def     _a				(      lowercase__  :			Optional[int]     ,  lowercase__  :			Dict ):







					'''simple docstring'''


					SCREAMING_SNAKE_CASE__				:				List[Any]			=		''
					for word_or_phrase in separated:
										if not isinstance(lowerCamelCase__     ,  lowerCamelCase__ ):
															raise Exception('join() accepts only strings to be joined' )
										joined += word_or_phrase + separator
					return joined.strip(lowerCamelCase__ )


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

						testmod()




from __future__ import annotations







def     _a				(      lowercase__  :			list[int | float]     ,  lowercase__  :			int     ,  lowercase__  :			int ):







     '''simple docstring'''


     if len(lowercase__ ) == 0:
          raise ValueError('find_max() arg is an empty sequence' )
     if (
         left >= len(lowercase__ )
         or left < -len(lowercase__ )
         or right >= len(lowercase__ )
         or right < -len(lowercase__ )
     ):
          raise IndexError('list index out of range' )
     if left == right:
          return nums[left]
     SCREAMING_SNAKE_CASE__				:				Union[str, Any]			=		(left + right) >> 1  # the middle
     SCREAMING_SNAKE_CASE__				:				int			=		find_max(lowercase__     ,  lowercase__     ,  lowercase__ )  # find max in range[left, mid]
     SCREAMING_SNAKE_CASE__				:				Tuple			=		find_max(lowercase__     ,  mid + 1     ,  lowercase__ )  # find max in range[mid + 1, right]

     return left_max if left_max >= right_max else right_max


if __name__ == "__main__":
      import doctest

      doctest.testmod(verbose=True)



