#include<bits/stdc++.h>
using namespace std;
int main()
{
	int N;
	cin >> N;
	int x,y,z;
	int c[10005]={0};
	for(x = 1; x <= 105; x++){
		for(y = 1; y <= 105; y++){
			for(z = 1; z <= 105; z++){
				int sum = x*x+y*y+z*z+x*y+z*x+y*z;
				if(sum < 10001){
					c[sum]++;
				}
			}	
		}		
	}	
	for(int i = 0;i < N;i++){
		cout << c[i+1] << endl;
	}			
	return 0;		
}
### Prompt

Develop a solution in Cpp to the problem described below:

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;
	cin >> N;
	int x,y,z;
	int c[10005]={0};
	for(x = 1; x <= 105; x++){
		for(y = 1; y <= 105; y++){
			for(z = 1; z <= 105; z++){
				int sum = x*x+y*y+z*z+x*y+z*x+y*z;
				if(sum < 10001){
					c[sum]++;
				}
			}	
		}		
	}	
	for(int i = 0;i < N;i++){
		cout << c[i+1] << endl;
	}			
	return 0;		
}
```