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 <iostream>

using namespace std;

int main(void)
{
    int N;
    int cnt;
    int i;

    cin >> N;

    i = 1;
    while( i <= N )
    {
        cnt = 0;
        for(int x = 1; x <= 41; x++)
        {
            for(int y = 1; y <= 41; y++)
            {
                for(int z = 1; z <= 41; z++)
                {
                    int func = x*x + y*y + z*z + x*y + y*z + z*x - i;
                    if( func == 0 )
                    {
                        cnt++;
                    } 
                }
            }
        }
        cout << cnt << endl;
        i++;
    }

    return 0;
}