code: 
  
  
  
  
  
  
  """simple docstring"""
  
  import os
  
  def 	__lowerCamelCase			(						)		->					Tuple:
  
  		"""simple docstring"""
  
  
  
  
  
  
  
  		lowerCAmelCase_     :							Dict             =    os.path.dirname(os.path.realpath(__UpperCamelCase ) )
  		lowerCAmelCase_     :							str             =    os.path.join(__UpperCamelCase   , "triangle.txt" )
  
  		with open(__UpperCamelCase ) as f:
  				lowerCAmelCase_     :							Optional[Any]             =    f.readlines()
  
  		lowerCAmelCase_     :							List[str]             =    [[int(__UpperCamelCase ) for y in x.rstrip("\r\n" ).split(" " )] for x in triangle]
  
  		for i in range(1   , len(__UpperCamelCase ) ):
  				for j in range(len(a[i] ) ):
  						lowerCAmelCase_     :							str             =    a[i - 1][j] if j != len(a[i - 1] ) else 0
  						lowerCAmelCase_     :							Any             =    a[i - 1][j - 1] if j > 0 else 0
  						a[i][j] += max(__UpperCamelCase   , __UpperCamelCase )
  		return max(a[-1] )
  
  
  if __name__ == "__main__":
  					print(solution())
  
style_context: 
  
  
  
  
  
  
  """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()
  