





'''simple docstring'''




def 	_lowerCAmelCase      (  __snake_case  :			str			,							__snake_case  :			str      )					->					float:

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

          return "".join(__snake_case      )

     # matching characters
     __A						:			Any								=	get_matched_characters(__snake_case			,							__snake_case      )
     __A						:			str								=	get_matched_characters(__snake_case			,							__snake_case      )
     __A						:			str								=	len(__snake_case      )

     # transposition
     __A						:			Tuple								=	(
         len([(ca, ca) for ca, ca in zip(__snake_case			,							__snake_case      ) if ca != ca]      ) // 2
     )

     if not match_count:
          __A						:			int								=	0.0
     else:
          __A						:			Union[str, Any]								=	(
              1
              / 3
              * (
                  match_count / len(__snake_case      )
                  + match_count / len(__snake_case      )
                  + (match_count - transpositions) / match_count
              )
          )

     # common prefix up to 4 characters
     __A						:			Tuple								=	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'''))






'''simple docstring'''




import math






def 	_lowerCAmelCase      (  __snake_case  :			int      )					->					bool:

     if 1 < number < 4:
          # 2 and 3 are primes
          return True
     elif number < 2 or number % 2 == 0 or number % 3 == 0:
          # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
          return False

     # All primes number are in format of 6k +/- 1
     for i in range(5			,							int(math.sqrt(__snake_case      ) + 1      )			,							6      ):
          if number % i == 0 or number % (i + 2) == 0:
               return False
     return True






def 	_lowerCAmelCase      (  __snake_case  :			float = 0.1      )					->					int:
     __A						:			Dict								=	3
     __A						:			int								=	3

     while primes / (2 * j - 1) >= ratio:
          for i in range(j * j + j + 1			,							(j + 2) * (j + 2)			,							j + 1      ):
               primes += is_prime(__snake_case      )
          j += 2
     return j


if __name__ == "__main__":
  import doctest

  doctest.testmod()