






"""simple docstring"""

import math

def 	__lowerCamelCase			(						__UpperCamelCase )		->					float:

		"""simple docstring"""







		lowerCAmelCase_     :							Union[str, Any]             =    math.log(2   , 10 ) * number
		lowerCAmelCase_     :							Any             =    round((log_number - int(__UpperCamelCase ))   , 15 )

		return difference

def 	__lowerCamelCase			(						__UpperCamelCase = 678910 )		->					int:

		"""simple docstring"""







		lowerCAmelCase_     :							Any             =    90
		lowerCAmelCase_     :							Tuple             =    0

		lowerCAmelCase_     :							Tuple             =    math.log(1.23   , 10 )
		lowerCAmelCase_     :							str             =    math.log(1.24   , 10 )
		lowerCAmelCase_     :							List[Any]             =    0

		while position < number:
				lowerCAmelCase_     :							Union[str, Any]             =    log_difference(__UpperCamelCase )

				if difference >= upper_limit:
						power_iterator += 93

				elif difference < lower_limit:
						power_iterator += 196

				else:
						lowerCAmelCase_     :							int             =    power_iterator
						power_iterator += 196
						position += 1

		return previous_power


if __name__ == "__main__":
					import doctest

					doctest.testmod()

					print(F"""{solution() = }""")








"""simple docstring"""

from __future__ import annotations

from PIL import Image

# Define the first generation of cells
# fmt: off
lowercase__      =				[[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
          0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]

def 	__lowerCamelCase			(						__UpperCamelCase )		->					list[int]:

		"""simple docstring"""







		return [int(__UpperCamelCase ) for c in f'''{ruleset:08}'''[:8]]

def 	__lowerCamelCase			(						__UpperCamelCase   , __UpperCamelCase   , __UpperCamelCase )		->					list[int]:

		"""simple docstring"""







		lowerCAmelCase_     :							int             =    len(cells[0] )  # 31
		lowerCAmelCase_     :							List[Any]             =    []
		for i in range(__UpperCamelCase ):
				# Get the neighbors of each cell
				# Handle neighbours outside bounds by using 0 as their value
				lowerCAmelCase_     :							List[str]             =    0 if i == 0 else cells[time][i - 1]
				lowerCAmelCase_     :							Optional[int]             =    0 if i == population - 1 else cells[time][i + 1]
				# Define a new cell and add it to the new generation
				lowerCAmelCase_     :							List[Any]             =    7 - int(f'''{left_neighbor}{cells[time][i]}{right_neighbor}'''   , 2 )
				next_generation.append(rule[situation] )
		return next_generation

def 	__lowerCamelCase			(						__UpperCamelCase )		->					Image.Image:

		"""simple docstring"""







		lowerCAmelCase_     :							List[str]             =    Image.new("RGB"   , (len(cells[0] ), len(__UpperCamelCase )) )
		lowerCAmelCase_     :							List[str]             =    img.load()
		# Generates image
		for w in range(img.width ):
				for h in range(img.height ):
						lowerCAmelCase_     :							Union[str, Any]             =    255 - int(255 * cells[h][w] )
						lowerCAmelCase_     :							List[str]             =    (color, color, color)
		return img


if __name__ == "__main__":
					lowercase__      =				bin(int(input("""Rule:\n""").strip()))[2:]
					lowercase__      =				format_ruleset(int(rule_num))
					for time in range(16):
										CELLS.append(new_generation(CELLS, rule, time))
					lowercase__      =				generate_image(CELLS)
					# Uncomment to save the image
					# img.save(f"rule_{rule_num}.png")
					img.show()
