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: Runtime Error)

#include <bits/stdc++.h>
#include <math.h>
using namespace std;
 
int main() {
  int N,b;
  cin>>N;
  b=N/3;
  vector<int> vec(N*100);
 for (int i = 1; i < b+1; i++) {
    for (int j = 1; j < b+1; j++) {
      for (int k = 1; k < b+1; k++) {
        vec.at(i*i+j*j+k*k+i*j+j*k+k*i-1)++;
      }
    }
 }
  vec.erase(vec.begin() + N, vec.begin() + N*100);
  for (int i = 0; i < N; i++) {
  cout<<vec.at(i)<<endl;
  }
}