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

int main(){
  int N,x,y,z,cnt;
  cin>>N;
  int C[10100]={};

  for(x=1;x<=100;x++){
    for(y=1;y<=100;y++){
      for(z=1;(x*x+y*y+z*z+x*y+x*z+y*z)<=10010;z++){
        C[x*x+y*y+z*z+x*y+x*z+y*z]++;
      }
    }
  }
  for(int i=1;i<=N;i++){
    cout<<C[i]<<endl;
  }
  
  return 0;
}

### Prompt

Your challenge is to write 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,x,y,z,cnt;
  cin>>N;
  int C[10100]={};

  for(x=1;x<=100;x++){
    for(y=1;y<=100;y++){
      for(z=1;(x*x+y*y+z*z+x*y+x*z+y*z)<=10010;z++){
        C[x*x+y*y+z*z+x*y+x*z+y*z]++;
      }
    }
  }
  for(int i=1;i<=N;i++){
    cout<<C[i]<<endl;
  }
  
  return 0;
}

```