#include<bits/stdc++.h>
using namespace std;
const int N=1e4+5;
int f[N];
int main(){
	int n,s,x;scanf("%d",&n),s=sqrt(n);
	for(int i=1;i<=s;i++)for(int j=1;j<=s;j++)for(int k=1;k<=s;k++){
		x=i*(i+j+k)+j*(j+k)+k*k;
		if(x<N)f[x]++;
	}
	for(int i=1;i<=n;i++)printf("%d\n",f[i]);
	return 0;
}
### Prompt

Your challenge is to write 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<bits/stdc++.h>
using namespace std;
const int N=1e4+5;
int f[N];
int main(){
	int n,s,x;scanf("%d",&n),s=sqrt(n);
	for(int i=1;i<=s;i++)for(int j=1;j<=s;j++)for(int k=1;k<=s;k++){
		x=i*(i+j+k)+j*(j+k)+k*k;
		if(x<N)f[x]++;
	}
	for(int i=1;i<=n;i++)printf("%d\n",f[i]);
	return 0;
}
```