
"""simple docstring"""







lowercase_         =       tuple[float, float, float]
lowercase_         =       tuple[float, float, float]




def       A_      (       lowercase    ,			lowercase   )  ->				Vectorad:


     """simple docstring"""







     UpperCAmelCase_    :     List[str]            =	end_pointa[0] - end_pointa[0]
     UpperCAmelCase_    :     List[str]            =	end_pointa[1] - end_pointa[1]
     UpperCAmelCase_    :     Tuple            =	end_pointa[2] - end_pointa[2]
     return (x, y, z)




def       A_      (       lowercase    ,			lowercase   )  ->				Vectorad:


     """simple docstring"""







     UpperCAmelCase_    :     Union[str, Any]            =	ab[1] * ac[2] - ab[2] * ac[1]  # *i
     UpperCAmelCase_    :     List[str]            =	(ab[0] * ac[2] - ab[2] * ac[0]) * -1  # *j
     UpperCAmelCase_    :     Dict            =	ab[0] * ac[1] - ab[1] * ac[0]  # *k
     return (x, y, z)




def       A_      (       lowercase    ,			lowercase   )  ->				bool:


     """simple docstring"""







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




def       A_      (       lowercase    ,			lowercase    ,			lowercase    ,			lowercase = 10   )  ->				bool:


     """simple docstring"""







     UpperCAmelCase_    :     Optional[int]            =	create_vector(lowercase    ,			lowercase   )
     UpperCAmelCase_    :     List[str]            =	create_vector(lowercase    ,			lowercase   )
     return is_zero_vector(get_ad_vectors_cross(lowercase    ,			lowercase   )    ,			lowercase   )



"""simple docstring"""







from string import ascii_lowercase, ascii_uppercase




def       A_      (       lowercase   )  ->				str:


     """simple docstring"""







     if not sentence:
          return ""
     UpperCAmelCase_    :     Any            =	dict(zip(lowercase    ,			lowercase   )   )
     return lower_to_upper.get(sentence[0]    ,			sentence[0]   ) + sentence[1:]


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

       testmod()

