





import math







def       lowerCAmelCase__(	lowercase       :    int				) ->    int:

  if 1 < number < 4:
    # 2 and 3 are primes
    return True
  elif number < 2 or number % 2 == 0 or number % 3 == 0:
    # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
    return False

  # All primes number are in format of 6k +/- 1
  for i in range(5   ,     int(math.sqrt(lowercase__				) + 1				)   ,     6				):
    if number % i == 0 or number % (i + 2) == 0:
      return False
  return True







def       lowerCAmelCase__(	lowercase       :    int = 6008_5147_5143				) ->    int:

  try:
    __snake_case   :				Dict        =       int(lowercase__				)
  except (TypeError, ValueError):
    raise TypeError("Parameter n must be int or castable to int."				)
  if n <= 0:
    raise ValueError("Parameter n must be greater than or equal to one."				)
  __snake_case   :				Tuple        =       0
  if is_prime(lowercase__				):
    return n
  while n % 2 == 0:
    n //= 2
  if is_prime(lowercase__				):
    return n
  for i in range(3   ,     int(math.sqrt(lowercase__				)				) + 1   ,     2				):
    if n % i == 0:
      if is_prime(n // i				):
        __snake_case   :				Any        =       n // i
        break
      elif is_prime(lowercase__				):
        __snake_case   :				int        =       i
  return max_number


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








def       lowerCAmelCase__(	lowercase       :    str				) ->    int:
  __snake_case   :				List[str]        =       str(lowercase				).strip()
  if not oct_string:
    raise ValueError("Empty string was passed to the function"				)
  __snake_case   :				int        =       oct_string[0] == "-"
  if is_negative:
    __snake_case   :				Union[str, Any]        =       oct_string[1:]
  if not oct_string.isdigit() or not all(0 <= int(lowercase				) <= 7 for char in oct_string				):
    raise ValueError("Non-octal value was passed to the function"				)
  __snake_case   :				List[Any]        =       0
  for char in oct_string:
    __snake_case   :				Optional[Any]        =       8 * decimal_number + int(lowercase				)
  if is_negative:
    __snake_case   :				Any        =       -decimal_number
  return decimal_number


if __name__ == "__main__":
     from doctest import testmod

     testmod()

