code: 
  '''simple docstring'''
  
  from __future__ import annotations
  
  
  def 	_UpperCAmelCase				(  _lowerCamelCase						:       Optional[int]		)    ->						List[str]:
    _lowerCAmelCase       :  Any   				=					42
    _lowerCAmelCase       :  Optional[Any]   				=					list(UpperCamelCase__		)
    _lowerCAmelCase				,					_lowerCAmelCase       :  int   				=					_vector[:-1], int(_vector[-1]		)
    _lowerCAmelCase       :  Dict   				=					[int(UpperCamelCase__		) for digit in __vector]
  
    vector.reverse()
    for i, digit in enumerate(UpperCamelCase__		):
      if i & 1 == 0:
        _lowerCAmelCase       :  int   				=					digit * 2
        if doubled > 9:
          doubled -= 9
        check_digit += doubled
      else:
        check_digit += digit
  
    return check_digit % 10 == 0
  
  
  if __name__ == "__main__":
       import doctest
  
       doctest.testmod()
       assert is_luhn("""79927398713""")
       assert not is_luhn("""79927398714""")
  
  
  
style_context: 
  '''simple docstring'''
  
  import random
  
  
  class   a_  :
  
  
  
  
         def __init__(     self   ,   snake_case_   ,   snake_case_  ):
           _lowerCAmelCase       :  List[str]   				=					x
           _lowerCAmelCase       :  List[str]   				=					y
  
  
  
  
         def 							__UpperCamelCase       (     self  ):
           return (self.x**2 + self.y**2) <= 1
  
  
  
  
  
  
  
         @classmethod
         def 							__UpperCamelCase       (     cls  ):
           return cls(x=random.random()   ,   y=random.random()  )
  
  
  
  def 	_UpperCAmelCase				(  _lowerCamelCase						:       int		)    ->						float:
    if number_of_simulations < 1:
      raise ValueError("""At least one simulation is necessary to estimate PI."""		)
  
    _lowerCAmelCase       :  Tuple   				=					0
    for _ in range(_lowerCamelCase		):
      _lowerCAmelCase       :  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
  
       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)}')
  
  
  