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: Wrong Answer)

def is_integer(n):
    try:
        float(n)
    except ValueError:
        return False
    else:
        return float(n).is_integer()

N = int(input())
for i in range(1, N+1):
    if i < 6:
        print(0)
        continue
    cnt = 0
    for x in range(1, 10):
        for y in range(1, 10):
             D = (((x+y)**2 - 4*(x**2+y**2+x*y-i)) ** (1/2))
             if ((x+y)**2 - 4*(x**2+y**2+x*y-i)) > 0 :
                 Z = (-(x+y) + D) / 2
                 if is_integer(Z) and Z>0:
                     cnt += 1
    print(cnt)