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

int N;

void solve()
{
	map<int, int> cnt;
	for(int x=1;x*x<=N;++x)for(int y=1;y*y<=N;++y)for(int z=1;z*z<=N;++z){
		cnt[x*x+y*y+z*z+x*y+y*z+x*z]++;
	}
	for(int i=1;i<=N;++i) cout << cnt[i] << '\n';
}

int main()
{
	cin >> N;
	solve();
	return 0;
}
### 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;
using ll = long long;

int N;

void solve()
{
	map<int, int> cnt;
	for(int x=1;x*x<=N;++x)for(int y=1;y*y<=N;++y)for(int z=1;z*z<=N;++z){
		cnt[x*x+y*y+z*z+x*y+y*z+x*z]++;
	}
	for(int i=1;i<=N;++i) cout << cnt[i] << '\n';
}

int main()
{
	cin >> N;
	solve();
	return 0;
}
```