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)

n = int(input())

a = [0] * 10010

# x = y = z
x = 1
while True:
  if 6 * x * x > n:
    break
  a[6 * x * x] += 1
  x += 1

# x = y, z
for x in range(1, n+1):
  for z in range(1, n+1):
    if x == z:
      continue
    if 3 * x*x + z*z + 2*x*z > n:
      break
    a[3 * x * x + z * z + 2 * x * z] += 2
  if x * x > n:
    break

# x,y,z
for x in range(1, n+1):
  if x*x > n:
    break
  for y in range(x+1, n+1):
    if x*x + y*y + x*y > n:
      break
    for z in range(y+1, n+1):
      if x*x + y*y + z*z + x*y + y*z + z*x > n:
        break
      a[x*x + y*y + z*z + x*y + y*z + z*x] += 6

for i in range(n):
  print(a[i])