



"""simple docstring"""
import colorsys

from PIL import Image  # type: ignore

def    _snake_case		(		UpperCamelCase		:	float    ,	UpperCamelCase		:	float    ,	UpperCamelCase		:	int		):
 UpperCAmelCase			:      List[Any]			=			x
 UpperCAmelCase			:      Optional[int]			=			y
 for step in range(UpperCamelCase		):  # noqa: B007
  UpperCAmelCase			:      str			=			a * a - b * b + x
  UpperCAmelCase			:      Union[str, Any]			=			2 * a * b + y
  UpperCAmelCase			:      Optional[Any]			=			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		(		UpperCamelCase		:	float		):
 if distance == 1:
  return (0, 0, 0)
 else:
  return (255, 255, 255)

def    _snake_case		(		UpperCamelCase		:	float		):
 if distance == 1:
  return (0, 0, 0)
 else:
  return tuple(round(i * 255		) for i in colorsys.hsv_to_rgb(UpperCamelCase    ,	1    ,	1		)		)

def    _snake_case		(		UpperCamelCase		:	int = 800    ,	UpperCamelCase		:	int = 600    ,	UpperCamelCase		:	float = -0.6    ,	UpperCamelCase		:	float = 0    ,	UpperCamelCase		:	float = 3.2    ,	UpperCamelCase		:	int = 50    ,	UpperCamelCase		:	bool = True    ,	):
 UpperCAmelCase			:      List[Any]			=			Image.new("""RGB"""    ,	(image_width, image_height)		)
 UpperCAmelCase			:      Union[str, Any]			=			img.load()

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

   UpperCAmelCase			:      str			=			get_distance(UpperCamelCase    ,	UpperCamelCase    ,	UpperCamelCase		)

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

 return img


if __name__ == "__main__":
      import doctest

      doctest.testmod()

      # colored version, full figure
      A:     Tuple										=	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()





"""simple docstring"""
from __future__ import annotations

from collections.abc import Iterable, Iterator
from dataclasses import dataclass

A:     List[Any]										=	(3, 9, -1_1, 0, 7, 5, 1, -1)
A:     Union[str, Any]										=	(4, 6, 2, 0, 8, 1_0, 3, -2)



@dataclass
class    SCREAMING_SNAKE_CASE__						:
   __lowerCAmelCase						:     int
   __lowerCAmelCase						:     Node | None



class    SCREAMING_SNAKE_CASE__						:

   def __init__(     self   ,  _SCREAMING_SNAKE_CASE		)						->   None:





    '''simple docstring'''




    UpperCAmelCase			:      Node | None			=			None
    for i in sorted(_SCREAMING_SNAKE_CASE   ,  reverse=_SCREAMING_SNAKE_CASE		):
     UpperCAmelCase			:      Union[str, Any]			=			Node(_SCREAMING_SNAKE_CASE   ,  self.head		)

   def __iter__(     self		)						->   Iterator[int]:





    '''simple docstring'''




    UpperCAmelCase			:      Optional[Any]			=			self.head
    while node:
     yield node.data
     UpperCAmelCase			:      List[str]			=			node.next_node

   def __len__(     self		)						->   int:





    '''simple docstring'''




    return sum(1 for _ in self		)




   def __str__(     self		)						->   str:





    '''simple docstring'''




    return " -> ".join([str(_SCREAMING_SNAKE_CASE		) for node in self]		)

def    _snake_case		(		UpperCamelCase		:	SortedLinkedList    ,	UpperCamelCase		:	SortedLinkedList		):
 return SortedLinkedList(list(UpperCamelCase		) + list(UpperCamelCase		)		)


if __name__ == "__main__":
      import doctest

      doctest.testmod()
      A:     Dict										=	SortedLinkedList
      print(merge_lists(SSL(test_data_odd), SSL(test_data_even)))
