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>
#define rep(i,n) for(i=1; i<=n; ++i)
using namespace std;
int main(void){
  int N;
  cin >> N;
  int i,score,n,x,y,z,max,max2,max3;
  rep(i,N){
    max = N;
    max2 = N;
    max3 = N;
    score = 0;
    for(x=1; x<=max; ++x)for(y=1; y<=max2; ++y){for(z=1; z<=max3; ++z){
          n = (x*x+y*y+z*z+x*y+y*z+z*x);
          if(n==i){
            ++score;
            if(max3==N)
              max = z;
            max3 = z;
            break;
          }
          else if(n>i){
            if(max3==N)
              max = z;
            break;
          }
      }
      max2 = max-x+2;
    }
    cout << score << endl;
  }

  return 0;
}