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: Accepted)

def main():
  n = int(input())
  ans = []
  flg = 1
  for i in range(1,n+1):
    flg = 1
    anstmp = 0
    for x in range(1,int(i**0.5+1)):
      if flg == 0:
        break
      for y in range(x,int(i**0.5+1)):
        if i-(x**2+y**2+x*y) > x+y:
          j = i-(x**2+y**2+x*y)
          z = int((j+(x+y)**2/4)**0.5-(x+y)/2+0.5)
          if (x+y+z)*z == j:
            if x < y:
              anstmp += 2
            else:
              anstmp += 1
        elif y == 1:
          flg = 0
          break
        else:
          break
    ans.append(anstmp)
  print(*ans,sep="\n")
main()