#include <bits/stdc++.h>
using namespace std;
long long ans[100005], n;
int main (){
ios::sync_with_stdio(0);
cin.tie(0); cout.tie(0);
cin >> n;
for (int i=1; n>=i*i; i++){
	for (int j=1; n>=j*j; j++){
		for (int k=1; n>=k*k; k++){
			ans[i*i+j*j+k*k+i*j+i*k+j*k]++;
		}
	}	
}
for (int i=1; i<=n; i++)
	cout << ans[i] << endl;
return 0;
}

### Prompt

Your challenge is to write a Cpp solution 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;
long long ans[100005], n;
int main (){
ios::sync_with_stdio(0);
cin.tie(0); cout.tie(0);
cin >> n;
for (int i=1; n>=i*i; i++){
	for (int j=1; n>=j*j; j++){
		for (int k=1; n>=k*k; k++){
			ans[i*i+j*j+k*k+i*j+i*k+j*k]++;
		}
	}	
}
for (int i=1; i<=n; i++)
	cout << ans[i] << endl;
return 0;
}

```