






"""simple docstring"""
class _lowerCAmelCase						:







						def __init__(    self							)		->							Tuple:
										_SCREAMING_SNAKE_CASE   :		Tuple       		=    0
										_SCREAMING_SNAKE_CASE   :		Optional[Any]       		=    0
										_SCREAMING_SNAKE_CASE   :		Tuple       		=    {}







						def 			A      (    self   ,				lowerCAmelCase_							)		->							Tuple:
										if vertex not in self.adjacency:
														_SCREAMING_SNAKE_CASE   :		Any       		=    {}
														self.num_vertices += 1







						def 			A      (    self   ,				lowerCAmelCase_   ,				lowerCAmelCase_   ,				lowerCAmelCase_							)		->							Optional[int]:
										self.add_vertex(lowerCAmelCase_							)
										self.add_vertex(lowerCAmelCase_							)

										if head == tail:
														return

										_SCREAMING_SNAKE_CASE   :		Optional[Any]       		=    weight
										_SCREAMING_SNAKE_CASE   :		str       		=    weight







						def 			A      (    self							)		->							str:
										_SCREAMING_SNAKE_CASE   :		List[Any]       		=    self.get_edges()
										for edge in edges:
														_SCREAMING_SNAKE_CASE		,						_SCREAMING_SNAKE_CASE		,						_SCREAMING_SNAKE_CASE   :		List[Any]       		=    edge
														edges.remove((tail, head, weight)							)
										for i in range(len(lowerCAmelCase_							)							):
														_SCREAMING_SNAKE_CASE   :		int       		=    list(edges[i]							)

										edges.sort(key=lambda lowerCAmelCase_							: e[2]							)
										for i in range(len(lowerCAmelCase_							) - 1							):
														if edges[i][2] >= edges[i + 1][2]:
																		_SCREAMING_SNAKE_CASE   :		Any       		=    edges[i][2] + 1
										for edge in edges:
														_SCREAMING_SNAKE_CASE		,						_SCREAMING_SNAKE_CASE		,						_SCREAMING_SNAKE_CASE   :		Optional[int]       		=    edge
														_SCREAMING_SNAKE_CASE   :		Any       		=    weight
														_SCREAMING_SNAKE_CASE   :		Tuple       		=    weight







						def __str__(    self							)		->							Optional[Any]:
										_SCREAMING_SNAKE_CASE   :		str       		=    ''
										for tail in self.adjacency:
														for head in self.adjacency[tail]:
																		_SCREAMING_SNAKE_CASE   :		Tuple       		=    self.adjacency[head][tail]
																		string += F"""{head} -> {tail} == {weight}\n"""
										return string.rstrip('\n'							)







						def 			A      (    self							)		->							Union[str, Any]:
										_SCREAMING_SNAKE_CASE   :		Optional[int]       		=    []
										for tail in self.adjacency:
														for head in self.adjacency[tail]:
																		output.append((tail, head, self.adjacency[head][tail])							)
										return output







						def 			A      (    self							)		->							List[Any]:
										return self.adjacency.keys()







						@staticmethod
						def 			A      (    lowerCAmelCase_=None   ,				lowerCAmelCase_=None							)		->							Optional[int]:
										_SCREAMING_SNAKE_CASE   :		Optional[int]       		=    Graph()
										if vertices is None:
														_SCREAMING_SNAKE_CASE   :		List[str]       		=    []
										if edges is None:
														_SCREAMING_SNAKE_CASE   :		Any       		=    []
										for vertex in vertices:
														g.add_vertex(lowerCAmelCase_							)
										for edge in edges:
														g.add_edge(*lowerCAmelCase_							)
										return g


						class _lowerCAmelCase						:







												def __init__(    self							)		->							int:
																_SCREAMING_SNAKE_CASE   :		Union[str, Any]       		=    {}
																_SCREAMING_SNAKE_CASE   :		List[Any]       		=    {}







												def __len__(    self							)		->							str:
																return len(self.parent							)







												def 			A      (    self   ,				lowerCAmelCase_							)		->							str:
																if item in self.parent:
																				return self.find(lowerCAmelCase_							)

