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

int n, c[10005];
int main() {
	int i, j, k, x;
	cin >> n;
	for(i=1; i*i<=n; i++) for(j=1; j*j<=n; j++) for(k=1; k*k<=n; k++) {
		x = i*i + j*j + k*k + i*j + j*k + k*i;
		if(x<=n) c[x]++;
	}
	for(i=1; i<=n; i++) printf("%d\n", c[i]);
	return 0;
}

### Prompt

Create a solution in CPP for 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 <iostream>
#include <cstdio>
using namespace std;

int n, c[10005];
int main() {
	int i, j, k, x;
	cin >> n;
	for(i=1; i*i<=n; i++) for(j=1; j*j<=n; j++) for(k=1; k*k<=n; k++) {
		x = i*i + j*j + k*k + i*j + j*k + k*i;
		if(x<=n) c[x]++;
	}
	for(i=1; i<=n; i++) printf("%d\n", c[i]);
	return 0;
}

```