



'''simple docstring'''

__lowerCAmelCase									=   tuple[float, float, float]
__lowerCAmelCase									=   tuple[float, float, float]



def      __lowerCamelCase     (      lowerCAmelCase_						,			lowerCAmelCase_  )			->      Vectorad:
		_a     :      str        =							end_pointa[0] - end_pointa[0]
		_a     :      Optional[int]        =							end_pointa[1] - end_pointa[1]
		_a     :      str        =							end_pointa[2] - end_pointa[2]
		return (x, y, z)



def      __lowerCamelCase     (      lowerCAmelCase_						,			lowerCAmelCase_  )			->      Vectorad:
		_a     :      Optional[Any]        =							ab[1] * ac[2] - ab[2] * ac[1]  # *i
		_a     :      List[str]        =							(ab[0] * ac[2] - ab[2] * ac[0]) * -1  # *j
		_a     :      Dict        =							ab[0] * ac[1] - ab[1] * ac[0]  # *k
		return (x, y, z)



def      __lowerCamelCase     (      lowerCAmelCase_						,			lowerCAmelCase_  )			->      bool:
		return tuple(round(lowerCAmelCase_						,			lowerCAmelCase_  ) for x in vector  ) == (0, 0, 0)



def      __lowerCamelCase     (      lowerCAmelCase_						,			lowerCAmelCase_						,			lowerCAmelCase_						,			lowerCAmelCase_ = 10  )			->      bool:
		_a     :      Optional[int]        =							create_vector(lowerCAmelCase_						,			lowerCAmelCase_  )
		_a     :      List[str]        =							create_vector(lowerCAmelCase_						,			lowerCAmelCase_  )
		return is_zero_vector(get_ad_vectors_cross(lowerCAmelCase_						,			lowerCAmelCase_  )						,			lowerCAmelCase_  )






"""simple docstring"""




UpperCAmelCase__      :    List[str]    							= [
    9_9_9,
    8_0_0,
    7_9_9,
    6_0_0,
    5_9_9,
    5_0_0,
    4_0_0,
    3_9_9,
    3_7_7,
    3_5_5,
    3_3_3,
    3_1_1,
    2_8_8,
    2_6_6,
    2_4_4,
    2_2_2,
    2_0_0,
    1_9_9,
    1_7_7,
    1_5_5,
    1_3_3,
    1_1_1,
    8_8,
    6_6,
    4_4,
    2_2,
    0,
]

UpperCAmelCase__      :    int    							= [
    9_9_9,
    9_7_6,
    9_5_2,
    9_2_8,
    9_0_5,
    8_8_2,
    8_5_8,
    8_5_7,
    8_1_0,
    7_6_2,
    7_1_5,
    7_1_4,
    5_7_2,
    4_2_9,
    4_2_8,
    2_8_6,
    2_8_5,
    2_3_8,
    1_9_0,
    1_4_3,
    1_4_2,
    1_1_8,
    9_5,
    7_1,
    4_7,
    2_4,
    0,
]

UpperCAmelCase__      :    int    							= [
    9_9_9,
    9_8_8,
    9_7_7,
    9_6_6,
    9_5_5,
    9_4_4,
    9_3_3,
    9_2_2,
    9_1_1,
    9_0_0,
    8_9_9,
    8_7_9,
    8_5_9,
    8_4_0,
    8_2_0,
    8_0_0,
    7_9_9,
    7_6_6,
    7_3_3,
    7_0_0,
    6_9_9,
    6_5_0,
    6_0_0,
    5_9_9,
    5_0_0,
    4_9_9,
    4_0_0,
    3_9_9,
    3_5_0,
    3_0_0,
    2_9_9,
    2_6_6,
    2_3_3,
    2_0_0,
    1_9_9,
    1_7_9,
    1_5_9,
    1_4_0,
    1_2_0,
    1_0_0,
    9_9,
    8_8,
    7_7,
    6_6,
    5_5,
    4_4,
    3_3,
    2_2,
    1_1,
    0,
]

