



from __future__ import annotations

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

UpperCAmelCase				:							int								=TypeVar("""T""")
UpperCAmelCase				:							List[str]								=TypeVar("""U""")


class  _lowercase				(Generic[T, U] ):
				'''simple docstring'''







				def __init__(	self       ,	snake_case__       ,	snake_case__      ):

									'''simple docstring'''


									UpperCamelCase_											=				key
									UpperCamelCase_											=				val
									UpperCamelCase_											=				0
									UpperCamelCase_											=				None
									UpperCamelCase_											=				None

				def __repr__(	self      ):

									'''simple docstring'''


									return "Node: key: {}, val: {}, freq: {}, has next: {}, has prev: {}".format(
									    self.key       ,	self.val       ,	self.freq       ,	self.next is not None       ,	self.prev is not None      )




class  _lowercase				(Generic[T, U] ):
				'''simple docstring'''







				def __init__(	self      ):

									'''simple docstring'''


									UpperCamelCase_											=				DoubleLinkedListNode(snake_case__       ,	snake_case__      )
									UpperCamelCase_											=				DoubleLinkedListNode(snake_case__       ,	snake_case__      )
									UpperCamelCase_					,      UpperCamelCase_											=				self.rear, self.head

				def __repr__(	self      ):

									'''simple docstring'''


									UpperCamelCase_											=				["DoubleLinkedList"]
									UpperCamelCase_											=				self.head
									while node.next is not None:
														rep.append(str(snake_case__      )      )
														UpperCamelCase_											=				node.next
									rep.append(str(self.rear      )      )
									return ",\n    ".join(snake_case__      )

				def  _lowerCamelCase   (	self       ,	snake_case__      ):

									'''simple docstring'''


									UpperCamelCase_											=				self.rear.prev

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

									UpperCamelCase_											=				node
									UpperCamelCase_											=				previous
									UpperCamelCase_											=				node
									UpperCamelCase_											=				self.rear
									node.freq += 1
									self._position_node(snake_case__      )

				def  _lowerCamelCase   (	self       ,	snake_case__      ):

									'''simple docstring'''


									while node.prev is not None and node.prev.freq > node.freq:
														# swap node with previous node
														UpperCamelCase_											=				node.prev

														UpperCamelCase_											=				previous_node.prev
														UpperCamelCase_											=				node.prev
														UpperCamelCase_											=				previous_node
														UpperCamelCase_											=				node

				def  _lowerCamelCase   (	self       ,	snake_case__      ):

									'''simple docstring'''


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

									UpperCamelCase_											=				node.next
									UpperCamelCase_											=				node.prev
									UpperCamelCase_											=				None
									UpperCamelCase_											=				None
									return node




class  _lowercase				(Generic[T, U] ):
				'''simple docstring'''







				lowercase__				  =  {}

				def __init__(	self       ,	snake_case__      ):

									'''simple docstring'''


									UpperCamelCase_											=				DoubleLinkedList()
									UpperCamelCase_											=				capacity
									UpperCamelCase_											=				0
									UpperCamelCase_											=				0
									UpperCamelCase_											=				0
									UpperCamelCase_											=				{}

				def __repr__(	self      ):

									'''simple docstring'''


									return (
									    F"""CacheInfo(hits={self.hits}, misses={self.miss}, """
									    F"""capacity={self.capacity}, current_size={self.num_keys})"""
									)

				def __contains__(	self       ,	snake_case__      ):

									'''simple docstring'''


									return key in self.cache

				def  _lowerCamelCase   (	self       ,	snake_case__      ):

									'''simple docstring'''


									if key in self.cache:
														self.hits += 1
														UpperCamelCase_											=				self.cache[key]
														UpperCamelCase_											=				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(snake_case__      )
														return node.val
									self.miss += 1
									return None

				def  _lowerCamelCase   (	self       ,	snake_case__       ,	snake_case__      ):

									'''simple docstring'''


									if key not in self.cache:
														if self.num_keys >= self.capacity:
																			# delete first node when over capacity
																			UpperCamelCase_											=				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(snake_case__      ) is not None
																			# first_node guaranteed to be in list

																			del self.cache[first_node.key]
																			self.num_keys -= 1
														UpperCamelCase_											=				DoubleLinkedListNode(snake_case__       ,	snake_case__      )
														self.list.add(self.cache[key]      )
														self.num_keys += 1

									else:
														UpperCamelCase_											=				self.list.remove(self.cache[key]      )
														assert node is not None  # node guaranteed to be in list
														UpperCamelCase_											=				value
														self.list.add(snake_case__      )

				@classmethod
				def  _lowerCamelCase   (	cls       ,	snake_case__ = 128      ):

									'''simple docstring'''


									def cache_decorator_inner(snake_case__      ) -> Callable[..., U]:
														def cache_decorator_wrapper(*snake_case__      ) -> U:
																			if func not in cls.decorator_function_to_instance_map:
																								UpperCamelCase_											=				LFUCache(snake_case__      )

																			UpperCamelCase_											=				cls.decorator_function_to_instance_map[func].get(args[0]      )
																			if result is None:
																								UpperCamelCase_											=				func(*snake_case__      )
																								cls.decorator_function_to_instance_map[func].put(args[0]       ,	snake_case__      )
																			return result

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

														setattr(snake_case__       ,	"cache_info"       ,	snake_case__      )  # noqa: B010

														return cache_decorator_wrapper

									return cache_decorator_inner


if __name__ == "__main__":
	import doctest

	doctest.testmod()





def 				_lowerCAmelCase      (_lowerCAmelCase				,		_lowerCAmelCase):
					UpperCamelCase_											=				0
					for ele in arr:
										total_sum += product_sum(_lowerCAmelCase				,		depth + 1) if isinstance(_lowerCAmelCase				,		_lowerCAmelCase) else ele
					return total_sum * depth



def 				_lowerCAmelCase      (_lowerCAmelCase):
					return product_sum(_lowerCAmelCase				,		1)


if __name__ == "__main__":
	import doctest

	doctest.testmod()
