


'''simple docstring'''






a_   :      Optional[Any]				    =      tuple[float, float, float]
a_   :      List[Any]				    =      tuple[float, float, float]






def 		_A			(lowerCAmelCase__					:Optional[Any]			,  lowerCAmelCase__					:int						)				->					Vectorad:




     '''simple docstring'''



     _a      =							end_pointa[0] - end_pointa[0]
     _a      =							end_pointa[1] - end_pointa[1]
     _a      =							end_pointa[2] - end_pointa[2]
     return (x, y, z)






def 		_A			(lowerCAmelCase__					:int			,  lowerCAmelCase__					:Union[str, Any]						)				->					Vectorad:




     '''simple docstring'''



     _a      =							ab[1] * ac[2] - ab[2] * ac[1]  # *i
     _a      =							(ab[0] * ac[2] - ab[2] * ac[0]) * -1  # *j
     _a      =							ab[0] * ac[1] - ab[1] * ac[0]  # *k
     return (x, y, z)






def 		_A			(lowerCAmelCase__					:Optional[int]			,  lowerCAmelCase__					:str						)				->					bool:




     '''simple docstring'''



     return tuple(round(lowerCAmelCase__			,  lowerCAmelCase__						) for x in vector						) == (0, 0, 0)






def 		_A			(lowerCAmelCase__					:str			,  lowerCAmelCase__					:Dict			,  lowerCAmelCase__					:List[Any]			,  lowerCAmelCase__					:Optional[Any] = 10						)				->					bool:




     '''simple docstring'''



     _a      =							create_vector(lowerCAmelCase__			,  lowerCAmelCase__						)
     _a      =							create_vector(lowerCAmelCase__			,  lowerCAmelCase__						)
     return is_zero_vector(get_ad_vectors_cross(lowerCAmelCase__			,  lowerCAmelCase__						)			,  lowerCAmelCase__						)






'''simple docstring'''






from __future__ import annotations






def 		_A			(lowerCAmelCase__					:int						)				->					list[int]:




     '''simple docstring'''



     _a      =							2
     _a      =							[]
     while i * i <= n:
          if n % i:
               i += 1
          else:
               n //= i
               factors.append(lowerCAmelCase__						)
     if n > 1:
          factors.append(lowerCAmelCase__						)
     return factors


if __name__ == "__main__":
 import doctest

 doctest.testmod()

