#include <bits/stdc++.h>
#define f(i) for (int i=1 ; i<100 ; i++)
using namespace std;

int main(){
	
	int f[100000]={0},n; cin >> n;
		
	f(a)
		f(b)
			f(c) f[a*a+b*b+c*c+a*c+a*b+b*c]++;
				
	for (int i=1 ; i<=n ; i++) cout << f[i] << "\n";
	
	return 0;
}
### Prompt

Create a solution in cpp for 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>
#define f(i) for (int i=1 ; i<100 ; i++)
using namespace std;

int main(){
	
	int f[100000]={0},n; cin >> n;
		
	f(a)
		f(b)
			f(c) f[a*a+b*b+c*c+a*c+a*b+b*c]++;
				
	for (int i=1 ; i<=n ; i++) cout << f[i] << "\n";
	
	return 0;
}
```