#include<bits/stdc++.h>
using namespace std;
typedef long long ll;

int main(){

ll n;
cin>>n;
ll a[10005]={0};
for(ll i=1;i<=105;i++){
    for(ll j=1;j<=105;j++){
        for(ll k=1;k<=105;k++){
            ll v=i*i+j*j+k*k+i*j+i*k+j*k;
            if(v<10005)
                a[v]+=1;
        }
    }
}

for(ll i=1;i<=n;i++)
    cout<<a[i]<<"\n";
return 0;
}

### 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;
typedef long long ll;

int main(){

ll n;
cin>>n;
ll a[10005]={0};
for(ll i=1;i<=105;i++){
    for(ll j=1;j<=105;j++){
        for(ll k=1;k<=105;k++){
            ll v=i*i+j*j+k*k+i*j+i*k+j*k;
            if(v<10005)
                a[v]+=1;
        }
    }
}

for(ll i=1;i<=n;i++)
    cout<<a[i]<<"\n";
return 0;
}

```