


'''simple docstring'''



def       _UpperCamelCase (						UpperCamelCase__ = 1_0   ):
			if not isinstance(UpperCamelCase__	, UpperCamelCase__   ) or n < 0:
						raise ValueError("""Invalid input"""   )
			UpperCAmelCase__					:   Optional[Any]       				=       1_0**n
			UpperCAmelCase__					:   List[str]       				=       2_8_4_3_3 * (pow(2	, 7_8_3_0_4_5_7	, UpperCamelCase__   )) + 1
			return str(number % modulus   )


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

		testmod()
		print(f"""{solution(10) = }""")



'''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()