


'''simple docstring'''





__lowerCamelCase												=						tuple[float, float, float]
__lowerCamelCase												=						tuple[float, float, float]


def        a__     (					UpperCamelCase_						:      Any,   UpperCamelCase_						:      Optional[int]						):
   UpperCAmelCase__	:Union[str, Any]      =      end_pointa[0] - end_pointa[0]
   UpperCAmelCase__	:str      =      end_pointa[1] - end_pointa[1]
   UpperCAmelCase__	:Union[str, Any]      =      end_pointa[2] - end_pointa[2]
   return (x, y, z)


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


def        a__     (					UpperCamelCase_						:      str,   UpperCamelCase_						:      Dict						):
   return tuple(round(_A,   _A						) for x in vector						) == (0, 0, 0)


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











"""simple docstring"""







def      UpperCamelCase       ( _A )     ->       int:
				lowercase    :      Dict       = 0
				while num > 0:
								digit_sum += num % 10
								num //= 10
				return digit_sum


def      UpperCamelCase       ( _A = 100 )     ->       int:
				lowercase    :      Union[str, Any]       = 1
				lowercase    :      Tuple       = 2

				for i in range(2  ,				max_n + 1 ):
								lowercase    :      Any       = pre_numerator
								lowercase    :      Dict       = 2 * i // 3 if i % 3 == 0 else 1
								lowercase    :      Optional[Any]       = cur_numerator
								lowercase    :      str       = e_cont * pre_numerator + temp

				return sum_digits(_A )


if __name__ == "__main__":
				print(F'{solution() = }')
