





from __future__ import annotations

from collections.abc import Callable
from typing import Generic, TypeVar

lowerCAmelCase_						   =    TypeVar("""T""")
lowerCAmelCase_						   =    TypeVar("""U""")



class        _lowerCAmelCase    (			Generic[T, U]							):


		'''simple docstring'''







		def __init__(      self      :					List[str]      ,				UpperCamelCase      :					T | None      ,				UpperCamelCase      :					U | None							):


				'''simple docstring'''





				_snake_case   :				Optional[Any]														=	key
				_snake_case   :				List[Any]														=	val
				_snake_case   :				DoubleLinkedListNode[T, U] | None														=	None
				_snake_case   :				DoubleLinkedListNode[T, U] | None														=	None







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


				'''simple docstring'''





				return (
				    f"""Node: key: {self.key}, val: {self.val}, """
				    f"""has next: {bool(self.next							)}, has prev: {bool(self.prev							)}"""
				)




class        _lowerCAmelCase    (			Generic[T, U]							):


		'''simple docstring'''







		def __init__(      self      :					str							):


				'''simple docstring'''





				_snake_case   :				DoubleLinkedListNode[T, U]														=	DoubleLinkedListNode(UpperCamelCase      ,				UpperCamelCase							)
				_snake_case   :				DoubleLinkedListNode[T, U]														=	DoubleLinkedListNode(UpperCamelCase      ,				UpperCamelCase							)
				_snake_case   :				List[str]														=	self.rear, self.head







		def __repr__(      self      :					Optional[int]							):


				'''simple docstring'''





				_snake_case   :				List[str]														=	['DoubleLinkedList']
				_snake_case   :				Dict														=	self.head
				while node.next is not None:
						rep.append(str(UpperCamelCase							)							)
						_snake_case   :				Dict														=	node.next
				rep.append(str(self.rear							)							)
				return ",\n    ".join(UpperCamelCase							)







		def UpperCamelCase_ (      self      :					Dict      ,				UpperCamelCase      :					DoubleLinkedListNode[T, U]							):


				'''simple docstring'''





				_snake_case   :				str														=	self.rear.prev

				# All nodes other than self.head are guaranteed to have non-None previous
				assert previous is not None

				_snake_case   :				Tuple														=	node
				_snake_case   :				int														=	previous
				_snake_case   :				int														=	node
				_snake_case   :				int														=	self.rear







		def UpperCamelCase_ (      self      :					Union[str, Any]      ,				UpperCamelCase      :					DoubleLinkedListNode[T, U]							):


				'''simple docstring'''





				if node.prev is None or node.next is None:
						return None

				_snake_case   :				str														=	node.next
				_snake_case   :				List[str]														=	node.prev
				_snake_case   :				Union[str, Any]														=	None
				_snake_case   :				Optional[int]														=	None
				return node




class        _lowerCAmelCase    (			Generic[T, U]							):


		'''simple docstring'''
		a_							:       dict[Callable[[T], U], LRUCache[T, U]]      					={}







		def __init__(      self      :					List[Any]      ,				UpperCamelCase      :					int							):


				'''simple docstring'''





				_snake_case   :				DoubleLinkedList[T, U]														=	DoubleLinkedList()
				_snake_case   :				Dict														=	capacity
				_snake_case   :				Tuple														=	0
				_snake_case   :				Optional[Any]														=	0
				_snake_case   :				Optional[Any]														=	0
				_snake_case   :				dict[T, DoubleLinkedListNode[T, U]]														=	{}







		def __repr__(      self      :					Dict							):


				'''simple docstring'''





				return (
				    f"""CacheInfo(hits={self.hits}, misses={self.miss}, """
				    f"""capacity={self.capacity}, current size={self.num_keys})"""
				)







		def __contains__(      self      :					List[str]      ,				UpperCamelCase      :					T							):


				'''simple docstring'''





				return key in self.cache







		def UpperCamelCase_ (      self      :					Any      ,				UpperCamelCase      :					T							):


				'''simple docstring'''





				if key in self.cache:
						self.hits += 1
						_snake_case   :				DoubleLinkedListNode[T, U]														=	self.cache[key]
						_snake_case   :				Dict														=	self.list.remove(self.cache[key]							)
						assert node == value_node

						# node is guaranteed not None because it is in self.cache
						assert node is not None
						self.list.add(UpperCamelCase							)
						return node.val
				self.miss += 1
				return None







		def UpperCamelCase_ (      self      :					int      ,				UpperCamelCase      :					T      ,				UpperCamelCase      :					U							):


				'''simple docstring'''





				if key not in self.cache:
						if self.num_keys >= self.capacity:
								# delete first node (oldest) when over capacity
								_snake_case   :				Dict														=	self.list.head.next

								# guaranteed to have a non-None first node when num_keys > 0
								# explain to type checker via assertions
								assert first_node is not None
								assert first_node.key is not None
								assert (
								    self.list.remove(UpperCamelCase							) is not None
								)  # node guaranteed to be in list assert node.key is not None

								del self.cache[first_node.key]
								self.num_keys -= 1
						_snake_case   :				Any														=	DoubleLinkedListNode(UpperCamelCase      ,				UpperCamelCase							)
						self.list.add(self.cache[key]							)
						self.num_keys += 1

				else:
						# bump node to the end of the list, update value
						_snake_case   :				Optional[Any]														=	self.list.remove(self.cache[key]							)
						assert node is not None  # node guaranteed to be in list
						_snake_case   :				Optional[Any]														=	value
						self.list.add(UpperCamelCase							)







