'''simple docstring'''

lowerCAmelCase_ : Union[str, Any]						  =      tuple[float, float, float]
lowerCAmelCase_ : List[Any]						  =      tuple[float, float, float]


def __a (	__lowerCamelCase			:						Pointad ,		__lowerCamelCase			:						Pointad				)	->							Vectorad:
      '''simple docstring'''


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


def __a (	__lowerCamelCase			:						Vectorad ,		__lowerCamelCase			:						Vectorad				)	->							Vectorad:
      '''simple docstring'''


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


def __a (	__lowerCamelCase			:						Vectorad ,		__lowerCamelCase			:						int				)	->							bool:
      '''simple docstring'''


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






def __a (	__lowerCamelCase			:						Pointad ,		__lowerCamelCase			:						Pointad ,		__lowerCamelCase			:						Pointad ,		__lowerCamelCase			:						int = 10				)	->							bool:
      '''simple docstring'''


      lowercase_     =      create_vector(__lowerCamelCase ,		__lowerCamelCase				)
      lowercase_     =      create_vector(__lowerCamelCase ,		__lowerCamelCase				)
      return is_zero_vector(get_ad_vectors_cross(__lowerCamelCase ,		__lowerCamelCase				) ,		__lowerCamelCase				)







'''simple docstring'''

def __a (	__lowerCamelCase			:						int = 200				)	->							int:
      '''simple docstring'''


      lowercase_     =      [1, 2, 5, 10, 20, 50, 100, 200]
      lowercase_     =      [0] * (pence + 1)
      lowercase_     =      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(200) == 73_682






