





lowercase      :       List[str]									=  tuple[float, float, float]
lowercase      :       int									=  tuple[float, float, float]



def A_	(		A__		,      A__				)  ->		Vectorad:
       a__						:	Optional[int] =				end_pointa[0] - end_pointa[0]
       a__						:	str =				end_pointa[1] - end_pointa[1]
       a__						:	Dict =				end_pointa[2] - end_pointa[2]
       return (x, y, z)



def A_	(		A__		,      A__				)  ->		Vectorad:
       a__						:	Tuple =				ab[1] * ac[2] - ab[2] * ac[1]  # *i
       a__						:	Dict =				(ab[0] * ac[2] - ab[2] * ac[0]) * -1  # *j
       a__						:	Optional[int] =				ab[0] * ac[1] - ab[1] * ac[0]  # *k
       return (x, y, z)



def A_	(		A__		,      A__				)  ->		bool:
       return tuple(round(A__		,      A__				) for x in vector				) == (0, 0, 0)



def A_	(		A__		,      A__		,      A__		,      A__ = 10				)  ->		bool:
       a__						:	Tuple =				create_vector(A__		,      A__				)
       a__						:	str =				create_vector(A__		,      A__				)
       return is_zero_vector(get_ad_vectors_cross(A__		,      A__				)		,      A__				)



'''simple docstring'''





from __future__ import annotations





def 	lowerCAmelCase_				(					snake_case_       : list					,    snake_case_       : int | None = None					,    snake_case_       : int | None = None			)    ->      None:


     '''simple docstring'''




     if start is None:
          UpperCAmelCase_           =   0

     if end is None:
          UpperCAmelCase_           =   len(snake_case_			) - 1

     if start >= end:
          return

     UpperCAmelCase_           =   (start + end) // 2

     slowsort(snake_case_					,    snake_case_					,    snake_case_			)
     slowsort(snake_case_					,    mid + 1					,    snake_case_			)

     if sequence[end] < sequence[mid]:
          UpperCAmelCase_    , UpperCAmelCase_           =   sequence[mid], sequence[end]

     slowsort(snake_case_					,    snake_case_					,    end - 1			)


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

    testmod()




