#include<bits/stdc++.h>
using namespace std;
int n;
const int N=1e4+10;
int a[N];
int main(){
	cin>>n;
	for(int i=1;i<=110;i++){
		for(int j=1;j<=110;j++){
			for(int k=1;k<=110;k++){
				if((long long)i*i+j*j+k*k+i*j+i*k+j*k>n){
					break;
				}
				else a[i*i+j*j+k*k+i*j+i*k+j*k]++;
			}
		}
	}
	for(int i=1;i<=n;i++)
	printf("%d\n",a[i]);
	
	
	return 0;
} 
### Prompt

Generate 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;
int n;
const int N=1e4+10;
int a[N];
int main(){
	cin>>n;
	for(int i=1;i<=110;i++){
		for(int j=1;j<=110;j++){
			for(int k=1;k<=110;k++){
				if((long long)i*i+j*j+k*k+i*j+i*k+j*k>n){
					break;
				}
				else a[i*i+j*j+k*k+i*j+i*k+j*k]++;
			}
		}
	}
	for(int i=1;i<=n;i++)
	printf("%d\n",a[i]);
	
	
	return 0;
} 
```