
from __future__ import annotations

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

lowerCamelCase_						     =					TypeVar('''T''')
lowerCamelCase_						     =					TypeVar('''U''')




class      __A(    Generic[T, U]			):

  """simple docstring"""







  def __init__(self	,      SCREAMING_SNAKE_CASE_	,      SCREAMING_SNAKE_CASE_						):
       UpperCamelCase__				=    key
       UpperCamelCase__				=    val
       UpperCamelCase__				=    None
       UpperCamelCase__				=    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      __A(    Generic[T, U]			):

  """simple docstring"""







  def __init__(self						):
       UpperCamelCase__				=    DoubleLinkedListNode(SCREAMING_SNAKE_CASE_	,      SCREAMING_SNAKE_CASE_						)
       UpperCamelCase__				=    DoubleLinkedListNode(SCREAMING_SNAKE_CASE_	,      SCREAMING_SNAKE_CASE_						)
       UpperCamelCase__		,	UpperCamelCase__				=    self.rear, self.head







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







  def 	UpperCAmelCase_ (self	,      SCREAMING_SNAKE_CASE_						):
       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







  def 	UpperCAmelCase_ (self	,      SCREAMING_SNAKE_CASE_						):

       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      __A(    Generic[T, U]			):

  """simple docstring"""
  SCREAMING_SNAKE_CASE__         =      {}







  def __init__(self	,      SCREAMING_SNAKE_CASE_						):
       UpperCamelCase__				=    DoubleLinkedList()
       UpperCamelCase__				=    capacity
       UpperCamelCase__				=    0
       UpperCamelCase__				=    0
       UpperCamelCase__				=    0
       UpperCamelCase__				=    {}







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







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







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

       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(SCREAMING_SNAKE_CASE_						)
            return node.val
       self.miss += 1
       return None







  def 	UpperCAmelCase_ (self	,      SCREAMING_SNAKE_CASE_	,      SCREAMING_SNAKE_CASE_						):

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

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







  @classmethod
  def 	UpperCAmelCase_ (cls	,      SCREAMING_SNAKE_CASE_ = 1_28						):

       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__				=    LRUCache(SCREAMING_SNAKE_CASE_						)

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

            def cache_info() -> LRUCache[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()







from __future__ import annotations






def 						__magic_name__			(   __a      :	list[list[int]]						):



     '''simple docstring'''




     for i in range(1	,		len(matrix[0]						)						):
          matrix[0][i] += matrix[0][i - 1]

     # preprocessing the first column
     for i in range(1	,		len(__a						)						):
          matrix[i][0] += matrix[i - 1][0]

     # updating the path cost for current position
     for i in range(1	,		len(__a						)						):
          for j in range(1	,		len(matrix[0]						)						):
               matrix[i][j] += min(matrix[i - 1][j]	,		matrix[i][j - 1]						)

     return matrix[-1][-1]


if __name__ == "__main__":
    import doctest

    doctest.testmod()





