




'''simple docstring'''



def   lowercase__(			__UpperCamelCase:					str      ,__UpperCamelCase:					str    ):

      """simple docstring"""






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

            return "".join(__UpperCamelCase    )

      # matching characters
      SCREAMING_SNAKE_CASE   :      Tuple    					=						get_matched_characters(__UpperCamelCase      ,__UpperCamelCase    )
      SCREAMING_SNAKE_CASE   :      List[str]    					=						get_matched_characters(__UpperCamelCase      ,__UpperCamelCase    )
      SCREAMING_SNAKE_CASE   :      str    					=						len(__UpperCamelCase    )

      # transposition
      SCREAMING_SNAKE_CASE   :      Any    					=						(
          len([(ca, ca) for ca, ca in zip(__UpperCamelCase      ,__UpperCamelCase    ) if ca != ca]    ) // 2
      )

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

      # common prefix up to 4 characters
      SCREAMING_SNAKE_CASE   :      List[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"))



'''simple docstring'''

from math import factorial, radians







def __UpperCamelCase( _A       :					float	,      _A       :					int = 18	,      _A       :					int = 10     ):
   '''simple docstring'''
   UpperCAmelCase__				:					int 					=	angle_in_degrees - ((angle_in_degrees // 3_6_0.0) * 3_6_0.0)

   # Converting from degrees to radians
   UpperCAmelCase__				:					Dict 					=	radians(_A     )

   UpperCAmelCase__				:					Union[str, Any] 					=	angle_in_radians
   UpperCAmelCase__				:					List[str] 					=	3
   UpperCAmelCase__				:					int 					=	-1

   for _ in range(_A     ):
      result += (b * (angle_in_radians**a)) / factorial(_A     )

      UpperCAmelCase__				:					List[str] 					=	-b  # One positive term and the next will be negative and so on...
      a += 2  # Increased by 2 for every term.

   return round(_A	,      _A     )


if __name__ == "__main__":
  __import__('doctest').testmod()




