#include<bits/stdc++.h>
using namespace std;
int main(){
  int n;
  cin>>n;
  vector<int> ans(10001,0);
  for(int x=1;x<=100;x++){
    for(int y=1;y<=100;y++){
      for(int z=1;z<=100;z++){
        if(x*x+y*y+z*z+x*y+y*z+z*x>10000) continue;
        ans[x*x+y*y+z*z+x*y+y*z+z*x]++;
      }
    }
  }for(int i=1;i<=n;i++){
    cout<<ans[i]<<endl;
  }
}
### 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;
  cin>>n;
  vector<int> ans(10001,0);
  for(int x=1;x<=100;x++){
    for(int y=1;y<=100;y++){
      for(int z=1;z<=100;z++){
        if(x*x+y*y+z*z+x*y+y*z+z*x>10000) continue;
        ans[x*x+y*y+z*z+x*y+y*z+z*x]++;
      }
    }
  }for(int i=1;i<=n;i++){
    cout<<ans[i]<<endl;
  }
}
```