

import random
class      SCREAMING_SNAKE_CASE__      :




    def __init__( self    ,					lowercase__    ,					lowercase__      ):






          """simple docstring"""






          SCREAMING_SNAKE_CASE_				:      Dict					=	x
          SCREAMING_SNAKE_CASE_				:      Any					=	y




    def   __lowerCamelCase				( self      ):






          """simple docstring"""






          return (self.x**2 + self.y**2) <= 1







    @classmethod
    def   __lowerCamelCase				( cls      ):






          """simple docstring"""






          return cls(x=random.random()    ,					y=random.random()      )






def  __lowerCamelCase      (				SCREAMING_SNAKE_CASE_					:     Dict   )							->       List[str]:
      """simple docstring"""

      if number_of_simulations < 1:
            raise ValueError("At least one simulation is necessary to estimate PI."   )

      SCREAMING_SNAKE_CASE_				:      Any					=	0
      for _ in range(SCREAMING_SNAKE_CASE_   ):
            SCREAMING_SNAKE_CASE_				:      Union[str, Any]					=	Point.random_unit_square()

            if random_point.is_in_unit_circle():
                  number_in_unit_circle += 1

      return 4 * number_in_unit_circle / number_of_simulations


if __name__ == "__main__":
      # import doctest

      # doctest.testmod()
      from math import pi

      snake_case_					  =	'Please enter the desired number of Monte Carlo simulations: '
      snake_case_					  =	estimate_pi(int(input(prompt).strip()))
      print(F'''An estimate of PI is {my_pi} with an error of {abs(my_pi - pi)}''')




'''simple docstring'''






from __future__ import annotations

from PIL import Image

# Define the first generation of cells
# fmt: off
snake_case_					  =	[[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      (				SCREAMING_SNAKE_CASE_					:     int   )							->       list[int]:
      """simple docstring"""

      return [int(SCREAMING_SNAKE_CASE_   ) for c in F"{ruleset:08}"[:8]]


def  __lowerCamelCase      (				SCREAMING_SNAKE_CASE_					:     list[list[int]]  ,  SCREAMING_SNAKE_CASE_					:     list[int]  ,  SCREAMING_SNAKE_CASE_					:     int   )							->       list[int]:
      """simple docstring"""

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


def  __lowerCamelCase      (				SCREAMING_SNAKE_CASE_					:     list[list[int]]   )							->       Image.Image:
      """simple docstring"""

      SCREAMING_SNAKE_CASE_				:      Tuple					=	Image.new("RGB"  ,  (len(cells[0]   ), len(SCREAMING_SNAKE_CASE_   ))   )
      SCREAMING_SNAKE_CASE_				:      Optional[int]					=	img.load()
      # Generates image
      for w in range(img.width   ):
            for h in range(img.height   ):
                  SCREAMING_SNAKE_CASE_				:      List[Any]					=	2_5_5 - int(2_5_5 * cells[h][w]   )
                  SCREAMING_SNAKE_CASE_				:      Optional[int]					=	(color, color, color)
      return img


if __name__ == "__main__":
      snake_case_					  =	bin(int(input('Rule:\n').strip()))[2:]
      snake_case_					  =	format_ruleset(int(rule_num))
      for time in range(1_6):
            CELLS.append(new_generation(CELLS, rule, time))
      snake_case_					  =	generate_image(CELLS)
      # Uncomment to save the image
      # img.save(f"rule_{rule_num}.png")
      img.show()

