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: Runtime Error)

from math import sqrt
from sympy import exp, Symbol

x = Symbol('x')
y = Symbol('y')
z = Symbol('z')

n = int(input())

ans = 0
for x in range(1, n+1):
    y = exp(-x/2 - z/2 - sqrt(-3*x**2 - 2*x*z - 3*z**2 + x*4)/2)
    z = exp(-y/2 - x/2 - sqrt(-3*y**2 - 2*y*x - 3*x**2 + x*4)/2)
        
    if (x**2 + y**2 + z**2 + x*y + y*z + z*x - x*4 == 0) and (isinstance(x, int) and isinstance(y, int) and isinstance(z, int)):
        ans += 1

print(ans)