#include <bits/stdc++.h>
using namespace std;
#define rep1(i, n) for(int i=1; i<=n; i++)

int main() {
	int N;
	cin >> N;
	vector<int> v(10001);
	rep1(x, 100) {
		rep1(y, 100) {
			rep1(z, 100) {
				int f = x*(x+y+z) + y*(y+z) + z*z;
				if (f > 10000) break;
				else v.at(f)++;
			}
		}
	}
	rep1(i, N) {
		std::cout << v.at(i) << '\n';
	}
}

### Prompt

Please provide a CPP coded solution 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;
#define rep1(i, n) for(int i=1; i<=n; i++)

int main() {
	int N;
	cin >> N;
	vector<int> v(10001);
	rep1(x, 100) {
		rep1(y, 100) {
			rep1(z, 100) {
				int f = x*(x+y+z) + y*(y+z) + z*z;
				if (f > 10000) break;
				else v.at(f)++;
			}
		}
	}
	rep1(i, N) {
		std::cout << v.at(i) << '\n';
	}
}

```