
from __future__ import annotations

from sys import maxsize
from typing import Generic, TypeVar

lowercase__          =TypeVar('T')




def        __UpperCamelCase					(    lowerCAmelCase__							:    int  ):
 return (position - 1) // 2




def        __UpperCamelCase					(    lowerCAmelCase__							:    int  ):
 return (2 * position) + 1




def        __UpperCamelCase					(    lowerCAmelCase__							:    int  ):
 return (2 * position) + 2



class 		UpperCamelCase__  (	Generic[T]   ):
   def __init__(self			: Optional[int]       ):
    __a			:  list[tuple[T, int]]		    =  []
    __a			:  dict[T, int]		    =  {}
    __a			:  int		    =  0
   def __len__(self			: Optional[Any]       ):
    return self.elements
   def __repr__(self			: List[str]       ):
    return str(self.heap       )
   def 				lowerCAmelCase      (self			: Dict       ):
    # Check if the priority queue is empty
    return self.elements == 0
   def 				lowerCAmelCase      (self			: Dict ,    snake_case_			: T ,    snake_case_			: int       ):
    # Add an element with given priority to the queue
    self.heap.append((elem, weight)       )
    __a			:  Dict		    =  self.elements
    self.elements += 1
    self._bubble_up(snake_case_       )
   def 				lowerCAmelCase      (self			: Dict       ):
    # Remove and return the element with lowest weight (highest priority)
    if self.elements > 1:
     self._swap_nodes(0 ,    self.elements - 1       )
    __a    ,	__a			:  Tuple		    =  self.heap.pop()
    del self.position_map[elem]
    self.elements -= 1
    if self.elements > 0:
     __a    ,	__a			:  int		    =  self.heap[0]
     self._bubble_down(snake_case_       )
    return elem
   def 				lowerCAmelCase      (self			: List[Any] ,    snake_case_			: T ,    snake_case_			: int       ):
    # Update the weight of the given key
    __a			:  Dict		    =  self.position_map[elem]
    __a			:  Union[str, Any]		    =  (elem, weight)
    if position > 0:
     __a			:  Optional[Any]		    =  get_parent_position(snake_case_       )
     __a    ,	__a			:  List[Any]		    =  self.heap[parent_position]
     if parent_weight > weight:
      self._bubble_up(snake_case_       )
     else:
      self._bubble_down(snake_case_       )
    else:
     self._bubble_down(snake_case_       )
   def 				lowerCAmelCase      (self			: List[Any] ,    snake_case_			: T       ):
    # Place a node at the proper position (upward movement) [to be used internally
    # only]
    __a			:  Dict		    =  self.position_map[elem]
    if curr_pos == 0:
     return None
    __a			:  int		    =  get_parent_position(snake_case_       )
    __a    ,	__a			:  Dict		    =  self.heap[curr_pos]
    __a    ,	__a			:  Any		    =  self.heap[parent_position]
    if parent_weight > weight:
     self._swap_nodes(snake_case_ ,    snake_case_       )
     return self._bubble_up(snake_case_       )
    return None
   def 				lowerCAmelCase      (self			: Optional[Any] ,    snake_case_			: T       ):
    # Place a node at the proper position (downward movement) [to be used
    # internally only]
    __a			:  Optional[Any]		    =  self.position_map[elem]
    __a    ,	__a			:  Optional[int]		    =  self.heap[curr_pos]
    __a			:  List[str]		    =  get_child_left_position(snake_case_       )
    __a			:  int		    =  get_child_right_position(snake_case_       )
    if child_left_position < self.elements and child_right_position < self.elements:
     __a    ,	__a			:  Union[str, Any]		    =  self.heap[child_left_position]
     __a    ,	__a			:  int		    =  self.heap[child_right_position]
     if child_right_weight < child_left_weight and child_right_weight < weight:
      self._swap_nodes(snake_case_ ,    snake_case_       )
      return self._bubble_down(snake_case_       )
    if child_left_position < self.elements:
     __a    ,	__a			:  List[Any]		    =  self.heap[child_left_position]
     if child_left_weight < weight:
      self._swap_nodes(snake_case_ ,    snake_case_       )
      return self._bubble_down(snake_case_       )
    else:
     return None
    if child_right_position < self.elements:
     __a    ,	__a			:  List[Any]		    =  self.heap[child_right_position]
     if child_right_weight < weight:
      self._swap_nodes(snake_case_ ,    snake_case_       )
      return self._bubble_down(snake_case_       )
    return None