		@classmethod
		def UpperCamelCase_ (      cls      :					str      ,				UpperCamelCase      :					int = 1_28							):


				'''simple docstring'''





				def cache_decorator_inner(UpperCamelCase      :					Callable[[T], U]							) -> Callable[..., U]:
						def cache_decorator_wrapper(*UpperCamelCase      :					T							) -> U:
								if func not in cls.decorator_function_to_instance_map:
										_snake_case   :				Union[str, Any]														=	LRUCache(UpperCamelCase							)

								_snake_case   :				Union[str, Any]														=	cls.decorator_function_to_instance_map[func].get(args[0]							)
								if result is None:
										_snake_case   :				Any														=	func(*UpperCamelCase							)
										cls.decorator_function_to_instance_map[func].put(args[0]      ,				UpperCamelCase							)
								return result

						def cache_info() -> LRUCache[T, U]:
								return cls.decorator_function_to_instance_map[func]

						setattr(UpperCamelCase      ,				'cache_info'      ,				UpperCamelCase							)  # noqa: B010

						return cache_decorator_wrapper

				return cache_decorator_inner


if __name__ == "__main__":
						import doctest

						doctest.testmod()











from __future__ import annotations

from random import random



class        _lowerCAmelCase    :


  '''simple docstring'''







  def __init__(      self      :					Dict      ,				UpperCamelCase      :					int | None = None							):


    '''simple docstring'''





    _snake_case   :				str														=	value
    _snake_case   :				List[Any]														=	random()
    _snake_case   :				Node | None														=	None
    _snake_case   :				Node | None														=	None







  def __repr__(      self      :					Optional[Any]							):


    '''simple docstring'''





    from pprint import pformat

    if self.left is None and self.right is None:
      return f"""'{self.value}: {self.prior:.5}'"""
    else:
      return pformat(
          {f"""{self.value}: {self.prior:.5}""": (self.left, self.right)}      ,				indent=1							)







  def __str__(      self      :					Dict							):


    '''simple docstring'''





    _snake_case   :				List[str]														=	str(self.value							) + ' '
    _snake_case   :				List[Any]														=	str(self.left or ''							)
    _snake_case   :				int														=	str(self.right or ''							)
    return value + left + right




def     lowerCamelCase_	(      lowerCAmelCase:	Node | None    ,							lowerCAmelCase:	int				)->		tuple[Node | None, Node | None]:
  if root is None:  # None tree is split into 2 Nones
    return None, None
  elif root.value is None:
    return None, None
  else:
    if value < root.value:
      _snake_case							,					_snake_case   :				Optional[Any]														=	split(root.left    ,							lowerCAmelCase				)
      return left, root
    else:
      _snake_case							,					_snake_case   :				List[str]														=	split(root.right    ,							lowerCAmelCase				)
      return root, right


def     lowerCamelCase_	(      lowerCAmelCase:	Node | None    ,							lowerCAmelCase:	Node | None				)->		Node | None:
  if (not left) or (not right):  # If one node is None, return the other
    return left or right
  elif left.prior < right.prior:
    _snake_case   :				str														=	merge(left.right    ,							lowerCAmelCase				)
    return left
  else:
    _snake_case   :				Union[str, Any]														=	merge(lowerCAmelCase    ,							right.left				)
    return right


def     lowerCamelCase_	(      lowerCAmelCase:	Node | None    ,							lowerCAmelCase:	int				)->		Node | None:
  _snake_case   :				Tuple														=	Node(lowerCAmelCase				)
  _snake_case							,					_snake_case   :				Optional[int]														=	split(lowerCAmelCase    ,							lowerCAmelCase				)
  return merge(merge(lowerCAmelCase    ,							lowerCAmelCase				)    ,							lowerCAmelCase				)


def     lowerCamelCase_	(      lowerCAmelCase:	Node | None    ,							lowerCAmelCase:	int				)->		Node | None:
  _snake_case							,					_snake_case   :				Optional[int]														=	split(lowerCAmelCase    ,							value - 1				)
  _snake_case							,					_snake_case   :				List[str]														=	split(lowerCAmelCase    ,							lowerCAmelCase				)
  return merge(lowerCAmelCase    ,							lowerCAmelCase				)


def     lowerCamelCase_	(      lowerCAmelCase:	Node | None				)->		None:
  if not root:  # None
    return
  else:
    inorder(root.left				)
    print(root.value    ,							end=','				)
    inorder(root.right				)


def     lowerCamelCase_	(      lowerCAmelCase:	Node | None    ,							lowerCAmelCase:	str				)->		Node | None:
  for arg in args.split():
    if arg[0] == "+":
      _snake_case   :				List[str]														=	insert(lowerCAmelCase    ,							int(arg[1:]				)				)

    elif arg[0] == "-":
      _snake_case   :				Any														=	erase(lowerCAmelCase    ,							int(arg[1:]				)				)

    else:
      print('Unknown command'				)

  return root


def     lowerCamelCase_	(      )->		None:
  _snake_case   :				Tuple														=	None
  print(
      'enter numbers to create a tree, + value to add value into treap, '
      '- value to erase all nodes with value. \'q\' to quit. '				)

  _snake_case   :				List[Any]														=	input()
  while args != "q":
    _snake_case   :				int														=	interact_treap(lowerCAmelCase    ,							lowerCAmelCase				)
    print(lowerCAmelCase				)
    _snake_case   :				Tuple														=	input()

  print('good by!'				)


if __name__ == "__main__":
      import doctest

      doctest.testmod()
      main()




