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: Time Limit Exceeded)

// Example program
#include <iostream>
#include <string>
using namespace std;
#include<math.h>
void solve()
{
   int n;
   cin>>n; long long  cnt=0;
   for(int c=1;c<=n;c++){ cnt=0;
   for(int i=1;i<=sqrt(c);i++)
     {
         for(int j=1;j<=sqrt(c);j++)
            {
                for(int k=1;k<=sqrt(c);k++)
                   {
                       if(pow((i+j+k),2)-i*j -j*k -i*k == c)
                          cnt++;
                   }
            }
     }
   cout<<cnt<<endl;
   }
    
     
}

int main()
{
 //int t; cin>>t;
// while(t--)
    solve();
}