#include <bits/stdc++.h>
using namespace std;
using ll=long long;
#define rep(i,n) for (ll i=1; i<n; ++i)
#define all(c) begin(c),end(c)
/*
*/
int main(){
  ll N; cin>>N;
  vector<ll> ans(10010,0);
  rep(x,101) rep(y,101) rep(z,101){
    ll d=x*x+y*y+z*z+x*y+y*z+z*x;
    if(d > 10000) break;
    ans[d]++;
  }
  rep(i,N+1) cout<<ans[i]<<endl;
}
### Prompt

Generate 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;
using ll=long long;
#define rep(i,n) for (ll i=1; i<n; ++i)
#define all(c) begin(c),end(c)
/*
*/
int main(){
  ll N; cin>>N;
  vector<ll> ans(10010,0);
  rep(x,101) rep(y,101) rep(z,101){
    ll d=x*x+y*y+z*z+x*y+y*z+z*x;
    if(d > 10000) break;
    ans[d]++;
  }
  rep(i,N+1) cout<<ans[i]<<endl;
}
```