#import<bits/stdc++.h>
#define endl '\n'
using namespace std;
typedef long long LL;
LL i,j,k,m,n,a[1000005];
string s;
int main()
{
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	cout.tie(0);
	cin>>n;
	for(;i++<100;)
	{
		for(j=i-1;j++<100;)
		{
			for(k=j-1;k++<100;)a[i*i+j*j+k*k+i*j+j*k+k*i]+=i<j?j<k?6:3:j<k?3:1;
		}
	}
	for(i=0;i++<n;)cout<<a[i]<<endl;
}
### Prompt

Generate 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
#import<bits/stdc++.h>
#define endl '\n'
using namespace std;
typedef long long LL;
LL i,j,k,m,n,a[1000005];
string s;
int main()
{
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	cout.tie(0);
	cin>>n;
	for(;i++<100;)
	{
		for(j=i-1;j++<100;)
		{
			for(k=j-1;k++<100;)a[i*i+j*j+k*k+i*j+j*k+k*i]+=i<j?j<k?6:3:j<k?3:1;
		}
	}
	for(i=0;i++<n;)cout<<a[i]<<endl;
}
```