
from __future__ import annotations

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

lowercase__	:List[Any]										=					TypeVar("T")
lowercase__	:Optional[Any]										=					TypeVar("U")







class        lowercase	(      Generic[T, U]	):




							def __init__(       self     ,A__     ,A__):
												lowercase					=		key
												lowercase					=		val
												lowercase					=		None
												lowercase					=		None





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







class        lowercase	(      Generic[T, U]	):




							def __init__(       self):
												lowercase					=		DoubleLinkedListNode(A__     ,A__)
												lowercase					=		DoubleLinkedListNode(A__     ,A__)
												lowercase			,		lowercase					=		self.rear, self.head




							def __repr__(       self):
												lowercase					=		['''DoubleLinkedList''']
												lowercase					=		self.head
												while node.next is not None:
																	rep.append(str(A__))
																	lowercase					=		node.next
												rep.append(str(self.rear))
												return ",\n    ".join(A__)




							def 				A__   (       self     ,A__):
												lowercase					=		self.rear.prev

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

												lowercase					=		node
												lowercase					=		previous
												lowercase					=		node
												lowercase					=		self.rear





							def 				A__   (       self     ,A__):

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

												lowercase					=		node.next
												lowercase					=		node.prev
												lowercase					=		None
												lowercase					=		None
												return node







class        lowercase	(      Generic[T, U]	):
							lowercase_ : dict[Callable[[T], U], LRUCache[T, U]]       ={}




							def __init__(       self     ,A__):
												lowercase					=		DoubleLinkedList()
												lowercase					=		capacity
												lowercase					=		0
												lowercase					=		0
												lowercase					=		0
												lowercase					=		{}




							def __repr__(       self):
												return (
												    f'CacheInfo(hits={self.hits}, misses={self.miss}, '
												    f'capacity={self.capacity}, current size={self.num_keys})'
												)




							def __contains__(       self     ,A__):
												return key in self.cache




							def 				A__   (       self     ,A__):
												# Note: pythonic interface would throw KeyError rather than return None

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




							def 				A__   (       self     ,A__     ,A__):

												if key not in self.cache:
																	if self.num_keys >= self.capacity:
																						# delete first node (oldest) when over capacity
																						lowercase					=		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(A__) 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
																	lowercase					=		DoubleLinkedListNode(A__     ,A__)
																	self.list.add(self.cache[key])
																	self.num_keys += 1

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





							@classmethod
							def 				A__   (       cls     ,A__ = 1_2_8):

												def cache_decorator_inner(A__) -> Callable[..., U]:
																	def cache_decorator_wrapper(*A__) -> U:
																						if func not in cls.decorator_function_to_instance_map:
																											lowercase					=		LRUCache(A__)

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

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

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

																	return cache_decorator_wrapper

												return cache_decorator_inner


if __name__ == "__main__":
							import doctest

							doctest.testmod()






from numpy import exp, pi, sqrt



def  UpperCamelCase					(							lowerCAmelCase__				,    lowerCAmelCase__ = 0.0				,    lowerCAmelCase__ = 1.0	):
					'''simple docstring'''
					return 1 / sqrt(2 * pi * sigma**2	) * exp(-((x - mu) ** 2) / (2 * sigma**2)	)


if __name__ == "__main__":
							import doctest

							doctest.testmod()




