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 PyPy3 (7.3.0) (judge verdict: Time Limit Exceeded)

import math

N = int(input())

for i in range(N):
  n = i+1
  pair = []
  for x in range(1, int(math.sqrt(N)+1)):
    for y in range(x, int(math.sqrt(N-x**2)+1)):
      for z in reversed(range(y, int(math.sqrt(N-y**2-x**2)+1))):
        if x**2+y**2+z**2+x*y+y*z+z*x == n:
          pair.append((x, y, z))
  ans = 0
  for x, y, z in pair:
    if x == z:
      ans += 1
    elif x == y:
      ans += 3
    elif y == z:
      ans += 3
    else:
      ans += 6
  print(ans)