#include<bits/stdc++.h>
using namespace std;
int main(){
int n;
cin >>n;
vector<int>num(n,0);
  
for(int i=1;i<100;i++){
for(int j=1;j<100;j++){
for(int k=1;k<100;k++){
int suuzi =i*i + j*j + k*k + i*j + j*k + k*i ;
if(suuzi<=n)
num.at(suuzi - 1)+=1;

}
}
}
for(int i=0;i<n;i++){
cout << num.at(i)<<endl;
} 
}
### 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>
using namespace std;
int main(){
int n;
cin >>n;
vector<int>num(n,0);
  
for(int i=1;i<100;i++){
for(int j=1;j<100;j++){
for(int k=1;k<100;k++){
int suuzi =i*i + j*j + k*k + i*j + j*k + k*i ;
if(suuzi<=n)
num.at(suuzi - 1)+=1;

}
}
}
for(int i=0;i<n;i++){
cout << num.at(i)<<endl;
} 
}
```