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 Python (3.8.2) (judge verdict: Time Limit Exceeded)

import math
def is_integer_num(n):
    if isinstance(n, int):
        return True
    if isinstance(n, float):
        return n.is_integer()
    return False


def solve(n):
    ans = 0
    for x in range(1, n + 1):
        for y in range(1, n + 1):
            z1, z2 = 0, 0
            try:
                z1 = -(y + x) + math.sqrt(-3 * x ** 2 -
                                        3 * y ** 2 - 2 * x * y + 4 * n)
                z2 = -(y + x) - math.sqrt(-3 * x ** 2 -
                                        3 * y ** 2 - 2 * x * y + 4 * n)
            except:
                pass

            if z1 >= 1 and is_integer_num(z1):
                ans += 1
                continue
            if z2 >= 1 and is_integer_num(z2):
                ans += 1
                continue

    return ans


def resolve():
    N = int(input())
    for n in range(1, N + 1):
        print(solve(n))

    return

resolve()