





"""simple docstring"""
from __future__ import annotations

from typing import Generic, TypeVar

lowerCamelCase_       =		TypeVar("T")






class  _SCREAMING_SNAKE_CASE(       Generic[T]  ):




       def __init__(						self		,SCREAMING_SNAKE_CASE__							)      ->				None:





             """simple docstring"""






             __SCREAMING_SNAKE_CASE       :Any		    =  data
             __SCREAMING_SNAKE_CASE       :int		    =  self
             __SCREAMING_SNAKE_CASE       :Dict		    =  0






class  _SCREAMING_SNAKE_CASE(       Generic[T]  ):




       def __init__(						self							)      ->				None:





             """simple docstring"""






             __SCREAMING_SNAKE_CASE       :dict[T, DisjointSetTreeNode[T]]		    =  {}




       def    _UpperCamelCase					(						self		,SCREAMING_SNAKE_CASE__							)      ->				None:





             """simple docstring"""






             __SCREAMING_SNAKE_CASE       :List[str]		    =  DisjointSetTreeNode(SCREAMING_SNAKE_CASE__							)




       def    _UpperCamelCase					(						self		,SCREAMING_SNAKE_CASE__							)      ->				DisjointSetTreeNode[T]:





             """simple docstring"""






             __SCREAMING_SNAKE_CASE       :Optional[Any]		    =  self.map[data]
             if elem_ref != elem_ref.parent:
                   __SCREAMING_SNAKE_CASE       :Tuple		    =  self.find_set(elem_ref.parent.data							)
             return elem_ref.parent




       def    _UpperCamelCase					(						self		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__							)      ->				None:





             """simple docstring"""






             if nodea.rank > nodea.rank:
                   __SCREAMING_SNAKE_CASE       :Union[str, Any]		    =  nodea
             else:
                   __SCREAMING_SNAKE_CASE       :Optional[int]		    =  nodea
                   if nodea.rank == nodea.rank:
                         nodea.rank += 1




       def    _UpperCamelCase					(						self		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__							)      ->				None:





             """simple docstring"""






             self.link(self.find_set(SCREAMING_SNAKE_CASE__							)		,self.find_set(SCREAMING_SNAKE_CASE__							)							)






class  _SCREAMING_SNAKE_CASE(       Generic[T]  ):




       def __init__(						self							)      ->				None:





             """simple docstring"""






             __SCREAMING_SNAKE_CASE       :dict[T, dict[T, int]]		    =  {}




       def    _UpperCamelCase					(						self		,SCREAMING_SNAKE_CASE__							)      ->				None:





             """simple docstring"""






             if node not in self.connections:
                   __SCREAMING_SNAKE_CASE       :Any		    =  {}




       def    _UpperCamelCase					(						self		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__							)      ->				None:





             """simple docstring"""






             self.add_node(SCREAMING_SNAKE_CASE__							)
             self.add_node(SCREAMING_SNAKE_CASE__							)
             __SCREAMING_SNAKE_CASE       :Dict		    =  weight
             __SCREAMING_SNAKE_CASE       :Any		    =  weight




       def    _UpperCamelCase					(						self							)      ->				GraphUndirectedWeighted[T]:





             """simple docstring"""






             __SCREAMING_SNAKE_CASE       :Tuple		    =  []
             __SCREAMING_SNAKE_CASE       :Union[str, Any]		    =  set()
             for start in self.connections:
                   for end in self.connections[start]:
                         if (start, end) not in seen:
                               seen.add((end, start)							)
                               edges.append((start, end, self.connections[start][end])							)
             edges.sort(key=lambda SCREAMING_SNAKE_CASE__							: x[2]							)

             # creating the disjoint set
             __SCREAMING_SNAKE_CASE       :Optional[int]		    =  DisjointSetTree[T]()
             for node in self.connections:
                   disjoint_set.make_set(SCREAMING_SNAKE_CASE__							)

             # MST generation
             __SCREAMING_SNAKE_CASE       :Any		    =  0
             __SCREAMING_SNAKE_CASE       :Dict		    =  0
             __SCREAMING_SNAKE_CASE       :Tuple		    =  GraphUndirectedWeighted[T]()
             while num_edges < len(self.connections							) - 1:
                   __SCREAMING_SNAKE_CASE       :Optional[int]		    =  edges[index]
                   index += 1
                   __SCREAMING_SNAKE_CASE       :Dict		    =  disjoint_set.find_set(SCREAMING_SNAKE_CASE__							)
                   __SCREAMING_SNAKE_CASE       :str		    =  disjoint_set.find_set(SCREAMING_SNAKE_CASE__							)
                   if parent_u != parent_v:
                         num_edges += 1
                         graph.add_edge(SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__							)
                         disjoint_set.union(SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__							)
             return graph






"""simple docstring"""
from torch import nn






class  _SCREAMING_SNAKE_CASE(       nn.Module  ):




       def __init__(						self		,SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__							)      ->				List[str]:





             """simple docstring"""






             super().__init__()
             __SCREAMING_SNAKE_CASE       :Tuple		    =  class_size
             __SCREAMING_SNAKE_CASE       :str		    =  embed_size
             # self.mlp1 = nn.Linear(embed_size, embed_size)
             # self.mlp2 = (nn.Linear(embed_size, class_size))
             __SCREAMING_SNAKE_CASE       :Optional[Any]		    =  nn.Linear(SCREAMING_SNAKE_CASE__		,SCREAMING_SNAKE_CASE__							)




       def    _UpperCamelCase					(						self		,SCREAMING_SNAKE_CASE__							)      ->				Optional[int]:





             """simple docstring"""






             __SCREAMING_SNAKE_CASE       :Optional[Any]		    =  self.mlp(SCREAMING_SNAKE_CASE__							)
             return logits