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>
using namespace std;


typedef long long ll;
typedef pair<ll,int> P;

struct edge {int to; ll cost; };

int dx[] = {-1, 1, 0,  0};
int dy[] = { 0, 0, 1, -1};
 
int main(){
  int n;
  cin >> n;
  vector<int> ans(n+1, 0);
  for(int i=1; i*i<=n; i++){
    for(int j=1; j*j<=n; j++){
      for(int k=1; k*k<=n; k++){
        int tmp = i*i+j*j+k*k+i*j+j*k+k*i;
        if(tmp > n) continue;
        ans[tmp]++;
      }
    }
  }
  for(int i=1; i<=n; i++){
    cout << ans[i] << endl;
  }
  return 0;
}