   def 				lowerCAmelCase      (self			: List[Any] ,    snake_case_			: int ,    snake_case_			: int       ):
    # Swap the nodes at the given positions
    __a			:  Tuple		    =  self.heap[nodea_pos][0]
    __a			:  List[Any]		    =  self.heap[nodea_pos][0]
    __a    ,	__a			:  List[str]		    =  (
        self.heap[nodea_pos],
        self.heap[nodea_pos],
    )
    __a			:  Any		    =  nodea_pos
    __a			:  List[Any]		    =  nodea_pos





class 		UpperCamelCase__  (	Generic[T]   ):
   def __init__(self			: Any       ):
    __a			:  dict[T, dict[T, int]]		    =  {}
    __a			:  int		    =  0
   def __repr__(self			: str       ):
    return str(self.connections       )
   def __len__(self			: str       ):
    return self.nodes
   def 				lowerCAmelCase      (self			: List[Any] ,    snake_case_			: T       ):
    # Add a node in the graph if it is not in the graph
    if node not in self.connections:
     __a			:  str		    =  {}
     self.nodes += 1







   def 				lowerCAmelCase      (self			: Optional[int] ,    snake_case_			: T ,    snake_case_			: T ,    snake_case_			: int       ):
    # Add an edge between 2 nodes in the graph
    self.add_node(snake_case_       )
    self.add_node(snake_case_       )
    __a			:  Optional[int]		    =  weight
    __a			:  Optional[Any]		    =  weight





def        __UpperCamelCase					(    lowerCAmelCase__							:    GraphUndirectedWeighted[T]  ,       ):
 __a			:  dict[T, int]		    =  {node: maxsize for node in graph.connections}
 __a			:  dict[T, T | None]		    =  {node: None for node in graph.connections}

 __a			:  MinPriorityQueue[T]		    =  MinPriorityQueue()
 for node, weight in dist.items():
  priority_queue.push(lowerCAmelCase__  ,       lowerCAmelCase__  )

 if priority_queue.is_empty():
  return dist, parent

 # initialization
 __a			:  List[str]		    =  priority_queue.extract_min()
 __a			:  Union[str, Any]		    =  0
 for neighbour in graph.connections[node]:
  if dist[neighbour] > dist[node] + graph.connections[node][neighbour]:
   __a			:  str		    =  dist[node] + graph.connections[node][neighbour]
   priority_queue.update_key(lowerCAmelCase__  ,       dist[neighbour]  )
   __a			:  Optional[Any]		    =  node

    # running prim's algorithm
 while not priority_queue.is_empty():
  __a			:  Any		    =  priority_queue.extract_min()
  for neighbour in graph.connections[node]:
   if dist[neighbour] > dist[node] + graph.connections[node][neighbour]:
    __a			:  Optional[Any]		    =  dist[node] + graph.connections[node][neighbour]
    priority_queue.update_key(lowerCAmelCase__  ,       dist[neighbour]  )
    __a			:  List[Any]		    =  node
 return dist, parent


import unittest

from transformers import is_torch_available
from transformers.testing_utils import require_sentencepiece, require_tokenizers, require_torch, slow, torch_device


if is_torch_available():
      from transformers import AutoModelForSeqaSeqLM, AutoTokenizer



@require_torch
@require_sentencepiece
@require_tokenizers
class 		UpperCamelCase__  (	unittest.TestCase   ):
   @slow
   def 				lowerCAmelCase      (self			: Tuple       ):
    __a			:  List[str]		    =  AutoModelForSeqaSeqLM.from_pretrained('''google/mt5-small''' ,    return_dict=snake_case_       ).to(snake_case_       )
    __a			:  List[Any]		    =  AutoTokenizer.from_pretrained('''google/mt5-small'''       )

    __a			:  Optional[int]		    =  tokenizer('''Hello there''' ,    return_tensors='''pt'''       ).input_ids
    __a			:  Dict		    =  tokenizer('''Hi I am''' ,    return_tensors='''pt'''       ).input_ids

    __a			:  Optional[Any]		    =  model(input_ids.to(snake_case_       ) ,    labels=labels.to(snake_case_       )       ).loss
    __a			:  Tuple		    =  -(labels.shape[-1] * loss.item())

    __a			:  Dict		    =  -84.9127
    self.assertTrue(abs(mtf_score - EXPECTED_SCORE       ) < 1E-4       )
