import random







class 			__snake_case   :
 def __init__(  self		,   snake_case__		,   snake_case__						)	->							None:
       '''simple docstring'''





       UpperCAmelCase    : Optional[int]      =x
       UpperCAmelCase    : int      =y
 def 	UpperCAmelCase__       (  self						)	->							bool:
       '''simple docstring'''





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






 @classmethod
 def 	UpperCAmelCase__       (  cls						)	->							Any:
       '''simple docstring'''





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





def   lowerCAmelCase_ (				__lowerCAmelCase						)->  float:






      '''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(__lowerCAmelCase						):
            UpperCAmelCase    : Optional[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)}')

__snake_case			      =    [[0, 1, 1], [0, 0, 1], [1, 0, 0]]







class 			__snake_case   :
 def __init__(  self		,   snake_case__						)	->							Any:
       '''simple docstring'''





       UpperCAmelCase    : List[Any]      =name
       UpperCAmelCase    : Tuple      =[]
       UpperCAmelCase    : str      =[]
 def 	UpperCAmelCase__       (  self		,   snake_case__						)	->							int:
       '''simple docstring'''





       self.inbound.append(snake_case__						)
 def 	UpperCAmelCase__       (  self		,   snake_case__						)	->							Dict:
       '''simple docstring'''





       self.outbound.append(snake_case__						)






 def __repr__(  self						)	->							Union[str, Any]:
       '''simple docstring'''





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





def   lowerCAmelCase_ (				__lowerCAmelCase		,					__lowerCAmelCase=3		,					__lowerCAmelCase=0.85						)->  Any:






      '''simple docstring'''





      UpperCAmelCase    : List[Any]      ={}
      for node in nodes:
            UpperCAmelCase    : str      =1

      UpperCAmelCase    : str      ={}
      for node in nodes:
            UpperCAmelCase    : int      =len(node.outbound						)

      for i in range(__lowerCAmelCase						):
            print(f'''======= Iteration {i + 1} ======='''						)
            for _, node in enumerate(__lowerCAmelCase						):
                  UpperCAmelCase    : Optional[int]      =(1 - d) + d * sum(
                      ranks[ib] / outbounds[ib] for ib in node.inbound						)
            print(__lowerCAmelCase						)





def   lowerCAmelCase_ (				)->  Union[str, Any]:






      '''simple docstring'''





      UpperCAmelCase    : Union[str, Any]      =list(input('''Enter Names of the Nodes: '''						).split()						)

      UpperCAmelCase    : str      =[Node(__lowerCAmelCase						) for name in names]

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

      print('''======= Nodes ======='''						)
      for node in nodes:
            print(__lowerCAmelCase						)

      page_rank(__lowerCAmelCase						)


if __name__ == "__main__":
     main()
