#include<bits/stdc++.h>
using namespace std;
using ll = long long;
int main(){
  ll n;cin>>n;int a[10001]={0};
  for(int i=1;i*i<=10000;i++){
	for(int j=1;j*j<=10000;j++){
	  for(int k=1;k*k<=10000;k++){
	  	ll x=i*i+j*j+k*k+i*j+j*k+k*i;
	  	if(x<=10000)a[x]++;
      }
    }
  }
  for(int i=1;i<=n;i++){
    cout<<a[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>
using namespace std;
using ll = long long;
int main(){
  ll n;cin>>n;int a[10001]={0};
  for(int i=1;i*i<=10000;i++){
	for(int j=1;j*j<=10000;j++){
	  for(int k=1;k*k<=10000;k++){
	  	ll x=i*i+j*j+k*k+i*j+j*k+k*i;
	  	if(x<=10000)a[x]++;
      }
    }
  }
  for(int i=1;i<=n;i++){
    cout<<a[i]<<endl;
  }
}

```