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: Time Limit Exceeded)

#include <stdio.h>
#include <math.h>
#include <iostream>
#include <algorithm>
#include <vector>
#include <numeric>
#include <string>
#include <map>
#include <stack>
using namespace std;
typedef long long int lli;
#define urept(soeji, start, n) for (int soeji = start; soeji < n; soeji++)
#define drept(soeji, start, n) for (int soeji = start; soeji > n; soeji--)
int main(void)
{
    int N;
    cin >> N;
    int cnt[N + 1];
    fill(cnt, cnt + N + 1, 0);
    for (int i = 1; i <= N; i++)
    {
        for (int x = 1; x <= N / 6; x++)
        {
            for (int y = 1; y <= N / 6; y++)
            {
                for (int z = 1; z <= N / 6; z++)
                {
                    if ((x + y + z) * (x + y + z) == i + (x * y + y * z + z * x))
                    {
                        cnt[i]++;
                    }
                }
            }
        }
    }
    for (int i = 1; i <= N; i++)
    {
        cout << cnt[i] << endl;
    }
    return 0;
}