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: Time Limit Exceeded)

# -*- coding: utf-8 -*-
# スペース区切りの整数の入力
N = int(input())

if int(float(N)**0.5) <= 1:
  xyzMax = 1
else:
  xyzMax = int(float(N)**0.5)

Ans = 0

for i in range(1,N+1):
  for x in range(1,xyzMax+1):
    if x**2 > i:
      break
    else:
      for y in range(1,xyzMax+1):
        if x**2 + y**2 > i:
          break
        else:
          for z in range(1,xyzMax+1):
            if x**2 + y**2 + z**2 > i:
              break
            else:
              if x**2 + y**2 + z**2 + (x * y) + (y * z) + (z * x) == i:
                Ans += 1
  
  print(Ans)
  Ans = 0