#include <bits/stdc++.h>

using namespace std;

int main(){
	int N;
	cin >> N;

	vector<long> mem(N+1, 0);
	
	for(int i = 1; i < 110; i++){
		for(int j = 1; j < 110; j++){
			for(int k = 1; k < 110; k++){
				long v = i*i + j*j + k*k + i*j + j*k + k*i;
				if(v <= N) mem[v]++;
			}
		}
	}
	for(int i = 1; i <= N; i++){
		cout << mem[i] << endl;
	}
}
### 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;

	vector<long> mem(N+1, 0);
	
	for(int i = 1; i < 110; i++){
		for(int j = 1; j < 110; j++){
			for(int k = 1; k < 110; k++){
				long v = i*i + j*j + k*k + i*j + j*k + k*i;
				if(v <= N) mem[v]++;
			}
		}
	}
	for(int i = 1; i <= N; i++){
		cout << mem[i] << endl;
	}
}
```