


from __future__ import annotations

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

__UpperCAmelCase			:			Union[str, Any]			      =					TypeVar("T")
__UpperCAmelCase			:			int			      =					TypeVar("U")



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






       def __init__(  self			,       __SCREAMING_SNAKE_CASE			,       __SCREAMING_SNAKE_CASE    ):




              """simple docstring"""




              UpperCamelCase     :						str 						=		key
              UpperCamelCase     :						Any 						=		val
              UpperCamelCase     :						int 						=		0
              UpperCamelCase     :						DoubleLinkedListNode[T, U] | None 						=		None
              UpperCamelCase     :						DoubleLinkedListNode[T, U] | None 						=		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  UpperCAmelCase_						(				Generic[T, U]):
       '''simple docstring'''






       def __init__(  self    ):




              """simple docstring"""




              UpperCamelCase     :						DoubleLinkedListNode[T, U] 						=		DoubleLinkedListNode(__SCREAMING_SNAKE_CASE			,       __SCREAMING_SNAKE_CASE    )
              UpperCamelCase     :						DoubleLinkedListNode[T, U] 						=		DoubleLinkedListNode(__SCREAMING_SNAKE_CASE			,       __SCREAMING_SNAKE_CASE    )
              UpperCamelCase						,			UpperCamelCase     :						Any 						=		self.rear, self.head






       def __repr__(  self    ):




              """simple docstring"""




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






       def 			_lowercase (  self			,       __SCREAMING_SNAKE_CASE    ):




              """simple docstring"""




              UpperCamelCase     :						Optional[int] 						=		self.rear.prev

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

              UpperCamelCase     :						str 						=		node
              UpperCamelCase     :						Any 						=		previous
              UpperCamelCase     :						Any 						=		node
              UpperCamelCase     :						List[str] 						=		self.rear
              node.freq += 1
              self._position_node(__SCREAMING_SNAKE_CASE    )






       def 			_lowercase (  self			,       __SCREAMING_SNAKE_CASE    ):




              """simple docstring"""




              while node.prev is not None and node.prev.freq > node.freq:
                     # swap node with previous node
                     UpperCamelCase     :						Union[str, Any] 						=		node.prev

                     UpperCamelCase     :						Optional[int] 						=		previous_node.prev
                     UpperCamelCase     :						Optional[int] 						=		node.prev
                     UpperCamelCase     :						Dict 						=		previous_node
                     UpperCamelCase     :						Tuple 						=		node






       def 			_lowercase (  self			,       __SCREAMING_SNAKE_CASE    ):




              """simple docstring"""




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

              UpperCamelCase     :						Optional[int] 						=		node.next
              UpperCamelCase     :						Dict 						=		node.prev
              UpperCamelCase     :						str 						=		None
              UpperCamelCase     :						List[Any] 						=		None
              return node




class  UpperCAmelCase_						(				Generic[T, U]):
       '''simple docstring'''
       __UpperCamelCase   :  dict[Callable[[T], U], LFUCache[T, U]]				=       {}






       def __init__(  self			,       __SCREAMING_SNAKE_CASE    ):




              """simple docstring"""




              UpperCamelCase     :						DoubleLinkedList[T, U] 						=		DoubleLinkedList()
              UpperCamelCase     :						str 						=		capacity
              UpperCamelCase     :						int 						=		0
              UpperCamelCase     :						Tuple 						=		0
              UpperCamelCase     :						int 						=		0
              UpperCamelCase     :						dict[T, DoubleLinkedListNode[T, U]] 						=		{}






       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			,       __SCREAMING_SNAKE_CASE    ):




              """simple docstring"""




              return key in self.cache






       def 			_lowercase (  self			,       __SCREAMING_SNAKE_CASE    ):




              """simple docstring"""




              if key in self.cache:
                     self.hits += 1
                     UpperCamelCase     :						DoubleLinkedListNode[T, U] 						=		self.cache[key]
                     UpperCamelCase     :						Union[str, Any] 						=		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(__SCREAMING_SNAKE_CASE    )
                     return node.val
              self.miss += 1
              return None






       def 			_lowercase (  self			,       __SCREAMING_SNAKE_CASE			,       __SCREAMING_SNAKE_CASE    ):




              """simple docstring"""




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

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

              else:
                     UpperCamelCase     :						List[Any] 						=		self.list.remove(self.cache[key]    )
                     assert node is not None  # node guaranteed to be in list
                     UpperCamelCase     :						Union[str, Any] 						=		value
                     self.list.add(__SCREAMING_SNAKE_CASE    )






       @classmethod
       def 			_lowercase (  cls			,       __SCREAMING_SNAKE_CASE = 128    ):




              """simple docstring"""




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

                            UpperCamelCase     :						Dict 						=		cls.decorator_function_to_instance_map[func].get(args[0]    )
                            if result is None:
                                   UpperCamelCase     :						Optional[Any] 						=		func(*__SCREAMING_SNAKE_CASE    )
                                   cls.decorator_function_to_instance_map[func].put(args[0]			,       __SCREAMING_SNAKE_CASE    )
                            return result

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

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

                     return cache_decorator_wrapper

              return cache_decorator_inner


if __name__ == "__main__":
  import doctest

  doctest.testmod()





def   a						(				SCREAMING_SNAKE_CASE_   :		int							):






       """simple docstring"""





       UpperCamelCase     :						Tuple 						=		[True for i in range(n + 1							)]
       UpperCamelCase     :						Tuple 						=		[i - 1 for i in range(n + 1							)]
       UpperCamelCase     :						Optional[Any] 						=		[]
       for i in range(2				,      n + 1							):
              if is_prime[i]:
                     primes.append(SCREAMING_SNAKE_CASE_							)
              for j in range(0				,      len(SCREAMING_SNAKE_CASE_							)							):
                     if i * primes[j] >= n:
                            break
                     UpperCamelCase     :						Any 						=		False

                     if i % primes[j] == 0:
                            UpperCamelCase     :						int 						=		totients[i] * primes[j]
                            break

                     UpperCamelCase     :						Dict 						=		totients[i] * (primes[j] - 1)

       return totients


if __name__ == "__main__":
  import doctest

  doctest.testmod()

