Problem:
Score : 300 points

Problem Statement

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).

Sample Input 1

20

Sample Output 1

0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
3
3
0
0

For n=6, only (1,1,1) satisfies both of the conditions. Thus, f(6) = 1.

For n=11, three triples, (1,1,2), (1,2,1), and (2,1,1), satisfy both of the conditions. Thus, f(6) = 3.

For n=17, three triples, (1,2,2), (2,1,2), and (2,2,1), satisfy both of the conditions. Thus, f(17) = 3.

For n=18, three triples, (1,1,3), (1,3,1), and (3,1,1), satisfy both of the conditions. Thus, f(18) = 3.

Solution in C++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>

using namespace std;

#define IOS ios_base::sync_with_stdio(false);   cin.tie(NULL); cout.tie(NULL);

#define endl "\n";

#define loop(i,s,n)  for(ll i=s;i<n;i++)
#define test  ll t; cin>>t; while(t--)
#define p push_back
typedef long long ll;
int main()
{IOS
ll n,w;
cin>>n;
ll a[10001]={0};
for(auto x=1;x<=100;x++)
{for(auto y=1;y<=100;y++)
{for(auto z=1;z<=100;z++)
{w=(x*x)+(y*y)+(z*z)+(x*y)+(y*z)+(z*x);
if(w<=10000)
{a[w]++;}}}}


for(auto i=1;i<=n;i++)
{cout<<a[i]<<endl}





return 0;
}