


'''simple docstring'''






def 				UpperCamelCase_			(    A__					:   Optional[Any]					):
  '''simple docstring'''





  lowerCAmelCase_			:      Optional[int]			=   (1 + 24 * n) ** 0.5
  return ((1 + root) / 6) % 1 == 0







def 				UpperCamelCase_			(    A__					:   List[Any] = 50_00					):
  '''simple docstring'''





  lowerCAmelCase_			:      Tuple			=   [(i * (3 * i - 1)) // 2 for i in range(1							,    lowerCAmelCase__					)]
  for i, pentagonal_i in enumerate(lowerCAmelCase__					):
    for j in range(lowerCAmelCase__							,    len(lowerCAmelCase__					)					):
      lowerCAmelCase_			:      Any			=   pentagonal_nums[j]
      lowerCAmelCase_			:      Optional[int]			=   pentagonal_i + pentagonal_j
      lowerCAmelCase_			:      List[Any]			=   pentagonal_j - pentagonal_i
      if is_pentagonal(lowerCAmelCase__					) and is_pentagonal(lowerCAmelCase__					):
        return b

  return -1


if __name__ == "__main__":
  print(F'''{solution() = }''')







'''simple docstring'''
def 					a__       (					lowerCAmelCase__						)    ->	int:
    if a < 0:
        raise ValueError('''Input value must be a positive integer'''						)
    elif isinstance(lowerCAmelCase__  ,					lowerCAmelCase__						):
        raise TypeError('''Input value must be a \'int\' type'''						)
    return bin(lowerCAmelCase__						).count('''1'''						)


if __name__ == "__main__":
  import doctest

  doctest.testmod()
