#include <cstdio>
#include <queue>
using namespace std;

int main(){
	int n;
	scanf("%d", &n);
	vector <int> ans(n+1, 0);
	for(int i = 1;i <= 200;i ++){
		for(int j = 1;j <= 200;j ++){
			for(int k = 1;k <= 200;k ++){
				if(i*i+j*j+k*k+i*j+j*k+i*k<=n){
					ans[i*i+j*j+k*k+i*j+j*k+i*k]++;
				}
			}
		}
	}
	for(int i = 1;i <= n;i ++)
		printf("%d\n", ans[i]);
}
### Prompt

Please create a solution in Cpp 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 <cstdio>
#include <queue>
using namespace std;

int main(){
	int n;
	scanf("%d", &n);
	vector <int> ans(n+1, 0);
	for(int i = 1;i <= 200;i ++){
		for(int j = 1;j <= 200;j ++){
			for(int k = 1;k <= 200;k ++){
				if(i*i+j*j+k*k+i*j+j*k+i*k<=n){
					ans[i*i+j*j+k*k+i*j+j*k+i*k]++;
				}
			}
		}
	}
	for(int i = 1;i <= n;i ++)
		printf("%d\n", ans[i]);
}
```