#include <iostream>
int main(){int N,A[60000],i=0,j=1,x=1,c=101;std::cin>>N;for(;i<N;i++)A[i]=0;for(;x<c;x++)for(int y=1;y<c;y++)for(int z=1;z<c;z++)A[x*x+y*y+z*z+x*y+y*z+z*x]++;for(;j<=N;j++)std::cout<<A[j]<<std::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 <iostream>
int main(){int N,A[60000],i=0,j=1,x=1,c=101;std::cin>>N;for(;i<N;i++)A[i]=0;for(;x<c;x++)for(int y=1;y<c;y++)for(int z=1;z<c;z++)A[x*x+y*y+z*z+x*y+y*z+z*x]++;for(;j<=N;j++)std::cout<<A[j]<<std::endl;}

```