#include <bits/stdc++.h>

#define rep(i,n) for(int i=0;i<(n);i++)

using namespace std;

int main(){
	int n; scanf("%d",&n);
	vector<int> ans(n+1);
	for(int x=1;x*x<=n;x++) for(int y=1;y*y<=n;y++) for(int z=1;z*z<=n;z++) {
		int r=x*x+y*y+z*z+x*y+y*z+z*x;
		if(r<=n) ans[r]++;
	}
	rep(i,n) printf("%d\n",ans[i+1]);
	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>

#define rep(i,n) for(int i=0;i<(n);i++)

using namespace std;

int main(){
	int n; scanf("%d",&n);
	vector<int> ans(n+1);
	for(int x=1;x*x<=n;x++) for(int y=1;y*y<=n;y++) for(int z=1;z*z<=n;z++) {
		int r=x*x+y*y+z*z+x*y+y*z+z*x;
		if(r<=n) ans[r]++;
	}
	rep(i,n) printf("%d\n",ans[i+1]);
	return 0;
}

```