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

int main(){
	int n, i, j, k;
	cin >> n;
	int arr[1000001]={0};

	for(i=1; i<=100; i++){
		for(j=1; j<=100; j++){
			for(k=1; k<=100; k++){
				int x = i*i + j*j + k*k + i*j + j*k + k*i;
				// cout << "AA" << x << "\n";
				arr[x]++;
			}
		}
	}

	for(i=1; i<=n; i++)
		cout << arr[i] << "\n";
}
### 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>
using namespace std;

int main(){
	int n, i, j, k;
	cin >> n;
	int arr[1000001]={0};

	for(i=1; i<=100; i++){
		for(j=1; j<=100; j++){
			for(k=1; k<=100; k++){
				int x = i*i + j*j + k*k + i*j + j*k + k*i;
				// cout << "AA" << x << "\n";
				arr[x]++;
			}
		}
	}

	for(i=1; i<=n; i++)
		cout << arr[i] << "\n";
}
```