




class 		__lowerCAmelCase	:
							def __init__(						self						:List[str]				):







								'''simple docstring'''







								a										=							0
								a										=							0
								a										=							{}
							def       lowerCamelCase__							(						self						:int		,      __magic_name__						:Dict				):







								'''simple docstring'''







								if vertex not in self.adjacency:
									a										=							{}
									self.num_vertices += 1
							def       lowerCamelCase__							(						self						:int		,      __magic_name__						:Any		,      __magic_name__						:Dict		,      __magic_name__						:Union[str, Any]				):







								'''simple docstring'''







								self.add_vertex(__magic_name__				)
								self.add_vertex(__magic_name__				)

								if head == tail:
									return

								a										=							weight
								a										=							weight
							def       lowerCamelCase__							(						self						:Optional[int]				):







								'''simple docstring'''







								a										=							self.get_edges()
								for edge in edges:
									a				, a				, a										=							edge
									edges.remove((tail, head, weight)				)
								for i in range(len(__magic_name__				)				):
									a										=							list(edges[i]				)

								edges.sort(key=lambda __magic_name__				: e[2]				)
								for i in range(len(__magic_name__				) - 1				):
									if edges[i][2] >= edges[i + 1][2]:
										a										=							edges[i][2] + 1
								for edge in edges:
									a				, a				, a										=							edge
									a										=							weight
									a										=							weight
							def __str__(						self						:int				):







								'''simple docstring'''







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







								'''simple docstring'''







								a										=							[]
								for tail in self.adjacency:
									for head in self.adjacency[tail]:
										output.append((tail, head, self.adjacency[head][tail])				)
								return output
							def       lowerCamelCase__							(						self						:List[str]				):







								'''simple docstring'''







								return self.adjacency.keys()
							@staticmethod
							def       lowerCamelCase__							(						__magic_name__						:Tuple=None		,      __magic_name__						:int=None				):







								'''simple docstring'''







								a										=							Graph()
								if vertices is None:
									a										=							[]
								if edges is None:
									a										=							[]
								for vertex in vertices:
									g.add_vertex(__magic_name__				)
								for edge in edges:
									g.add_edge(*__magic_name__				)
								return g

							class 		__lowerCAmelCase	:
														def __init__(						self						:int				):







															'''simple docstring'''







															a										=							{}
															a										=							{}
														def __len__(						self						:Union[str, Any]				):







															'''simple docstring'''







															return len(self.parent				)
														def       lowerCamelCase__							(						self						:Tuple		,      __magic_name__						:List[str]				):







															'''simple docstring'''







															if item in self.parent:
																return self.find(__magic_name__				)

															a										=							item
															a										=							0
															return item
														def       lowerCamelCase__							(						self						:Optional[int]		,      __magic_name__						:List[str]				):







															'''simple docstring'''







															if item not in self.parent:
																return self.make_set(__magic_name__				)
															if item != self.parent[item]:
																a										=							self.find(self.parent[item]				)
															return self.parent[item]





														def       lowerCamelCase__							(						self						:Optional[Any]		,      __magic_name__						:Dict		,      __magic_name__						:List[str]				):







															'''simple docstring'''







															a										=							self.find(__magic_name__				)
															a										=							self.find(__magic_name__				)

															if roota == roota:
																return roota

															if self.rank[roota] > self.rank[roota]:
																a										=							roota
																return roota

															if self.rank[roota] < self.rank[roota]:
																a										=							roota
																return roota

															if self.rank[roota] == self.rank[roota]:
																self.rank[roota] += 1
																a										=							roota
																return roota
															return None







							@staticmethod
							def       lowerCamelCase__							(						__magic_name__						:Dict				):







								'''simple docstring'''







								a										=							graph.num_vertices

								a										=							Graph.UnionFind()
								a										=							[]
								while num_components > 1:
									a										=							{}
									for vertex in graph.get_vertices():
										a										=							-1

									a										=							graph.get_edges()
									for edge in edges:
										a				, a				, a										=							edge
										edges.remove((tail, head, weight)				)
									for edge in edges:
										a				, a				, a										=							edge
										a										=							union_find.find(__magic_name__				)
										a										=							union_find.find(__magic_name__				)
										if seta != seta:
											if cheap_edge[seta] == -1 or cheap_edge[seta][2] > weight:
												a										=							[head, tail, weight]

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







__UpperCamelCase					:       Optional[int]    					=      {
    "Pillow": "Pillow",
    "accelerate": "accelerate>=0.11.0",
    "compel": "compel==0.1.8",
    "black": "black~=23.1",
    "datasets": "datasets",
    "filelock": "filelock",
    "flax": "flax>=0.4.1",
    "hf-doc-builder": "hf-doc-builder>=0.3.0",
    "huggingface-hub": "huggingface-hub>=0.13.2",
    "requests-mock": "requests-mock==1.10.0",
    "importlib_metadata": "importlib_metadata",
    "invisible-watermark": "invisible-watermark",
    "isort": "isort>=5.5.4",
    "jax": "jax>=0.2.8,!=0.3.2",
    "jaxlib": "jaxlib>=0.1.65",
    "Jinja2": "Jinja2",
    "k-diffusion": "k-diffusion>=0.0.12",
    "torchsde": "torchsde",
    "note_seq": "note_seq",
    "librosa": "librosa",
    "numpy": "numpy",
    "omegaconf": "omegaconf",
    "parameterized": "parameterized",
    "protobuf": "protobuf>=3.20.3,<4",
    "pytest": "pytest",
    "pytest-timeout": "pytest-timeout",
    "pytest-xdist": "pytest-xdist",
    "ruff": "ruff>=0.0.241",
    "safetensors": "safetensors",
    "sentencepiece": "sentencepiece>=0.1.91,!=0.1.92",
    "scipy": "scipy",
    "onnx": "onnx",
    "regex": "regex!=2019.12.17",
    "requests": "requests",
    "tensorboard": "tensorboard",
    "torch": "torch>=1.4",
    "torchvision": "torchvision",
    "transformers": "transformers>=4.25.1",
    "urllib3": "urllib3<=2.0.0",
}

