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

int main() {
	int n; cin >> n;
	int a[6*n];
	
	memset(a,0,sizeof(a));
	
	for (int i=1; i<=int(sqrt(n)); ++i)
		for (int j=1; j<=n; ++j)
			for (int k=1; k<=int(sqrt(n)); ++k) {
				int v = i*i+j*j+k*k+i*j+j*k+i*k;
				if (v <= n) a[v]++;
			}
	for (int i=1; i<=n;++i) cout << a[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>
using namespace std;

int main() {
	int n; cin >> n;
	int a[6*n];
	
	memset(a,0,sizeof(a));
	
	for (int i=1; i<=int(sqrt(n)); ++i)
		for (int j=1; j<=n; ++j)
			for (int k=1; k<=int(sqrt(n)); ++k) {
				int v = i*i+j*j+k*k+i*j+j*k+i*k;
				if (v <= n) a[v]++;
			}
	for (int i=1; i<=n;++i) cout << a[i] << endl;
		
}
```