UpperCAmelCase__      :    int    							= [
    9_9_9,
    9_9_5,
    9_9_2,
    9_8_9,
    9_8_5,
    9_8_1,
    9_7_8,
    9_7_5,
    9_7_1,
    9_6_7,
    9_6_4,
    9_6_1,
    9_5_7,
    9_5_6,
    9_5_1,
    9_4_7,
    9_4_2,
    9_3_7,
    9_3_3,
    9_2_8,
    9_2_3,
    9_1_9,
    9_1_4,
    9_1_3,
    9_0_8,
    9_0_3,
    8_9_7,
    8_9_2,
    8_8_7,
    8_8_1,
    8_7_6,
    8_7_1,
    8_7_0,
    8_6_4,
    8_5_8,
    8_5_2,
    8_4_6,
    8_4_0,
    8_3_4,
    8_2_8,
    8_2_7,
    8_2_0,
    8_1_3,
    8_0_6,
    7_9_9,
    7_9_2,
    7_8_5,
    7_8_4,
    7_7_7,
    7_7_0,
    7_6_3,
    7_5_6,
    7_4_9,
    7_4_2,
    7_4_1,
    7_3_3,
    7_2_4,
    7_1_6,
    7_0_7,
    6_9_9,
    6_9_8,
    6_8_8,
    6_7_7,
    6_6_6,
    6_5_6,
    6_5_5,
    6_4_5,
    6_3_4,
    6_2_3,
    6_1_3,
    6_1_2,
    5_9_8,
    5_8_4,
    5_7_0,
    5_6_9,
    5_5_5,
    5_4_1,
    5_2_7,
    5_2_6,
    5_0_5,
    4_8_4,
    4_8_3,
    4_6_2,
    4_4_0,
    4_3_9,
    3_9_6,
    3_9_5,
    3_5_2,
    3_5_1,
    3_0_8,
    3_0_7,
    2_6_4,
    2_6_3,
    2_2_0,
    2_1_9,
    1_7_6,
    1_3_2,
    8_8,
    4_4,
    0,
]

UpperCAmelCase__      :    Tuple    							= [
    9_9_9,
    9_9_7,
    9_9_5,
    9_9_2,
    9_9_0,
    9_8_8,
    9_8_6,
    9_8_4,
    9_8_1,
    9_7_9,
    9_7_7,
    9_7_5,
    9_7_2,
    9_7_0,
    9_6_8,
    9_6_6,
    9_6_4,
    9_6_1,
    9_5_9,
    9_5_7,
    9_5_6,
    9_5_4,
    9_5_1,
    9_4_9,
    9_4_6,
    9_4_4,
    9_4_1,
    9_3_9,
    9_3_6,
    9_3_4,
    9_3_1,
    9_2_9,
    9_2_6,
    9_2_4,
    9_2_1,
    9_1_9,
    9_1_6,
    9_1_4,
    9_1_3,
    9_1_0,
    9_0_7,
    9_0_5,
    9_0_2,
    8_9_9,
    8_9_6,
    8_9_3,
    8_9_1,
    8_8_8,
    8_8_5,
    8_8_2,
    8_7_9,
    8_7_7,
    8_7_4,
    8_7_1,
    8_7_0,
    8_6_7,
    8_6_4,
    8_6_1,
    8_5_8,
    8_5_5,
    8_5_2,
    8_4_9,
    8_4_6,
    8_4_3,
    8_4_0,
    8_3_7,
    8_3_4,
    8_3_1,
    8_2_8,
    8_2_7,
    8_2_4,
    8_2_1,
    8_1_7,
    8_1_4,
    8_1_1,
    8_0_8,
    8_0_4,
    8_0_1,
    7_9_8,
    7_9_5,
    7_9_1,
    7_8_8,
    7_8_5,
    7_8_4,
    7_8_0,
    7_7_7,
    7_7_4,
    7_7_0,
    7_6_6,
    7_6_3,
    7_6_0,
    7_5_6,
    7_5_2,
    7_4_9,
    7_4_6,
    7_4_2,
    7_4_1,
    7_3_7,
    7_3_3,
    7_3_0,
    7_2_6,
    7_2_2,
    7_1_8,
    7_1_4,
    7_1_0,
    7_0_7,
    7_0_3,
    6_9_9,
    6_9_8,
    6_9_4,
    6_9_0,
    6_8_5,
    6_8_1,
    6_7_7,
    6_7_3,
    6_6_9,
    6_6_4,
    6_6_0,
    6_5_6,
    6_5_5,
    6_5_0,
    6_4_6,
    6_4_1,
    6_3_6,
    6_3_2,
    6_2_7,
    6_2_2,
    6_1_8,
    6_1_3,
    6_1_2,
    6_0_7,
    6_0_2,
    5_9_6,
    5_9_1,
    5_8_6,
    5_8_0,
    5_7_5,
    5_7_0,
    5_6_9,
    5_6_3,
    5_5_7,
    5_5_1,
    5_4_5,
    5_3_9,
    5_3_3,
    5_2_7,
    5_2_6,
    5_1_9,
    5_1_2,
    5_0_5,
    4_9_8,
    4_9_1,
    4_8_4,
    4_8_3,
    4_7_4,
    4_6_6,
    4_5_7,
    4_4_9,
    4_4_0,
    4_3_9,
    4_2_8,
    4_1_8,
    4_0_7,
    3_9_6,
    3_9_5,
    3_8_1,
    3_6_6,
    3_5_2,
    3_5_1,
    3_3_0,
    3_0_8,
    3_0_7,
    2_8_6,
    2_6_4,
    2_6_3,
    2_4_2,
    2_2_0,
    2_1_9,
    1_7_6,
    1_7_5,
    1_3_2,
    1_3_1,
    8_8,
    4_4,
    0,
]

