#include<bits/stdc++.h>
using namespace std;
int main(){
	int n;
	cin>>n;
	++n;
	map<int,int>a;
	for(int x=1;(x+2)*x<n;++x){
		for(int y=1;x*x+y*y+1+x*y+y<n;++y){
			for(int z=1;1;++z){
				int s=x*x+y*y+z*z+x*y+y*z+z*x;
				if(s>n)break;
				++a[s];
			}
		}
	}
	for(int i=1;i<n;++i){
		cout<<a[i]<<endl;
	}
	return 0;
}
### Prompt

Construct a CPP code solution to the problem outlined:

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 n;
	cin>>n;
	++n;
	map<int,int>a;
	for(int x=1;(x+2)*x<n;++x){
		for(int y=1;x*x+y*y+1+x*y+y<n;++y){
			for(int z=1;1;++z){
				int s=x*x+y*y+z*z+x*y+y*z+z*x;
				if(s>n)break;
				++a[s];
			}
		}
	}
	for(int i=1;i<n;++i){
		cout<<a[i]<<endl;
	}
	return 0;
}
```