#include<bits/stdc++.h>
using namespace std;
int main(){
	int n,m,k,a[10010]={0},x,y,z;
	scanf("%d",&n);
	for(x=1;x<=100;x++){
		for(y=1;y<=100;y++){
			for(z=1;z<=100;z++){
				k=x*x+y*y+z*z+x*y+x*z+y*z; 
				if(k<=10000) a[k]++;
			}
		}
    }
	for(int i=1;i<=n;i++){
		printf("%d\n",a[i]);
	}
    return 0;
}
### Prompt

In cpp, your task is to solve 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;
int main(){
	int n,m,k,a[10010]={0},x,y,z;
	scanf("%d",&n);
	for(x=1;x<=100;x++){
		for(y=1;y<=100;y++){
			for(z=1;z<=100;z++){
				k=x*x+y*y+z*z+x*y+x*z+y*z; 
				if(k<=10000) a[k]++;
			}
		}
    }
	for(int i=1;i<=n;i++){
		printf("%d\n",a[i]);
	}
    return 0;
}
```