






"""simple docstring"""
def        A	(							__snake_case:   int     )						->		int:

							"""simple docstring"""





							if not isinstance(__snake_case   ,    __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        A	(							__snake_case:   int     )						->		int:

							"""simple docstring"""





							if not isinstance(__snake_case   ,    __snake_case     ):
														raise TypeError('dynamic_lucas_number accepts only integer arguments.'     )
							__magic_name__							,     __magic_name__										=						2, 1
							for _ in range(__snake_case     ):
														__magic_name__							,     __magic_name__										=						b, a + b
							return a


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

	testmod()
	snake_case   :   Tuple    		=		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)))







"""simple docstring"""
def        A	(							__snake_case:   Dict   ,    __snake_case:   Tuple     )						->		int:

       """simple docstring"""





       sequence.append(__snake_case     )

       __magic_name__										=						0
       while sequence[index] != target:
              index += 1

       sequence.pop()

       if index == len(__snake_case     ):
              return None

       return index


if __name__ == "__main__":
 snake_case   :   Dict    		=		input("""Enter numbers separated by comma:\n""").strip()
 snake_case   :   List[str]    		=		[int(item) for item in user_input.split(""",""")]

 snake_case   :   Union[str, Any]    		=		input("""Enter a single number to be found in the list:\n""")
 snake_case   :   str    		=		int(target_input)
 snake_case   :   Any    		=		sentinel_linear_search(sequence, target)
 if result is not None:
  print(f"""{target} found at positions: {result}""")
 else:
  print("""Not found""")