





from __future__ import annotations

from sys import maxsize
from typing import Generic, TypeVar

_SCREAMING_SNAKE_CASE      	=		TypeVar("""T""")


def 							SCREAMING_SNAKE_CASE__						(    __a   ):
	return (position - 1) // 2


def 							SCREAMING_SNAKE_CASE__						(    __a   ):
	return (2 * position) + 1


def 							SCREAMING_SNAKE_CASE__						(    __a   ):
	return (2 * position) + 2
class SCREAMING_SNAKE_CASE_						(					Generic[T]					):






						def __init__(      self      :      int	)							->    None:







							"""simple docstring"""


							snake_case_		:			list[tuple[T, int]]											=	[]
							snake_case_		:			dict[T, int]											=	{}
							snake_case_		:			int											=	0






						def __len__(      self      :      List[Any]	)							->    int:







							"""simple docstring"""


							return self.elements






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







							"""simple docstring"""


							return str(self.heap	)






						def UpperCAmelCase_				(      self      :      Dict	)							->    bool:







							"""simple docstring"""


							return self.elements == 0






						def UpperCAmelCase_				(      self      :      List[str]		,   _A      :      T		,   _A      :      int	)							->    None:







							"""simple docstring"""


							self.heap.append((elem, weight)	)
							snake_case_		:			Optional[int]											=	self.elements
							self.elements += 1
							self._bubble_up(_A	)






						def UpperCAmelCase_				(      self      :      List[str]	)							->    T:







							"""simple docstring"""


							if self.elements > 1:
								self._swap_nodes(0		,   self.elements - 1	)
							snake_case_						,snake_case_		:			Optional[int]											=	self.heap.pop()
							del self.position_map[elem]
							self.elements -= 1
							if self.elements > 0:
								snake_case_						,snake_case_		:			List[str]											=	self.heap[0]
								self._bubble_down(_A	)
							return elem






						def UpperCAmelCase_				(      self      :      Optional[Any]		,   _A      :      T		,   _A      :      int	)							->    None:







							"""simple docstring"""


							snake_case_		:			List[str]											=	self.position_map[elem]
							snake_case_		:			int											=	(elem, weight)
							if position > 0:
								snake_case_		:			Any											=	get_parent_position(_A	)
								snake_case_						,snake_case_		:			Any											=	self.heap[parent_position]
								if parent_weight > weight:
									self._bubble_up(_A	)
								else:
									self._bubble_down(_A	)
							else:
								self._bubble_down(_A	)






						def UpperCAmelCase_				(      self      :      Union[str, Any]		,   _A      :      T	)							->    None:







							"""simple docstring"""


							snake_case_		:			Tuple											=	self.position_map[elem]
							if curr_pos == 0:
								return None
							snake_case_		:			Dict											=	get_parent_position(_A	)
							snake_case_						,snake_case_		:			Tuple											=	self.heap[curr_pos]
							snake_case_						,snake_case_		:			Optional[Any]											=	self.heap[parent_position]
							if parent_weight > weight:
								self._swap_nodes(_A		,   _A	)
								return self._bubble_up(_A	)
							return None






						def UpperCAmelCase_				(      self      :      Tuple		,   _A      :      T	)							->    None:







							"""simple docstring"""


							snake_case_		:			Tuple											=	self.position_map[elem]
							snake_case_						,snake_case_		:			List[Any]											=	self.heap[curr_pos]
							snake_case_		:			List[Any]											=	get_child_left_position(_A	)
							snake_case_		:			Optional[Any]											=	get_child_right_position(_A	)
							if child_left_position < self.elements and child_right_position < self.elements:
								snake_case_						,snake_case_		:			Union[str, Any]											=	self.heap[child_left_position]
								snake_case_						,snake_case_		:			Any											=	self.heap[child_right_position]
								if child_right_weight < child_left_weight and child_right_weight < weight:
									self._swap_nodes(_A		,   _A	)
									return self._bubble_down(_A	)
							if child_left_position < self.elements:
								snake_case_						,snake_case_		:			Optional[Any]											=	self.heap[child_left_position]
								if child_left_weight < weight:
									self._swap_nodes(_A		,   _A	)
									return self._bubble_down(_A	)
							else:
								return None
							if child_right_position < self.elements:
								snake_case_						,snake_case_		:			Tuple											=	self.heap[child_right_position]
								if child_right_weight < weight:
									self._swap_nodes(_A		,   _A	)
									return self._bubble_down(_A	)
							return None






						def UpperCAmelCase_				(      self      :      List[Any]		,   _A      :      int		,   _A      :      int	)							->    None:







							"""simple docstring"""


							snake_case_		:			Dict											=	self.heap[nodea_pos][0]
							snake_case_		:			Union[str, Any]											=	self.heap[nodea_pos][0]
							snake_case_						,snake_case_		:			Union[str, Any]											=	(
							    self.heap[nodea_pos],
							    self.heap[nodea_pos],
							)
							snake_case_		:			Dict											=	nodea_pos
							snake_case_		:			Dict											=	nodea_pos
class SCREAMING_SNAKE_CASE_						(					Generic[T]					):






						def __init__(      self      :      List[Any]	)							->    None:







							"""simple docstring"""


							snake_case_		:			dict[T, dict[T, int]]											=	{}
							snake_case_		:			int											=	0






						def __repr__(      self      :      int	)							->    str:







							"""simple docstring"""


							return str(self.connections	)






						def __len__(      self      :      Tuple	)							->    int:







							"""simple docstring"""


							return self.nodes






						def UpperCAmelCase_				(      self      :      str		,   _A      :      T	)							->    None:







							"""simple docstring"""


							if node not in self.connections:
								snake_case_		:			Any											=	{}
								self.nodes += 1






						def UpperCAmelCase_				(      self      :      Optional[Any]		,   _A      :      T		,   _A      :      T		,   _A      :      int	)							->    None:







							"""simple docstring"""


							self.add_node(_A	)
							self.add_node(_A	)
							snake_case_		:			str											=	weight
							snake_case_		:			Tuple											=	weight


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

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

	if priority_queue.is_empty():
		return dist, parent

	# initialization
	snake_case_		:			Tuple											=	priority_queue.extract_min()
	snake_case_		:			Dict											=	0
	for neighbour in graph.connections[node]:
		if dist[neighbour] > dist[node] + graph.connections[node][neighbour]:
			snake_case_		:			List[str]											=	dist[node] + graph.connections[node][neighbour]
			priority_queue.update_key(__a   , dist[neighbour]   )
			snake_case_		:			Tuple											=	node

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








from ....utils import logging


_SCREAMING_SNAKE_CASE      	=		logging.get_logger(__name__)
class SCREAMING_SNAKE_CASE_						(					snake_case_					):






						def __init__(      self      :      str		,   _A      :      List[Any]		,   _A      :      List[Any]=None		,   _A      :      str=2048	)							->    Optional[int]:







							"""simple docstring"""


							snake_case_		:			Tuple											=	config.__dict__
							snake_case_		:			List[str]											=	modal_hidden_size
							if num_labels:
								snake_case_		:			int											=	num_labels

