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: Wrong Answer)

#include<stdio.h>
#include<iostream>
#include<vector>
#include<math.h>
#include<queue>
#include<map>
#include<algorithm>
#include<string.h>
#include<functional>
#include<limits.h>
#include<stdlib.h>
#include<string>
#include<unordered_map>
#include<cmath>
using namespace std;

#define ll long long
int main(){
  int N;
  cin>>N;
  ll ans=0;
  for(int n=1;n<=N;n++){
    ans=0;
    for(int A=2;A<=100;A++){
      for(int B=2;B<=100;B++){
        if(A*A+B*B>2*n) break;
        int C=sqrt(2*n-A*A-B*B);
        int S=A+B+C;
        if(C*C==2*n-A*A-B*B && S%2==0 && S/2>max({A,B,C})){
          ans++;
          //cout<<2*n<<" "<<A<<" "<<B<<" "<<C<<endl;
        }
        
      }
    }
    cout<<ans<<endl;
    }
  return 0;}