

'''simple docstring'''

import random







class   UpperCamelCase__   :


		"""simple docstring"""

		def __init__(			self   ,      snake_case   ,      snake_case      ):


							'''simple docstring'''

							UpperCAmelCase		:							List[Any]        =       x
							UpperCAmelCase		:							List[Any]        =       y







		def 				A_	(			self      ):


							'''simple docstring'''

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







		@classmethod
		def 				A_	(			cls      ):


							'''simple docstring'''

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





def 				lowercase (					__magic_name__							):



					'''simple docstring'''







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

					UpperCAmelCase		:							Optional[int]        =       0
					for _ in range(__magic_name__							):
										UpperCAmelCase		:							str        =       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

				a       :      Union[str, Any]  	=			"Please enter the desired number of Monte Carlo simulations: "
				a       :      str  	=			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'''

a       :      str  	=			[[0, 1, 1], [0, 0, 1], [1, 0, 0]]







class   UpperCamelCase__   :


		"""simple docstring"""

		def __init__(			self   ,      snake_case      ):


							'''simple docstring'''

							UpperCAmelCase		:							Optional[int]        =       name
							UpperCAmelCase		:							Optional[Any]        =       []
							UpperCAmelCase		:							Tuple        =       []







		def 				A_	(			self   ,      snake_case      ):


							'''simple docstring'''

							self.inbound.append(snake_case      )







		def 				A_	(			self   ,      snake_case      ):


							'''simple docstring'''

							self.outbound.append(snake_case      )







		def __repr__(			self      ):


							'''simple docstring'''

							return f"<node={self.name} inbound={self.inbound} outbound={self.outbound}>"





def 				lowercase (					__magic_name__			,   __magic_name__=3			,   __magic_name__=0.8_5							):



					'''simple docstring'''







					UpperCAmelCase		:							str        =       {}
					for node in nodes:
										UpperCAmelCase		:							Tuple        =       1

					UpperCAmelCase		:							Optional[Any]        =       {}
					for node in nodes:
										UpperCAmelCase		:							List[str]        =       len(node.outbound							)

					for i in range(__magic_name__							):
										print(F"======= Iteration {i + 1} ======="							)
										for _, node in enumerate(__magic_name__							):
															UpperCAmelCase		:							Any        =       (1 - d) + d * sum(
															    ranks[ib] / outbounds[ib] for ib in node.inbound							)
										print(__magic_name__							)





def 				lowercase (					):



					'''simple docstring'''







					UpperCAmelCase		:							Dict        =       list(input("Enter Names of the Nodes: "							).split()							)

					UpperCAmelCase		:							Any        =       [Node(__magic_name__							) for name in names]

					for ri, row in enumerate(__magic_name__							):
										for ci, col in enumerate(__magic_name__							):
															if col == 1:
																				nodes[ci].add_inbound(names[ri]							)
																				nodes[ri].add_outbound(names[ci]							)

					print("======= Nodes ======="							)
					for node in nodes:
										print(__magic_name__							)

					page_rank(__magic_name__							)


if __name__ == "__main__":
				main()
