


'''simple docstring'''



import colorsys

from PIL import Image  # type: ignore







def       _UpperCamelCase (						UpperCamelCase__	, UpperCamelCase__	, UpperCamelCase__   ):
   UpperCAmelCase__					:   Optional[Any]       				=       x
   UpperCAmelCase__					:   Optional[int]       				=       y
   for step in range(UpperCamelCase__   ):  # noqa: B007
      UpperCAmelCase__					:   List[str]       				=       a * a - b * b + x
      UpperCAmelCase__					:   Optional[int]       				=       2 * a * b + y
      UpperCAmelCase__					:   int       				=       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       _UpperCamelCase (						UpperCamelCase__   ):
   if distance == 1:
      return (0, 0, 0)
   else:
      return (2_5_5, 2_5_5, 2_5_5)







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







def       _UpperCamelCase (						UpperCamelCase__ = 8_0_0	, UpperCamelCase__ = 6_0_0	, UpperCamelCase__ = -0.6	, UpperCamelCase__ = 0	, UpperCamelCase__ = 3.2	, UpperCamelCase__ = 5_0	, UpperCamelCase__ = True	, ):
   UpperCAmelCase__					:   str       				=       Image.new("""RGB"""	, (image_width, image_height)   )
   UpperCAmelCase__					:   Optional[int]       				=       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__					:   Union[str, Any]       				=       figure_width / image_width * image_height
         UpperCAmelCase__					:   Union[str, Any]       				=       figure_center_x + (image_x / image_width - 0.5) * figure_width
         UpperCAmelCase__					:   Tuple       				=       figure_center_y + (image_y / image_height - 0.5) * figure_height

         UpperCAmelCase__					:   List[str]       				=       get_distance(UpperCamelCase__	, UpperCamelCase__	, UpperCamelCase__   )

         # color the corresponding pixel based on the selected coloring-function
         if use_distance_color_coding:
            UpperCAmelCase__					:   Any       				=       get_color_coded_rgb(UpperCamelCase__   )
         else:
            UpperCAmelCase__					:   Tuple       				=       get_black_and_white_rgb(UpperCamelCase__   )

   return img


if __name__ == "__main__":
  import doctest

  doctest.testmod()

  # colored version, full figure
  __A		=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 (						UpperCamelCase__ = 4_0_0_0_0_0_0   ):
			UpperCAmelCase__					:   List[str]       				=       [0, 1]
			UpperCAmelCase__					:   Any       				=       0
			while fib[i] <= n:
						fib.append(fib[i] + fib[i + 1]   )
						if fib[i + 2] > n:
									break
						i += 1
			UpperCAmelCase__					:   str       				=       0
			for j in range(len(UpperCamelCase__   ) - 1   ):
						if fib[j] % 2 == 0:
									total += fib[j]

			return total


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