






'''simple docstring'''

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






class     a_						:

  def __init__(				self      ,		_SCREAMING_SNAKE_CASE				)  ->				str:



        """simple docstring"""






        UpperCamelCase      = str(id_				)
        UpperCamelCase      = None
        UpperCamelCase      = None
        UpperCamelCase      = []
        UpperCamelCase      = {}  # {vertex:distance}

  def __lt__(				self      ,		_SCREAMING_SNAKE_CASE				)  ->				Optional[int]:



        """simple docstring"""






        return self.key < other.key

  def __repr__(				self				)  ->				Union[str, Any]:



        """simple docstring"""






        return self.id

  def   A__						(				self      ,		_SCREAMING_SNAKE_CASE				)  ->				Dict:



        """simple docstring"""






        self.neighbors.append(_SCREAMING_SNAKE_CASE				)


  def   A__						(				self      ,		_SCREAMING_SNAKE_CASE      ,		_SCREAMING_SNAKE_CASE				)  ->				Any:



        """simple docstring"""






        UpperCamelCase      = weight







def    lowercase__			(				__UpperCamelCase		,						__UpperCamelCase		,						__UpperCamelCase		,						__UpperCamelCase   )->			List[str]:
      # add the neighbors:
      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]		,						__UpperCamelCase   )
      graph[b - 1].add_edge(graph[a - 1]		,						__UpperCamelCase   )







def    lowercase__			(				__UpperCamelCase		,						__UpperCamelCase   )->			list:
      UpperCamelCase      = []
      for u in graph:
            UpperCamelCase      = math.inf
            UpperCamelCase      = None
      UpperCamelCase      = 0
      UpperCamelCase      = graph[:]
      while q:
            UpperCamelCase      = min(__UpperCamelCase   )
            q.remove(__UpperCamelCase   )
            for v in u.neighbors:
                  if (v in q) and (u.edges[v.id] < v.key):
                        UpperCamelCase      = u
                        UpperCamelCase      = u.edges[v.id]
      for i in range(1		,						len(__UpperCamelCase   )   ):
            a.append((int(graph[i].id   ) + 1, int(graph[i].pi.id   ) + 1)   )
      return a







def    lowercase__			(				__UpperCamelCase		,						__UpperCamelCase   )->			Iterator[tuple]:
      for u in graph:
            UpperCamelCase      = math.inf
            UpperCamelCase      = None
      UpperCamelCase      = 0

      UpperCamelCase      = list(__UpperCamelCase   )
      hq.heapify(__UpperCamelCase   )

      while h:
            UpperCamelCase      = hq.heappop(__UpperCamelCase   )
            for v in u.neighbors:
                  if (v in h) and (u.edges[v.id] < v.key):
                        UpperCamelCase      = u
                        UpperCamelCase      = u.edges[v.id]
                        hq.heapify(__UpperCamelCase   )

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







def    lowercase__			(				)->			None:
      pass


if __name__ == "__main__":
     import doctest

     doctest.testmod()








'''simple docstring'''

from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


SCREAMING_SNAKE_CASE__     =       {
    'configuration_nllb_moe': [
        'NLLB_MOE_PRETRAINED_CONFIG_ARCHIVE_MAP',
        'NllbMoeConfig',
    ]
}

try:
     if not is_torch_available():
          raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
     pass
else:
     SCREAMING_SNAKE_CASE__     =       [
         'NLLB_MOE_PRETRAINED_MODEL_ARCHIVE_LIST',
         'NllbMoeForConditionalGeneration',
         'NllbMoeModel',
         'NllbMoePreTrainedModel',
         'NllbMoeTop2Router',
         'NllbMoeSparseMLP',
     ]


if TYPE_CHECKING:
     from .configuration_nllb_moe import (
         NLLB_MOE_PRETRAINED_CONFIG_ARCHIVE_MAP,
         NllbMoeConfig,
     )

     try:
          if not is_torch_available():
               raise OptionalDependencyNotAvailable()
     except OptionalDependencyNotAvailable:
          pass
     else:
          from .modeling_nllb_moe import (
              NLLB_MOE_PRETRAINED_MODEL_ARCHIVE_LIST,
              NllbMoeForConditionalGeneration,
              NllbMoeModel,
              NllbMoePreTrainedModel,
              NllbMoeSparseMLP,
              NllbMoeTopaRouter,
          )


else:
     import sys

     SCREAMING_SNAKE_CASE__     =       _LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)
