#include <bits/stdc++.h>
using namespace std;int main(){int N;cin>>N;int ANS[60000];for(int i=0;i<N;i++)ANS[i]=0;for(int x=1;x<101;x++)for(int y=1;y<101;y++)for(int z=1;z<101;z++)ANS[x*x+y*y+z*z+x*y+y*z+z*x-1]++;for(int i=0;i<N;i++)cout<<ANS[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(){int N;cin>>N;int ANS[60000];for(int i=0;i<N;i++)ANS[i]=0;for(int x=1;x<101;x++)for(int y=1;y<101;y++)for(int z=1;z<101;z++)ANS[x*x+y*y+z*z+x*y+y*z+z*x-1]++;for(int i=0;i<N;i++)cout<<ANS[i]<<endl;}

```