#include<bits/stdc++.h>
using namespace std;
int main(void){
	int n,ans,i,j,k;
	cin>>n;
	map<int,int>mp;
	for(i=1;i*i<=n;i++){
		for(j=1;j*j<=n;j++){
			for(k=1;k*k<=n;k++){
				ans=i*i+j*j+k*k+i*j+i*k+j*k;
				mp[ans]++;
			}
		}
	}
	for(i=1;i<=n;i++)
	cout<<mp[i]<<endl;
}

### Prompt

In Cpp, your task is to solve 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(void){
	int n,ans,i,j,k;
	cin>>n;
	map<int,int>mp;
	for(i=1;i*i<=n;i++){
		for(j=1;j*j<=n;j++){
			for(k=1;k*k<=n;k++){
				ans=i*i+j*j+k*k+i*j+i*k+j*k;
				mp[ans]++;
			}
		}
	}
	for(i=1;i<=n;i++)
	cout<<mp[i]<<endl;
}

```