#include <stdio.h>
int f[60005];
int main()
{
	for (int x = 1;x<=100;x++)
		for (int y = 1;y<= 100;y++)
			for (int z = 1;z <= 100;z++)
			{
				int ans = x*x+y*y+z*z+x*y+y*z+x*z;
				f[ans]++;
			}
	int n;
	scanf("%d",&n);
	for (int i = 1;i<= n;i++)
		printf("%d\n",f[i]);
	return 0;
}
### Prompt

Generate 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 <stdio.h>
int f[60005];
int main()
{
	for (int x = 1;x<=100;x++)
		for (int y = 1;y<= 100;y++)
			for (int z = 1;z <= 100;z++)
			{
				int ans = x*x+y*y+z*z+x*y+y*z+x*z;
				f[ans]++;
			}
	int n;
	scanf("%d",&n);
	for (int i = 1;i<= n;i++)
		printf("%d\n",f[i]);
	return 0;
}
```