#include<iostream>
#include<math.h>
using namespace std;

int main() {
    int n;
    scanf("%d",&n);
    for(int i=1;i<=n;i++) {
        int res=0;
        int m=sqrt(i)+1;
        for(int a=1;a<=m;a++)
        for(int b=1;b<=m;b++)
        for(int c=1;c<=m;c++)
        if(a*a+b*b+c*c+a*b+b*c+c*a==i) res++;
        printf("%d\n",res);
    }
    return 0;
}
### 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<iostream>
#include<math.h>
using namespace std;

int main() {
    int n;
    scanf("%d",&n);
    for(int i=1;i<=n;i++) {
        int res=0;
        int m=sqrt(i)+1;
        for(int a=1;a<=m;a++)
        for(int b=1;b<=m;b++)
        for(int c=1;c<=m;c++)
        if(a*a+b*b+c*c+a*b+b*c+c*a==i) res++;
        printf("%d\n",res);
    }
    return 0;
}
```