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 <bits/stdc++.h>
using namespace std;

#define all(v) v.begin(), v.end()
#define rep(i, n) for (int i = 1; i < (int)(n); i++)
#define intll int long long
const int INF = 1e9;
const int MOD = 1e9 + 7;

int main() {
  int n ;
  cin >> n ; 
  vector<int> v(n+1) ;
  
  rep(i,105){
    rep(j,105){
      rep(k,105){
        int now = i*i + j*j + k*k + i*j + j*k + k*i ;
        if( now < n ) v.at(now) ++  ;
      }
    }
  }
  
  rep(i,n+1) cout << v.at(i) <<endl ;


}