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

int main() {
 vector<int> vec(10001);
for(int i=1;i<101;i++){
  for(int j=1;j<101;j++){
    for(int k=1;k<101;k++){
      if(i*i+j*j+k*k+i*j+j*k+k*i<=10000){vec.at(i*i+j*j+k*k+i*j+j*k+k*i)++;}
    }
  }
}
  
int n;
  cin>>n;
  for(int i=1;i<=n;i++){cout<<vec.at(i)<<endl;}
}
### Prompt

Create a solution in cpp for 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() {
 vector<int> vec(10001);
for(int i=1;i<101;i++){
  for(int j=1;j<101;j++){
    for(int k=1;k<101;k++){
      if(i*i+j*j+k*k+i*j+j*k+k*i<=10000){vec.at(i*i+j*j+k*k+i*j+j*k+k*i)++;}
    }
  }
}
  
int n;
  cin>>n;
  for(int i=1;i<=n;i++){cout<<vec.at(i)<<endl;}
}
```