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>
using namespace std;
using Graph = vector<vector<int>>; // グラフ型
typedef long long ll;
#define _GLIBCXX_DEBUG




int main() {
  ll N;
  cin >> N;
  vector<ll> ans(1001, 0);
  //vector<vector<int>> data(3, vector<int>(4));

  int x, y, z;

  for (int x = 1; x <= 30; x++){
    for (int y = 1; y <= 30; y++){
      for (int z = 1; z <= 30; z++){
        int tmp = x*x + y*y + z*z + x*y + y*z + z*x;
        if (tmp > 1000) continue;
        
        if(x==y && y==z){
          ans[tmp] = 1;
        }else if(x==y || y==z || x==z){
          ans[tmp] = 3;
        }else{
          ans[tmp] = 6;
        }
      }
    }
  }
  for(int i=1; i<=N;i++){
    cout << ans[i] << endl;
  }
  
  return 0;
}