






"""simple docstring"""

import sys

lowercase    			=       (
    '''73167176531330624919225119674426574742355349194934'''
    '''96983520312774506326239578318016984801869478851843'''
    '''85861560789112949495459501737958331952853208805511'''
    '''12540698747158523863050715693290963295227443043557'''
    '''66896648950445244523161731856403098711121722383113'''
    '''62229893423380308135336276614282806444486645238749'''
    '''30358907296290491560440772390713810515859307960866'''
    '''70172427121883998797908792274921901699720888093776'''
    '''65727333001053367881220235421809751254540594752243'''
    '''52584907711670556013604839586446706324415722155397'''
    '''53697817977846174064955149290862569321978468622482'''
    '''83972241375657056057490261407972968652414535100474'''
    '''82166370484403199890008895243450658541227588666881'''
    '''16427171479924442928230863465674813919123162824586'''
    '''17866458359124566529476545682848912883142607690042'''
    '''24219022671055626321111109370544217506941658960408'''
    '''07198403850962455444362981230987879927244284909188'''
    '''84580156166097919133875499200524063689912560717606'''
    '''05886116467109405077541002256983155200055935729725'''
    '''71636269561882670428252483600823257530420752963450'''
)






def _lowerCAmelCase	(  __lowerCamelCase:str   ):

						'''simple docstring'''






						__magic_name__            =     1
						for digit in s:
												product *= int(__lowerCamelCase   )
						return product






def _lowerCAmelCase	(  __lowerCamelCase:str = N   ):

						'''simple docstring'''






						__magic_name__            =     -sys.maxsize - 1
						__magic_name__            =     n[:1_3]
						__magic_name__            =     1_3
						while cur_index < len(__lowerCamelCase   ) - 1_3:
												if int(n[cur_index]   ) >= int(substr[0]   ):
																		__magic_name__            =     substr[1:] + n[cur_index]
																		cur_index += 1
												else:
																		__magic_name__            =     max(__lowerCamelCase ,						str_eval(__lowerCamelCase   )   )
																		__magic_name__            =     n[cur_index : cur_index + 1_3]
																		cur_index += 1_3
						return largest_product


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











"""simple docstring"""

import colorsys

from PIL import Image  # type: ignore






def _lowerCAmelCase	(  __lowerCamelCase:float ,						__lowerCamelCase:float ,						__lowerCamelCase:int   ):

						'''simple docstring'''






						__magic_name__            =     x
						__magic_name__            =     y
						for step in range(__lowerCamelCase   ):  # noqa: B007
												__magic_name__            =     a * a - b * b + x
												__magic_name__            =     2 * a * b + y
												__magic_name__            =     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	(  __lowerCamelCase:float   ):

						'''simple docstring'''






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






def _lowerCAmelCase	(  __lowerCamelCase:float   ):

						'''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	(  __lowerCamelCase:int = 8_0_0 ,						__lowerCamelCase:int = 6_0_0 ,						__lowerCamelCase:float = -0.6 ,						__lowerCamelCase:float = 0 ,						__lowerCamelCase:float = 3.2 ,						__lowerCamelCase:int = 5_0 ,						__lowerCamelCase:bool = True ,						):

						'''simple docstring'''






						__magic_name__            =     Image.new("RGB" ,						(image_width, image_height)   )
						__magic_name__            =     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
																		__magic_name__            =     figure_width / image_width * image_height
																		__magic_name__            =     figure_center_x + (image_x / image_width - 0.5) * figure_width
																		__magic_name__            =     figure_center_y + (image_y / image_height - 0.5) * figure_height

																		__magic_name__            =     get_distance(__lowerCamelCase ,						__lowerCamelCase ,						__lowerCamelCase   )

																		# color the corresponding pixel based on the selected coloring-function
																		if use_distance_color_coding:
																								__magic_name__            =     get_color_coded_rgb(__lowerCamelCase   )
																		else:
																								__magic_name__            =     get_black_and_white_rgb(__lowerCamelCase   )

						return img


if __name__ == "__main__":
			import doctest

			doctest.testmod()

			# colored version, full figure
			lowercase    			=       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()



