


"""simple docstring"""






def       A_   (   _lowerCAmelCase     :					str,     _lowerCAmelCase     :					str       ):






     """simple docstring"""

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

          return "".join(_lowerCAmelCase       )

     # matching characters
     _a    	=				get_matched_characters(_lowerCAmelCase,     _lowerCAmelCase       )
     _a    	=				get_matched_characters(_lowerCAmelCase,     _lowerCAmelCase       )
     _a    	=				len(_lowerCAmelCase       )

     # transposition
     _a    	=				(
         len([(ca, ca) for ca, ca in zip(_lowerCAmelCase,     _lowerCAmelCase       ) if ca != ca]       ) // 2
     )

     if not match_count:
          _a    	=				0.0
     else:
          _a    	=				(
              1
              / 3
              * (
                  match_count / len(_lowerCAmelCase       )
                  + match_count / len(_lowerCAmelCase       )
                  + (match_count - transpositions) / match_count
              )
          )

     # common prefix up to 4 characters
     _a    	=				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"""






def       A_   (   _lowerCAmelCase     :					int = 10**12       ):






     """simple docstring"""

     _a    	=				1
     _a    	=				0

     _a    	=				1
     _a    	=				1

     while numerator <= 2 * min_total - 1:
          prev_numerator += 2 * numerator
          numerator += 2 * prev_numerator

          prev_denominator += 2 * denominator
          denominator += 2 * prev_denominator

     return (denominator + 1) // 2


if __name__ == "__main__":
   print(f'{solution() = }')