


UpperCAmelCase      =   tuple[float, float, float]
UpperCAmelCase      =   tuple[float, float, float]






def 	__lowerCAmelCase   (SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE )->  Vectorad:




      """simple docstring"""

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






def 	__lowerCAmelCase   (SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE )->  Vectorad:




      """simple docstring"""

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






def 	__lowerCAmelCase   (SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE )->  bool:




      """simple docstring"""

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






def 	__lowerCAmelCase   (SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE = 10 )->  bool:




      """simple docstring"""

      snake_case_	=				create_vector(SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE )
      snake_case_	=				create_vector(SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE )
      return is_zero_vector(get_ad_vectors_cross(SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE ) , SCREAMING_SNAKE_CASE )



def 	__lowerCAmelCase   (SCREAMING_SNAKE_CASE )->  int:




      """simple docstring"""

      if not isinstance(SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE ):
            snake_case_	=				f'''Input value of [number={number}] must be an integer'''
            raise TypeError(SCREAMING_SNAKE_CASE )

      if number < 1:
            snake_case_	=				f'''Input value of [number={number}] must be > 0'''
            raise ValueError(SCREAMING_SNAKE_CASE )

      snake_case_	=				1

      for i in range(1 , SCREAMING_SNAKE_CASE ):
            current_number *= 4 * i - 2
            current_number //= i + 1

      return current_number


if __name__ == "__main__":
   import doctest

   doctest.testmod()