#include<bits/stdc++.h>
using namespace std;
int f[10005];
int main()
{
	for(int i=1;i<=100;i++)
	for(int j=1;j<=100;j++)
	for(int k=1;k<=100;k++)
	{
		int t=i*i+j*j+k*k+i*j+i*k+j*k;
		if(t<=10000)f[t]++;
	}
	int n;
	scanf("%d",&n);
	for(int i=1;i<=n;i++)printf("%d\n",f[i]);
	return 0;
}

### 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;
int f[10005];
int main()
{
	for(int i=1;i<=100;i++)
	for(int j=1;j<=100;j++)
	for(int k=1;k<=100;k++)
	{
		int t=i*i+j*j+k*k+i*j+i*k+j*k;
		if(t<=10000)f[t]++;
	}
	int n;
	scanf("%d",&n);
	for(int i=1;i<=n;i++)printf("%d\n",f[i]);
	return 0;
}

```