






A_		:		Optional[Any]		     =			tuple[float, float, float]
A_		:		Union[str, Any]		     =			tuple[float, float, float]

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

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

def   snake_case (UpperCAmelCase__     ,   UpperCAmelCase__  )	->    bool:
  return tuple(round(a__     ,   a__  ) for x in vector  ) == (0, 0, 0)

def   snake_case (UpperCAmelCase__     ,   UpperCAmelCase__     ,   UpperCAmelCase__     ,   UpperCAmelCase__ = 1_0  )	->    bool:
  UpperCamelCase_: str   				=    create_vector(a__     ,   a__  )
  UpperCamelCase_: int   				=    create_vector(a__     ,   a__  )
  return is_zero_vector(get_ad_vectors_cross(a__     ,   a__  )     ,   a__  )







# A Bipartite Graph is a graph whose vertices can be divided into two independent sets,
# U and V such that every edge (u, v) either connects a vertex from U to V or a vertex
# from V to U. In other words, for every edge (u, v), either u belongs to U and v to V,
# or u belongs to V and v to U. We can also say that there is no edge that connects
# vertices of same set.

def   snake_case (UpperCAmelCase__  )	->    List[str]:
  UpperCamelCase_: int   				=    [False] * len(UpperCAmelCase__  )
  UpperCamelCase_: Any   				=    [-1] * len(UpperCAmelCase__  )

  def dfs(UpperCAmelCase__     ,   UpperCAmelCase__  ):
    UpperCamelCase_: Tuple   				=    True
    UpperCamelCase_: Optional[int]   				=    c
    for u in graph[v]:
      if not visited[u]:
        dfs(UpperCAmelCase__     ,   1 - c  )

  for i in range(len(UpperCAmelCase__  )  ):
    if not visited[i]:
      dfs(UpperCAmelCase__     ,   0  )

  for i in range(len(UpperCAmelCase__  )  ):
    for j in graph[i]:
      if color[i] == color[j]:
        return False

  return True


# Adjacency list of graph
A_		:		Dict		     =			{0: [1, 3], 1: [0, 2], 2: [1, 3], 3: [0, 2], 4: []}
print(check_bipartite_dfs(graph))