



'''simple docstring'''





class  lowerCamelCase_   :
  """simple docstring"""




  def __init__(			self				:     Optional[int]       ) -> None:
    __lowerCamelCase	:	Dict   	=			[0, 1]




  def 						_lowercase					(			self				:     List[str]      ,     _a				:     int       ) -> list:
    if (difference := index - (len(self.sequence       ) - 2)) >= 1:
      for _ in range(_a       ):
        self.sequence.append(self.sequence[-1] + self.sequence[-2]       )
    return self.sequence[:index]




def 	a_					(							)				->				None:
  print(
      'Fibonacci Series Using Dynamic Programming\n'	,'Enter the index of the Fibonacci number you want to calculate '	,'in the prompt below. (To exit enter exit or Ctrl-C)\n'	,sep=''	,)
  __lowerCamelCase	:	Tuple   	=			Fibonacci()

  while True:
    __lowerCamelCase	:	str   	=			input('>> '	)
    if prompt in {"exit", "quit"}:
      break

    try:
      __lowerCamelCase	:	int   	=			int(_lowerCAmelCase	)
    except ValueError:
      print('Enter a number or \'exit\''	)
      continue

    print(fibonacci.get(_lowerCAmelCase	)	)


if __name__ == "__main__":
   main()











'''simple docstring'''





import random






class  lowerCamelCase_   :
  """simple docstring"""




  def __init__(			self				:     Union[str, Any]      ,     _a				:     float      ,     _a				:     float       ) -> None:
    __lowerCamelCase	:	Optional[int]   	=			x
    __lowerCamelCase	:	Union[str, Any]   	=			y




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




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




def 	a_					(							_lowerCAmelCase	)				->				float:
  if number_of_simulations < 1:
    raise ValueError('At least one simulation is necessary to estimate PI.'	)

  __lowerCamelCase	:	Optional[int]   	=			0
  for _ in range(_lowerCAmelCase	):
    __lowerCamelCase	:	Dict   	=			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)}''')






