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

int main() {
  int n;
  cin>>n;
  map<int,int> m;

  for(int i=1;i<=100;i++) {
    for(int j=1;j<=100;j++) {
      for(int k=1;k<=100;k++) {
        int val=i*i+j*j+k*k+i*j+j*k+k*i;
        m[val]++;
      }
    }
  }

  for(int i=1;i<=n;i++) {
    cout<<m[i]<<endl;
  }
}

### 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;
  cin>>n;
  map<int,int> m;

  for(int i=1;i<=100;i++) {
    for(int j=1;j<=100;j++) {
      for(int k=1;k<=100;k++) {
        int val=i*i+j*j+k*k+i*j+j*k+k*i;
        m[val]++;
      }
    }
  }

  for(int i=1;i<=n;i++) {
    cout<<m[i]<<endl;
  }
}

```