#include <bits/stdc++.h>
typedef long long ll;
using namespace std;

int main() {
	cin.tie(0);
	ios::sync_with_stdio(false);
	map<ll,ll>mp;
	int n;
	cin>>n;
	for(ll x=1;x<100;x++){
		for(ll y=1;y<100;y++){
			for(ll z=1;z<100;z++){
				mp[x*x+y*y+z*z+x*y+y*z+z*x]++;
			}
		}
	}
	for(int i=1;i<=n;i++){
		cout<<mp[i]<<endl;
	}
	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>
typedef long long ll;
using namespace std;

int main() {
	cin.tie(0);
	ios::sync_with_stdio(false);
	map<ll,ll>mp;
	int n;
	cin>>n;
	for(ll x=1;x<100;x++){
		for(ll y=1;y<100;y++){
			for(ll z=1;z<100;z++){
				mp[x*x+y*y+z*z+x*y+y*z+z*x]++;
			}
		}
	}
	for(int i=1;i<=n;i++){
		cout<<mp[i]<<endl;
	}
	return 0;
}


```