#include<bits/stdc++.h>
using namespace std;
const int N=1e4+10;
int res[N*10];
int main(){
	int n;
	cin>>n;
	int r=sqrt(n);
	for(int i=1;i<=r;i++){
		for(int j=1;j<=r;j++){
			for(int k=1;k<=r;k++){
				int key=i*i+j*j+k*k+i*j+j*k+i*k;
				if(key>N)break;
				else res[key]++;
			}
		}
	}
	for(int i=1;i<=n;i++){
		printf("%d\n",res[i]);
	}
}
### Prompt

Construct a CPP code solution to the problem outlined:

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;
const int N=1e4+10;
int res[N*10];
int main(){
	int n;
	cin>>n;
	int r=sqrt(n);
	for(int i=1;i<=r;i++){
		for(int j=1;j<=r;j++){
			for(int k=1;k<=r;k++){
				int key=i*i+j*j+k*k+i*j+j*k+i*k;
				if(key>N)break;
				else res[key]++;
			}
		}
	}
	for(int i=1;i<=n;i++){
		printf("%d\n",res[i]);
	}
}
```