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)

N = int(input())
l = [-1]*N
def triplets(n):
  counter = 0
  lower = 1
  upper = round((n-2)**0.5-1)
  for x in range(1, upper+1):
    y_upper = round(0.5*((4*n-3*x**2)**0.5-x))
    for y in range(1, y_upper+1):
      root = (4*n-3*x**2-3*y**2-2*x*y)**0.5
      z = 0.5*(root-x-y)
      if z%1==0 and z>0:
        counter += 1
  return counter
for m in range(1, N+1):
  if l[m-1] == -1:
    tmp = triplets(m)
    l[m-1] = tmp
    if tmp != 0:
      for k in range(2,round((N/m)**0.5)):
        l[m*k**2-1] = tmp
for x in l:
  print(x)