#include<bits/stdc++.h>
using namespace std;
int ans[1000200];
int main() {
	int n;
	scanf("%d",&n);
	for(int i=1; i*i<=n; ++i) {
		for(int j=1; j*j<=n; ++j) {
			for(int k=1; k*k<=n; ++k) {
				int t;
				t=i*i+j*j+k*k+i*j+i*k+j*k;
				ans[t]++;
			}
		}
	}
	for(int i=1;i<=n;++i){
		printf("%d\n",ans[i]);
	}
	return 0;
}
### Prompt

Develop a solution in Cpp to the problem described below:

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 ans[1000200];
int main() {
	int n;
	scanf("%d",&n);
	for(int i=1; i*i<=n; ++i) {
		for(int j=1; j*j<=n; ++j) {
			for(int k=1; k*k<=n; ++k) {
				int t;
				t=i*i+j*j+k*k+i*j+i*k+j*k;
				ans[t]++;
			}
		}
	}
	for(int i=1;i<=n;++i){
		printf("%d\n",ans[i]);
	}
	return 0;
}
```