#include<bits/stdc++.h>

using namespace std;

int main(){
	int f[10005];
	for(int i=0;i<=10004;i++){
		f[i]=0;
	}
	for(int x=1;x<=105;x++){
		for(int y=1;y<=105;y++){
			for(int z=1;z<=105;z++){
				int tmp=x*x+y*y+z*z+x*y+y*z+x*z;
				if(tmp<=10004)
					f[tmp]++;
			}
		}
	}
		
	int n;
	cin>>n;
	for(int i=1;i<=n;i++){
		cout<<f[i]<<'\n';
	}
	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<bits/stdc++.h>

using namespace std;

int main(){
	int f[10005];
	for(int i=0;i<=10004;i++){
		f[i]=0;
	}
	for(int x=1;x<=105;x++){
		for(int y=1;y<=105;y++){
			for(int z=1;z<=105;z++){
				int tmp=x*x+y*y+z*z+x*y+y*z+x*z;
				if(tmp<=10004)
					f[tmp]++;
			}
		}
	}
		
	int n;
	cin>>n;
	for(int i=1;i<=n;i++){
		cout<<f[i]<<'\n';
	}
	return 0;
}
```