

'''simple docstring'''



import colorsys

from PIL import Image  # type: ignore

def 	lowerCamelCase__							(   a__      ,   a__      ,   a__)		->     float:



    """simple docstring"""







    _snake_case			:			Tuple				       =		x
    _snake_case			:			List[Any]				       =		y
    for step in range(lowerCAmelCase__):  # noqa: B007
        _snake_case			:			str				       =		a * a - b * b + x
        _snake_case			:			List[str]				       =		2 * a * b + y
        _snake_case			:			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 	lowerCamelCase__							(   a__)		->     tuple:



    """simple docstring"""







    if distance == 1:
        return (0, 0, 0)
    else:
        return (2_5_5, 2_5_5, 2_5_5)

def 	lowerCamelCase__							(   a__)		->     tuple:



    """simple docstring"""







    if distance == 1:
        return (0, 0, 0)
    else:
        return tuple(round(i * 2_5_5) for i in colorsys.hsv_to_rgb(lowerCAmelCase__      ,   1      ,   1))

def 	lowerCamelCase__							(   a__ = 8_0_0      ,   a__ = 6_0_0      ,   a__ = -0.6      ,   a__ = 0      ,   a__ = 3.2      ,   a__ = 5_0      ,   a__ = True      ,   )		->     Image.Image:



    """simple docstring"""







    _snake_case			:			str				       =		Image.new('RGB'      ,   (image_width, image_height))
    _snake_case			:			str				       =		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
            _snake_case			:			Tuple				       =		figure_width / image_width * image_height
            _snake_case			:			Union[str, Any]				       =		figure_center_x + (image_x / image_width - 0.5) * figure_width
            _snake_case			:			Dict				       =		figure_center_y + (image_y / image_height - 0.5) * figure_height

            _snake_case			:			Tuple				       =		get_distance(lowerCAmelCase__      ,   lowerCAmelCase__      ,   lowerCAmelCase__)

            # color the corresponding pixel based on the selected coloring-function
            if use_distance_color_coding:
                _snake_case			:			List[str]				       =		get_color_coded_rgb(lowerCAmelCase__)
            else:
                _snake_case			:			Union[str, Any]				       =		get_black_and_white_rgb(lowerCAmelCase__)

    return img


if __name__ == "__main__":
   import doctest

   doctest.testmod()

   # colored version, full figure
   SCREAMING_SNAKE_CASE_     = 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"""






def      UpperCAmelCase__			(							lowerCAmelCase__	:int = 5_0						)					->       int:
      '''simple docstring'''


      lowercase								=      [1] * (length + 1)

      for row_length in range(3   ,						length + 1						):
            for block_length in range(3   ,						row_length + 1						):
                  for block_start in range(row_length - block_length						):
                        ways_number[row_length] += ways_number[
                            row_length - block_start - block_length - 1
                        ]

                  ways_number[row_length] += 1

      return ways_number[length]


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



