

a_     =			{
    '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',
}






"""simple docstring"""




import heapq as hq
import math
from collections.abc import Iterator


class        __UpperCamelCase				:






							def __init__(   self      ,					lowerCAmelCase__      )	-> Optional[int]:
								a      :		List[str]	=				str(id_      )
								a      :		Optional[Any]	=				None
								a      :		Tuple	=				None
								a      :		str	=				[]
								a      :		Any	=				{}  # {vertex:distance}






							def __lt__(   self      ,					lowerCAmelCase__      )	-> Any:
								return self.key < other.key






							def __repr__(   self      )	-> Optional[Any]:
								return self.id






							def     __a   (   self      ,					lowerCAmelCase__      )	-> Any:
								self.neighbors.append(lowerCAmelCase__      )






							def     __a   (   self      ,					lowerCAmelCase__      ,					lowerCAmelCase__      )	-> Tuple:
								a      :		Optional[Any]	=				weight






def       _SCREAMING_SNAKE_CASE		(	_lowercase						:    int    ,       _lowercase						:    int    ,       _lowercase						:    int    ,       _lowercase						:    Union[str, Any]					) ->str:






	'''simple docstring'''






	graph[a - 1].add_neighbor(graph[b - 1]					)
	graph[b - 1].add_neighbor(graph[a - 1]					)
	# add the edges:
	graph[a - 1].add_edge(graph[b - 1]    ,       _lowercase					)
	graph[b - 1].add_edge(graph[a - 1]    ,       _lowercase					)






def       _SCREAMING_SNAKE_CASE		(	_lowercase						:    list    ,       _lowercase						:    Vertex					) ->list:






	'''simple docstring'''






	a      :		int	=				[]
	for u in graph:
		a      :		List[str]	=				math.inf
		a      :		int	=				None
	a      :		str	=				0
	a      :		Union[str, Any]	=				graph[:]
	while q:
		a      :		List[Any]	=				min(_lowercase					)
		q.remove(_lowercase					)
		for v in u.neighbors:
			if (v in q) and (u.edges[v.id] < v.key):
				a      :		List[Any]	=				u
				a      :		Optional[int]	=				u.edges[v.id]
	for i in range(1    ,       len(_lowercase					)					):
		a.append((int(graph[i].id					) + 1, int(graph[i].pi.id					) + 1)					)
	return a






def       _SCREAMING_SNAKE_CASE		(	_lowercase						:    list    ,       _lowercase						:    Vertex					) ->Iterator[tuple]:






	'''simple docstring'''






	for u in graph:
		a      :		str	=				math.inf
		a      :		Dict	=				None
	a      :		Dict	=				0

	a      :		List[Any]	=				list(_lowercase					)
	hq.heapify(_lowercase					)

	while h:
		a      :		Dict	=				hq.heappop(_lowercase					)
		for v in u.neighbors:
			if (v in h) and (u.edges[v.id] < v.key):
				a      :		Dict	=				u
				a      :		Optional[Any]	=				u.edges[v.id]
				hq.heapify(_lowercase					)

	for i in range(1    ,       len(_lowercase					)					):
		yield (int(graph[i].id					) + 1, int(graph[i].pi.id					) + 1)






def       _SCREAMING_SNAKE_CASE		(	) ->None:






	'''simple docstring'''








if __name__ == "__main__":
		import doctest

		doctest.testmod()


