#include<iostream>

using namespace std;
int a[1000010]; 
int main() {
	int n;
	cin>>n;
	for(int i=1;i<100;i++) 
		for(int j=1;j<100;j++)
			for(int k=1;k<100;k++) {
				int t = i+j+k;
				t*=t;
				t-=i*j+i*k+j*k;
				a[t]++;
			}
	
	for(int i=1;i<=n;i++) printf("%d\n",a[i]);
	return 0;
}

### Prompt

Please formulate a CPP solution 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<iostream>

using namespace std;
int a[1000010]; 
int main() {
	int n;
	cin>>n;
	for(int i=1;i<100;i++) 
		for(int j=1;j<100;j++)
			for(int k=1;k<100;k++) {
				int t = i+j+k;
				t*=t;
				t-=i*j+i*k+j*k;
				a[t]++;
			}
	
	for(int i=1;i<=n;i++) printf("%d\n",a[i]);
	return 0;
}

```