




'''simple docstring'''



from __future__ import annotations




def   lowercase__(			__UpperCamelCase:					list[int]    ):  # This function is recursive

      """simple docstring"""






      SCREAMING_SNAKE_CASE   :      Optional[int]    					=						len(__UpperCamelCase    )
      # If the array contains only one element, we return it (it's the stop condition of
      # recursion)
      if array_length <= 1:
            return array
            # Else
      SCREAMING_SNAKE_CASE   :      Optional[Any]    					=						array[0]
      SCREAMING_SNAKE_CASE   :      List[str]    					=						False
      SCREAMING_SNAKE_CASE   :      Any    					=						1
      SCREAMING_SNAKE_CASE   :      list[int]    					=						[]
      while not is_found and i < array_length:
            if array[i] < pivot:
                  SCREAMING_SNAKE_CASE   :      int    					=						True
                  SCREAMING_SNAKE_CASE   :      Optional[int]    					=						[element for element in array[i:] if element >= array[i]]
                  SCREAMING_SNAKE_CASE   :      List[str]    					=						longest_subsequence(__UpperCamelCase    )
                  if len(__UpperCamelCase    ) > len(__UpperCamelCase    ):
                        SCREAMING_SNAKE_CASE   :      List[str]    					=						temp_array
            else:
                  i += 1

      SCREAMING_SNAKE_CASE   :      Tuple    					=						[element for element in array[1:] if element >= pivot]
      SCREAMING_SNAKE_CASE   :      Optional[Any]    					=						[pivot, *longest_subsequence(__UpperCamelCase    )]
      if len(__UpperCamelCase    ) > len(__UpperCamelCase    ):
            return temp_array
      else:
            return longest_subseq


if __name__ == "__main__":
      import doctest

      doctest.testmod()









'''simple docstring'''






from __future__ import annotations







def 					_a						(       _lowerCamelCase    ,	_lowerCamelCase = None    ,	_lowerCamelCase = None ) ->				None:



			"""simple docstring"""


			if start is None:
						__snake_case					:      Optional[Any]							      =     0

			if end is None:
						__snake_case					:      Optional[Any]							      =     len(_lowerCamelCase ) - 1

			if start >= end:
						return

			__snake_case					:      Tuple							      =     (start + end) // 2

			slowsort(_lowerCamelCase    ,	_lowerCamelCase    ,	_lowerCamelCase )
			slowsort(_lowerCamelCase    ,	mid + 1    ,	_lowerCamelCase )

			if sequence[end] < sequence[mid]:
						__snake_case      ,     __snake_case					:      str							      =     sequence[mid], sequence[end]

			slowsort(_lowerCamelCase    ,	_lowerCamelCase    ,	end - 1 )


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

	testmod()


