#include<bits/stdc++.h>
typedef long long ll;
using namespace std;
int main()
{
	ll n,error=0;
	cin >> n;
	ll f[10005];
	memset(f,0,sizeof(f));
	for(ll i=1;i<=100;i++){
		for(ll j=1;j<=100;j++){
			for(ll k=1;k<=100;k++){
				ll x=i*i+j*j+k*k+i*j+i*k+j*k;
				if(x<=10000){
					f[x]++;
				}
			}
		}
	}
	for(ll i=1;i<=n;i++){
		cout << f[i] << endl;
	}
}
### 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>
typedef long long ll;
using namespace std;
int main()
{
	ll n,error=0;
	cin >> n;
	ll f[10005];
	memset(f,0,sizeof(f));
	for(ll i=1;i<=100;i++){
		for(ll j=1;j<=100;j++){
			for(ll k=1;k<=100;k++){
				ll x=i*i+j*j+k*k+i*j+i*k+j*k;
				if(x<=10000){
					f[x]++;
				}
			}
		}
	}
	for(ll i=1;i<=n;i++){
		cout << f[i] << endl;
	}
}
```