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)

import math
N = int(input())
x = 1
for m in range(1,N+1):
  count =0
  y =1
  z =1
  for i in range(m):
    x = i+1
    if 6*x**2>=m:
      if x**2>m:
        break
      if 9*x*x >= m:
        for k in range(x):
          y = k+1
          nn = x*x+y*y+x*y
          if nn > m:
            break
          if nn >=m/2:
            xy = (x+2*y)**2-x*y
            if xy >= m:
              for j in range(y):
                z = j+1
                n = nn+z*z+y*z+z*x
                if n>m:
                  break
                if n==m:
                  if  x==y or y==z or z==x:
                    if x==y and y == z:
                      count =count+1
                    else:
                      count = count+3
                  else:
                    count =count+6
  print(count)