UpperCAmelCase__      :    Union[str, Any]    							= [
    9_9_9,
    9_9_1,
    9_8_2,
    9_7_4,
    9_6_6,
    9_5_8,
    9_5_0,
    9_4_1,
    9_3_3,
    9_2_5,
    9_1_6,
    9_0_8,
    9_0_0,
    8_9_9,
    8_7_4,
    8_5_0,
    8_2_5,
    8_0_0,
    7_9_9,
    7_0_0,
    6_0_0,
    5_0_0,
    4_0_0,
    3_0_0,
    2_0_0,
    1_0_0,
    0,
]

UpperCAmelCase__      :    str    							= [
    9_9_9,
    9_9_2,
    9_8_5,
    9_7_8,
    9_7_1,
    9_6_4,
    9_5_7,
    9_4_9,
    9_4_2,
    9_3_5,
    9_2_8,
    9_2_1,
    9_1_4,
    9_0_7,
    9_0_0,
    8_9_9,
    8_7_9,
    8_5_9,
    8_4_0,
    8_2_0,
    8_0_0,
    7_9_9,
    7_6_6,
    7_3_3,
    7_0_0,
    6_9_9,
    6_5_0,
    6_0_0,
    5_9_9,
    5_0_0,
    4_9_9,
    4_0_0,
    3_9_9,
    3_0_0,
    2_9_9,
    2_0_0,
    1_9_9,
    1_0_0,
    9_9,
    0,
]

UpperCAmelCase__      :    str    							= [
    9_9_9,
    9_9_6,
    9_9_2,
    9_8_9,
    9_8_5,
    9_8_2,
    9_7_9,
    9_7_5,
    9_7_2,
    9_6_8,
    9_6_5,
    9_6_1,
    9_5_8,
    9_5_5,
    9_5_1,
    9_4_8,
    9_4_4,
    9_4_1,
    9_3_8,
    9_3_4,
    9_3_1,
    9_2_7,
    9_2_4,
    9_2_0,
    9_1_7,
    9_1_4,
    9_1_0,
    9_0_7,
    9_0_3,
    9_0_0,
    8_9_9,
    8_9_1,
    8_8_4,
    8_7_6,
    8_6_9,
    8_6_1,
    8_5_3,
    8_4_6,
    8_3_8,
    8_3_0,
    8_2_3,
    8_1_5,
    8_0_8,
    8_0_0,
    7_9_9,
    7_8_8,
    7_7_7,
    7_6_6,
    7_5_5,
    7_4_4,
    7_3_3,
    7_2_2,
    7_1_1,
    7_0_0,
    6_9_9,
    6_8_8,
    6_7_7,
    6_6_6,
    6_5_5,
    6_4_4,
    6_3_3,
    6_2_2,
    6_1_1,
    6_0_0,
    5_9_9,
    5_8_5,
    5_7_1,
    5_5_7,
    5_4_2,
    5_2_8,
    5_1_4,
    5_0_0,
    4_9_9,
    4_8_5,
    4_7_1,
    4_5_7,
    4_4_2,
    4_2_8,
    4_1_4,
    4_0_0,
    3_9_9,
    3_7_9,
    3_5_9,
    3_4_0,
    3_2_0,
    3_0_0,
    2_9_9,
    2_7_9,
    2_5_9,
    2_4_0,
    2_2_0,
    2_0_0,
    1_9_9,
    1_6_6,
    1_3_3,
    1_0_0,
    9_9,
    6_6,
    3_3,
    0,
]




