(int i=1;i<=n;i++)cout<<vec[i]<<endl;



}
### 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;
           cin >>n;

    vector<int> vec(10005,0);
  int v=0;
  for(int i=1;i<=sqrt(n);i++){
  for(int j=1;j<=sqrt(n);j++){
  for(int k=1;k<=sqrt(n);k++){
    
v=j*(i+j+k)+k*(i+k)+i*i;
    if(v<=10000){vec[v]++;}
  
  }
  }
  }
 for(int i=1;i<=n;i++)cout<<vec[i]<<endl;



}
```