



class 						snake_case  :



   '''simple docstring'''






   def __init__(   self							:     Dict)			->			Optional[Any]:

    """simple docstring"""







    _snake_case      :					dict[int, list[int]]					=   {}
    # indexmap keys are an index and it's values are the number at that index
    _snake_case      :					dict[int, int]					=   {}

   def        UpperCamelCase_					(   self							:     Any			,						lowerCAmelCase							:     int			,						lowerCAmelCase							:     Optional[Any])			->			List[Any]:

    """simple docstring"""







    if isinstance(_A			,						(range, str)):
     _snake_case      :					Tuple					=   list(_A)
    elif not isinstance(_A			,						_A):
     raise TypeError(
         """binary_search_delete() only accepts either a list, range or str""")

    _snake_case      :					Optional[int]					=   0
    _snake_case      :					int					=   len(_A) - 1

    while low <= high:
     _snake_case      :					List[str]					=   (low + high) // 2
     if array[mid] == item:
      array.pop(_A)
      return array
     elif array[mid] < item:
      _snake_case      :					Union[str, Any]					=   mid + 1
     else:
      _snake_case      :					str					=   mid - 1
    raise ValueError(
        """Either the item is not in the array or the array was unsorted""")

   def        UpperCamelCase_					(   self							:     Union[str, Any]			,						lowerCAmelCase							:     Optional[Any]			,						lowerCAmelCase							:     Optional[Any])			->			Optional[int]:

    """simple docstring"""







    if isinstance(_A			,						(range, str)):
     _snake_case      :					int					=   list(_A)
    elif not isinstance(_A			,						_A):
     raise TypeError(
         """binary_search_insert() only accepts either a list, range or str""")

    _snake_case      :					List[str]					=   0
    _snake_case      :					int					=   len(_A) - 1

    while low <= high:
     _snake_case      :					List[Any]					=   (low + high) // 2
     if array[mid] == index:
      # If the item already exists in the array,
      # insert it after the existing item
      array.insert(mid + 1			,						_A)
      return array
     elif array[mid] < index:
      _snake_case      :					Dict					=   mid + 1
     else:
      _snake_case      :					Any					=   mid - 1

        # If the item doesn't exist in the array, insert it at the appropriate position
    array.insert(_A			,						_A)
    return array

   def        UpperCamelCase_					(   self							:     Union[str, Any]			,						lowerCAmelCase							:     str			,						lowerCAmelCase							:     Tuple)			->			int:

    """simple docstring"""







    if index in self.indexmap:
     _snake_case      :					Any					=   self.indexmap[index]
     if len(self.numbermap[n]) == 1:
      del self.numbermap[n]
     else:
      _snake_case      :					Optional[int]					=   self.binary_search_delete(self.numbermap[n]			,						_A)

        # Set new index
    _snake_case      :					str					=   number

    # Number not seen before or empty so insert number value
    if number not in self.numbermap:
     _snake_case      :					Dict					=   [index]

    # Here we need to perform a binary search insertion in order to insert
    # The item in the correct place
    else:
     _snake_case      :					str					=   self.binary_search_insert(
         self.numbermap[number]			,						_A)


   def        UpperCamelCase_					(   self							:     Optional[int]			,						lowerCAmelCase							:     List[str])			->			List[Any]:

    """simple docstring"""







    return self.numbermap.get(_A			,						[-1])[0]


if __name__ == "__main__":
 import doctest

 doctest.testmod()





def  lowercase    (				SCREAMING_SNAKE_CASE__    :		int			)					->       int:
 if not isinstance(SCREAMING_SNAKE_CASE__			,    SCREAMING_SNAKE_CASE__			):
  raise TypeError("""recursive_lucas_number accepts only integer arguments."""			)
 if n_th_number == 0:
  return 2
 if n_th_number == 1:
  return 1

 return recursive_lucas_number(n_th_number - 1			) + recursive_lucas_number(
     n_th_number - 2			)



def  lowercase    (				SCREAMING_SNAKE_CASE__    :		int			)					->       int:
 if not isinstance(SCREAMING_SNAKE_CASE__			,    SCREAMING_SNAKE_CASE__			):
  raise TypeError("""dynamic_lucas_number accepts only integer arguments."""			)
 _snake_case		,      _snake_case      :					Any					=   2, 1
 for _ in range(SCREAMING_SNAKE_CASE__			):
  _snake_case		,      _snake_case      :					Union[str, Any]					=   b, a + b
 return a


if __name__ == "__main__":
  from doctest import testmod

  testmod()
  a__      =		int(input("""Enter the number of terms in lucas series:\n""").strip())
  print("""Using recursive function to calculate lucas series:""")
  print(""" """.join(str(recursive_lucas_number(i)) for i in range(n)))
  print("""\nUsing dynamic function to calculate lucas series:""")
  print(""" """.join(str(dynamic_lucas_number(i)) for i in range(n)))
