






from __future__ import annotations







def 		SCREAMING_SNAKE_CASE							( __lowerCAmelCase ,   __lowerCAmelCase ,   __lowerCAmelCase      )			->     Union[str, Any]:






     """simple docstring"""




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







from __future__ import annotations







def 		SCREAMING_SNAKE_CASE							( __lowerCAmelCase ,   __lowerCAmelCase = None ,   __lowerCAmelCase = None      )			->     None:
     if start is None:
          UpperCamelCase__      :       Union[str, Any]	    =  0

     if end is None:
          UpperCamelCase__      :       List[Any]	    =  len(__lowerCAmelCase      ) - 1

     if start >= end:
          return

     UpperCamelCase__      :       Union[str, Any]	    =  (start + end) // 2

     slowsort(__lowerCAmelCase ,   __lowerCAmelCase ,   __lowerCAmelCase      )
     slowsort(__lowerCAmelCase ,   mid + 1 ,   __lowerCAmelCase      )

     if sequence[end] < sequence[mid]:
          UpperCamelCase__    ,					UpperCamelCase__      :       Optional[int]	    =  sequence[mid], sequence[end]

     slowsort(__lowerCAmelCase ,   __lowerCAmelCase ,   end - 1      )


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

 testmod()