#include<bits/stdc++.h>
using namespace std;
int i,n,k,j,u;
int a[10010];
int main(){
	cin>>n;
	for(i=1;i<sqrt(n);i++){
		for(j=1;j<sqrt(n);j++){
			for(k=1;k<sqrt(n);k++){
				u=pow(i,2)+pow(j,2)+pow(k,2)+i*j+i*k+j*k;
				if(u<=n)a[u]++;
			}
		}
	}
	for(i=1;i<=n;i++)cout<<a[i]<<endl;
	return 0;
}
### Prompt

Your task is to create 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 i,n,k,j,u;
int a[10010];
int main(){
	cin>>n;
	for(i=1;i<sqrt(n);i++){
		for(j=1;j<sqrt(n);j++){
			for(k=1;k<sqrt(n);k++){
				u=pow(i,2)+pow(j,2)+pow(k,2)+i*j+i*k+j*k;
				if(u<=n)a[u]++;
			}
		}
	}
	for(i=1;i<=n;i++)cout<<a[i]<<endl;
	return 0;
}
```