#include <bits/stdc++.h>
using namespace std;
#define rep(i,n) for(int i=0; i<(n); i++)
typedef long long ll;

int main(){
	int n; cin>>n;
	vector<int> v(10001);
	for(int x=1; x<101; x++){
		for(int y=1; y<101; y++){
			for(int z=1; z<101; z++){
				int a=x*x+y*y+z*z+x*y+y*z+z*x;
				if (a<10001) v[a]+=1;
			}
		}
	}
	rep(i,n) cout<<v[i+1]<<endl;
}
### 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;
#define rep(i,n) for(int i=0; i<(n); i++)
typedef long long ll;

int main(){
	int n; cin>>n;
	vector<int> v(10001);
	for(int x=1; x<101; x++){
		for(int y=1; y<101; y++){
			for(int z=1; z<101; z++){
				int a=x*x+y*y+z*z+x*y+y*z+z*x;
				if (a<10001) v[a]+=1;
			}
		}
	}
	rep(i,n) cout<<v[i+1]<<endl;
}
```