																_SCREAMING_SNAKE_CASE   :		str       		=    item
																_SCREAMING_SNAKE_CASE   :		Optional[int]       		=    0
																return item







												def 			A      (    self   ,				lowerCAmelCase_							)		->							Optional[int]:
																if item not in self.parent:
																				return self.make_set(lowerCAmelCase_							)
																if item != self.parent[item]:
																				_SCREAMING_SNAKE_CASE   :		int       		=    self.find(self.parent[item]							)
																return self.parent[item]







												def 			A      (    self   ,				lowerCAmelCase_   ,				lowerCAmelCase_							)		->							Dict:
																_SCREAMING_SNAKE_CASE   :		List[str]       		=    self.find(lowerCAmelCase_							)
																_SCREAMING_SNAKE_CASE   :		Union[str, Any]       		=    self.find(lowerCAmelCase_							)

																if roota == roota:
																				return roota

																if self.rank[roota] > self.rank[roota]:
																				_SCREAMING_SNAKE_CASE   :		List[str]       		=    roota
																				return roota

																if self.rank[roota] < self.rank[roota]:
																				_SCREAMING_SNAKE_CASE   :		Optional[int]       		=    roota
																				return roota

																if self.rank[roota] == self.rank[roota]:
																				self.rank[roota] += 1
																				_SCREAMING_SNAKE_CASE   :		List[Any]       		=    roota
																				return roota
																return None







						@staticmethod
						def 			A      (    lowerCAmelCase_							)		->							List[Any]:
										_SCREAMING_SNAKE_CASE   :		List[Any]       		=    graph.num_vertices

										_SCREAMING_SNAKE_CASE   :		Optional[Any]       		=    Graph.UnionFind()
										_SCREAMING_SNAKE_CASE   :		Dict       		=    []
										while num_components > 1:
														_SCREAMING_SNAKE_CASE   :		Tuple       		=    {}
														for vertex in graph.get_vertices():
																		_SCREAMING_SNAKE_CASE   :		str       		=    -1

														_SCREAMING_SNAKE_CASE   :		Optional[Any]       		=    graph.get_edges()
														for edge in edges:
																		_SCREAMING_SNAKE_CASE		,						_SCREAMING_SNAKE_CASE		,						_SCREAMING_SNAKE_CASE   :		Any       		=    edge
																		edges.remove((tail, head, weight)							)
														for edge in edges:
																		_SCREAMING_SNAKE_CASE		,						_SCREAMING_SNAKE_CASE		,						_SCREAMING_SNAKE_CASE   :		int       		=    edge
																		_SCREAMING_SNAKE_CASE   :		Tuple       		=    union_find.find(lowerCAmelCase_							)
																		_SCREAMING_SNAKE_CASE   :		Any       		=    union_find.find(lowerCAmelCase_							)
																		if seta != seta:
																						if cheap_edge[seta] == -1 or cheap_edge[seta][2] > weight:
																										_SCREAMING_SNAKE_CASE   :		str       		=    [head, tail, weight]

																						if cheap_edge[seta] == -1 or cheap_edge[seta][2] > weight:
																										_SCREAMING_SNAKE_CASE   :		Optional[int]       		=    [head, tail, weight]
														for vertex in cheap_edge:
																		if cheap_edge[vertex] != -1:
																						_SCREAMING_SNAKE_CASE		,						_SCREAMING_SNAKE_CASE		,						_SCREAMING_SNAKE_CASE   :		Optional[int]       		=    cheap_edge[vertex]
																						if union_find.find(lowerCAmelCase_							) != union_find.find(lowerCAmelCase_							):
																										union_find.union(lowerCAmelCase_   ,				lowerCAmelCase_							)
																										mst_edges.append(cheap_edge[vertex]							)
																										_SCREAMING_SNAKE_CASE   :		List[Any]       		=    num_components - 1
										_SCREAMING_SNAKE_CASE   :		Any       		=    Graph.build(edges=lowerCAmelCase_							)
										return mst









"""simple docstring"""
from ...utils import is_torch_available, is_transformers_available


if is_transformers_available() and is_torch_available():
			from .pipeline_vq_diffusion import LearnedClassifierFreeSamplingEmbeddings, VQDiffusionPipeline

