






def  a__ (__lowercase							:int   )		-> bool:

				if p < 2:
								raise ValueError('''p should not be less than 2!'''   )
				elif p == 2:
								return True

				_A	:				Any   =      4
				_A	:				List[Any]   =      (1 << p) - 1
				for _ in range(p - 2   ):
								_A	:				Optional[Any]   =      ((s * s) - 2) % m
				return s == 0


if __name__ == "__main__":
	print(lucas_lehmer_test(7))
	print(lucas_lehmer_test(11))











def  a__ (__lowercase							:str					,  __lowercase							:str   )		-> float:

				def get_matched_characters(__lowercase							:str					,  __lowercase							:str   ) -> str:
								_A	:				Union[str, Any]   =      []
								_A	:				Dict   =      min(len(_stra   )					,  len(_stra   )   ) // 2
								for i, l in enumerate(_stra   ):
												_A	:				Tuple   =      int(max(0					,  i - limit   )   )
												_A	:				Union[str, Any]   =      int(min(i + limit + 1					,  len(_stra   )   )   )
												if l in _stra[left:right]:
																matched.append(__lowercase   )
																_A	:				List[Any]   =      f"""{_stra[0:_stra.index(__lowercase   )]} {_stra[_stra.index(__lowercase   ) + 1:]}"""

								return "".join(__lowercase   )

				# matching characters
				_A	:				str   =      get_matched_characters(__lowercase					,  __lowercase   )
				_A	:				Optional[Any]   =      get_matched_characters(__lowercase					,  __lowercase   )
				_A	:				Any   =      len(__lowercase   )

				# transposition
				_A	:				str   =      (
				    len([(ca, ca) for ca, ca in zip(__lowercase					,  __lowercase   ) if ca != ca]   ) // 2
				)

				if not match_count:
								_A	:				Optional[int]   =      0.0
				else:
								_A	:				str   =      (
								    1
								    / 3
								    * (
								        match_count / len(__lowercase   )
								        + match_count / len(__lowercase   )
								        + (match_count - transpositions) / match_count
								    )
								)

				# common prefix up to 4 characters
				_A	:				Any   =      0
				for ca, ca in zip(stra[:4]					,  stra[:4]   ):
								if ca == ca:
												prefix_len += 1
								else:
												break

				return jaro + 0.1 * prefix_len * (1 - jaro)


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	print(jaro_winkler('hello', 'world'))



