#include <bits/stdc++.h>
#define maxn 102333
using namespace std;
int ans[maxn];
int main() {
	for(int i = 1; i <= 100; ++i) {
		for(int j = 1; j <= 100; ++j) {
			for(int k = 1; k <= 100; ++k) {
				++ans[i*i + j*j + k*k + i*j + j*k + k*i];
			}
		} 
	}
	int n;
	scanf("%d", &n);
	for(int i = 1; i <= n; ++i) {
		cout << ans[i] << 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>
#define maxn 102333
using namespace std;
int ans[maxn];
int main() {
	for(int i = 1; i <= 100; ++i) {
		for(int j = 1; j <= 100; ++j) {
			for(int k = 1; k <= 100; ++k) {
				++ans[i*i + j*j + k*k + i*j + j*k + k*i];
			}
		} 
	}
	int n;
	scanf("%d", &n);
	for(int i = 1; i <= n; ++i) {
		cout << ans[i] << endl;
	}
	return 0;
}
```