#include<bits/stdc++.h>
using namespace std;
int n,a[10001];
int main(){
	//freopen("1.out","w",stdout);
	cin>>n;
	for(int x=1;x*x<n;++x){
		for(int y=1;x*x+y*y+x*y<n;++y){
			for(int z=1;x*x+y*y+z*z+x*y+y*z+x*z<=n;++z){
				++a[x*x+y*y+z*z+x*y+y*z+x*z];
			}
		}
	}
	for(int i=1;i<=n;++i)cout<<a[i]<<endl;
} 
### 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 n,a[10001];
int main(){
	//freopen("1.out","w",stdout);
	cin>>n;
	for(int x=1;x*x<n;++x){
		for(int y=1;x*x+y*y+x*y<n;++y){
			for(int z=1;x*x+y*y+z*z+x*y+y*z+x*z<=n;++z){
				++a[x*x+y*y+z*z+x*y+y*z+x*z];
			}
		}
	}
	for(int i=1;i<=n;++i)cout<<a[i]<<endl;
} 
```