





import colorsys

from PIL import Image  # type: ignore

def    __snake_case  (    _lowerCAmelCase       :       List[str] , _lowerCAmelCase       :       Tuple , _lowerCAmelCase       :       Dict		)       ->  float:
   A_    : List[str]								=	x
   A_    : str								=	y
   for step in range(_lowerCAmelCase		):  # noqa: B007
      A_    : Union[str, Any]								=	a * a - b * b + x
      A_    : Optional[int]								=	2 * a * b + y
      A_    : List[str]								=	a_new

      # divergence happens for all complex number with an absolute value
      # greater than 4
      if a * a + b * b > 4:
         break
   return step / (max_step - 1)

def    __snake_case  (    _lowerCAmelCase       :       str		)       ->  tuple:
   if distance == 1:
      return (0, 0, 0)
   else:
      return (255, 255, 255)

def    __snake_case  (    _lowerCAmelCase       :       List[str]		)       ->  tuple:
   if distance == 1:
      return (0, 0, 0)
   else:
      return tuple(round(i * 255		) for i in colorsys.hsv_to_rgb(_lowerCAmelCase , 1 , 1		)		)

def    __snake_case  (    _lowerCAmelCase       :       Optional[int] = 800 , _lowerCAmelCase       :       Union[str, Any] = 600 , _lowerCAmelCase       :       Optional[int] = -0.6 , _lowerCAmelCase       :       Optional[int] = 0 , _lowerCAmelCase       :       Union[str, Any] = 3.2 , _lowerCAmelCase       :       List[Any] = 50 , _lowerCAmelCase       :       int = True , )       ->  Image.Image:
   A_    : str								=	Image.new("RGB" , (image_width, image_height)		)
   A_    : Dict								=	img.load()

   # loop through the image-coordinates
   for image_x in range(_lowerCAmelCase		):
      for image_y in range(_lowerCAmelCase		):
         # determine the figure-coordinates based on the image-coordinates
         A_    : Dict								=	figure_width / image_width * image_height
         A_    : Union[str, Any]								=	figure_center_x + (image_x / image_width - 0.5) * figure_width
         A_    : Optional[Any]								=	figure_center_y + (image_y / image_height - 0.5) * figure_height

         A_    : Union[str, Any]								=	get_distance(_lowerCAmelCase , _lowerCAmelCase , _lowerCAmelCase		)

         # color the corresponding pixel based on the selected coloring-function
         if use_distance_color_coding:
            A_    : Optional[Any]								=	get_color_coded_rgb(_lowerCAmelCase		)
         else:
            A_    : Dict								=	get_black_and_white_rgb(_lowerCAmelCase		)

   return img


if __name__ == "__main__":
 import doctest

 doctest.testmod()

 # colored version, full figure
 _lowerCAmelCase							:					str		    =		get_image()

 # uncomment for colored version, different section, zoomed in
 # img = get_image(figure_center_x = -0.6, figure_center_y = -0.4,
 # figure_width = 0.8)

 # uncomment for black and white version, full figure
 # img = get_image(use_distance_color_coding = False)

 # uncomment to save the image
 # img.save("mandelbrot.png")

 img.show()







def  _SCREAMING_SNAKE_CASE				(   a  )      ->      bool:
					return str(a  ) == str(a  )[::-1]







def  _SCREAMING_SNAKE_CASE				(   a  )      ->      int:
					return int(a  ) + int(str(a  )[::-1]  )







def  _SCREAMING_SNAKE_CASE				(   a = 1_00_00  )      ->      int:
					__A	:						int       =				[]
					for num in range(1					,						a  ):
										__A	:						List[str]       =				0
										__A	:						List[Any]       =				num
										while iterations < 50:
															__A	:						str       =				sum_reverse(a  )
															iterations += 1
															if is_palindrome(a  ):
																				break
										else:
															lychrel_nums.append(a  )
					return len(a  )


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




