





'''simple docstring'''







from __future__ import annotations

from PIL import Image

# Define the first generation of cells
# fmt: off
snake_case_  :							List[Any]            =	[[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__   :      Optional[Any] )			->						list[int]:
						return [int(__UpperCAmelCase ) for c in F"""{ruleset:08}"""[:8]]





def 							lowerCamelCase_   (	SCREAMING_SNAKE_CASE__   :      Any,      SCREAMING_SNAKE_CASE__   :      Tuple,      SCREAMING_SNAKE_CASE__   :      int )			->						list[int]:
						UpperCAmelCase_      :   int      =	len(cells[0] )  # 31
						UpperCAmelCase_      :   Optional[int]      =	[]
						for i in range(__UpperCAmelCase ):
												# Get the neighbors of each cell
												# Handle neighbours outside bounds by using 0 as their value
												UpperCAmelCase_      :   Dict      =	0 if i == 0 else cells[time][i - 1]
												UpperCAmelCase_      :   Dict      =	0 if i == population - 1 else cells[time][i + 1]
												# Define a new cell and add it to the new generation
												UpperCAmelCase_      :   int      =	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[Any] )			->						Image.Image:
						UpperCAmelCase_      :   Dict      =	Image.new('''RGB''',      (len(cells[0] ), len(__UpperCAmelCase )) )
						UpperCAmelCase_      :   Dict      =	img.load()
						# Generates image
						for w in range(img.width ):
												for h in range(img.height ):
																		UpperCAmelCase_      :   int      =	255 - int(255 * cells[h][w] )
																		UpperCAmelCase_      :   List[str]      =	(color, color, color)
						return img


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










import random







class 				a_    :

						def __init__(       self      :Union[str, Any]  ,		_lowercase      :float  ,		_lowercase      :float)						->   None:
												UpperCAmelCase_					=	x
												UpperCAmelCase_					=	y

						def       __a			(       self      :str)						->   bool:
												return (self.x**2 + self.y**2) <= 1




						@classmethod
						def       __a			(       cls      :Optional[Any])						->   str:
												return cls(x=random.random()  ,		y=random.random())







def 							A     (						__UpperCAmelCase      )			->			float:



						'''simple docstring'''






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

						UpperCAmelCase_					=	0
						for _ in range(__UpperCAmelCase      ):
												UpperCAmelCase_					=	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

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





