





SCREAMING_SNAKE_CASE__							:      Union[str, Any]         =    tuple[float, float, float]
SCREAMING_SNAKE_CASE__							:      str         =    tuple[float, float, float]






def    _A	(   lowerCamelCase				,			lowerCamelCase ):
   a__						:    Optional[int]   		=	end_pointa[0] - end_pointa[0]
   a__						:    List[Any]   		=	end_pointa[1] - end_pointa[1]
   a__						:    List[Any]   		=	end_pointa[2] - end_pointa[2]
   return (x, y, z)






def    _A	(   lowerCamelCase				,			lowerCamelCase ):
   a__						:    int   		=	ab[1] * ac[2] - ab[2] * ac[1]  # *i
   a__						:    List[Any]   		=	(ab[0] * ac[2] - ab[2] * ac[0]) * -1  # *j
   a__						:    Tuple   		=	ab[0] * ac[1] - ab[1] * ac[0]  # *k
   return (x, y, z)






def    _A	(   lowerCamelCase				,			lowerCamelCase ):
   return tuple(round(lowerCamelCase				,			lowerCamelCase ) for x in vector ) == (0, 0, 0)






def    _A	(   lowerCamelCase				,			lowerCamelCase				,			lowerCamelCase				,			lowerCamelCase = 10 ):
   a__						:    Optional[int]   		=	create_vector(lowerCamelCase				,			lowerCamelCase )
   a__						:    Any   		=	create_vector(lowerCamelCase				,			lowerCamelCase )
   return is_zero_vector(get_ad_vectors_cross(lowerCamelCase				,			lowerCamelCase )				,			lowerCamelCase )








def    _A	(   lowerCamelCase = 200 ):
   a__						:    List[str]   		=	[1, 2, 5, 10, 20, 50, 100, 200]
   a__						:    Dict   		=	[0] * (pence + 1)
   a__						:    int   		=	1  # base case: 1 way to make 0 pence

   for coin in coins:
      for i in range(lowerCamelCase				,			pence + 1				,			1 ):
         number_of_ways[i] += number_of_ways[i - coin]
   return number_of_ways[pence]


if __name__ == "__main__":
  assert solution(2_0_0) == 7_3_6_8_2

