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

int main()
{
	ll n;
	cin >> n;
	vector<ll> cnt(n+1);

	for(int i = 1;i*i<=n;i++)
		for(int j = 1;j*j<=n;j++)
			for(int k = 1;k*k<=n;k++)
			{
				ll now = i*i+j*j+k*k+i*j+j*k+i*k;
				if(now>n)continue;
				cnt[now] ++ ;
			}
	for(int i = 1;i<=n;i++)cout << cnt[i] << endl;
}

### Prompt

Please create a solution in Cpp 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>
#include <vector>
using namespace std;
using ll = long long;

int main()
{
	ll n;
	cin >> n;
	vector<ll> cnt(n+1);

	for(int i = 1;i*i<=n;i++)
		for(int j = 1;j*j<=n;j++)
			for(int k = 1;k*k<=n;k++)
			{
				ll now = i*i+j*j+k*k+i*j+j*k+i*k;
				if(now>n)continue;
				cnt[now] ++ ;
			}
	for(int i = 1;i<=n;i++)cout << cnt[i] << endl;
}

```