#include<bits/stdc++.h>
using namespace std;
const int N=1e4+5;
int f[N];
int main(){
	int n;
	scanf("%d",&n);
	for(int a=1;a<=100;a++){
		for(int b=1;b<=100;b++){
			for(int c=1;c<=100;c++){
				int sum=a*a+b*b+c*c+a*b+b*c+c*a;
				if(sum<=n) f[sum]++; 
			}
		}
	}
	for(int i=1;i<=n;i++) printf("%d\n",f[i]);
	return 0;
}
### Prompt

Your task is to create 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;
	scanf("%d",&n);
	for(int a=1;a<=100;a++){
		for(int b=1;b<=100;b++){
			for(int c=1;c<=100;c++){
				int sum=a*a+b*b+c*c+a*b+b*c+c*a;
				if(sum<=n) f[sum]++; 
			}
		}
	}
	for(int i=1;i<=n;i++) printf("%d\n",f[i]);
	return 0;
}
```