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>
#define LL long long
#define maxn 100005

using namespace std;
int jishu(int a,int b,int c)
{
    return a*a+b*b+c*c+a*b+b*c+c*a;
}
int main()
{
   int n;
   cin>>n;
   LL ans[10000+5];
   memset(ans,0,sizeof(ans));
   for(int i=1;i<=100;i++)
   {
       for(int j=i;j<=100;j++)
       {
           for(int k=j;k<=100;k++)
           {
               if(jishu(i,j,k)>10000)
               {
                   break;
               }
               else
               {
                   int tmp=jishu(i,j,k);
                   if(i==j&&j==k)
                   {
                       ans[tmp]++;
                   }
                   else if(i==j||j==k||k==i)
                    ans[tmp]+=3;
                   else
                    ans[tmp]+=6;
               }
           }
       }
   }
   for(int i=1;i<=n;i++)
    cout<<ans[i]<<endl;
}