from __future__ import annotations






class 		_lowerCamelCase		:
    def __init__(	self			,			lowerCAmelCase = 0 )							->       List[str]:
     SCREAMING_SNAKE_CASE__: Tuple=   key
    def     UpperCamelCase_					(	self			,			lowerCAmelCase			,			lowerCAmelCase )							->       list[str]:
     assert isinstance(lowerCAmelCase			,			lowerCAmelCase ) and isinstance(lowerCAmelCase			,			lowerCAmelCase )

     SCREAMING_SNAKE_CASE__: Union[str, Any]=   key or self.__key or 1

     # make sure key is an appropriate size
     key %= 255

     return [chr(ord(lowerCAmelCase ) ^ key ) for ch in content]
    def     UpperCamelCase_					(	self			,			lowerCAmelCase			,			lowerCAmelCase )							->       list[str]:
     assert isinstance(lowerCAmelCase			,			lowerCAmelCase ) and isinstance(lowerCAmelCase			,			lowerCAmelCase )

     SCREAMING_SNAKE_CASE__: Dict=   key or self.__key or 1

     # make sure key is an appropriate size
     key %= 255

     return [chr(ord(lowerCAmelCase ) ^ key ) for ch in content]
    def     UpperCamelCase_					(	self			,			lowerCAmelCase			,			lowerCAmelCase = 0 )							->       str:
     assert isinstance(lowerCAmelCase			,			lowerCAmelCase ) and isinstance(lowerCAmelCase			,			lowerCAmelCase )

     SCREAMING_SNAKE_CASE__: Any=   key or self.__key or 1

     # make sure key can be any size
     while key > 255:
      key -= 255

     # This will be returned
     SCREAMING_SNAKE_CASE__: Union[str, Any]=   ''''''

     for ch in content:
      ans += chr(ord(lowerCAmelCase ) ^ key )

     return ans
    def     UpperCamelCase_					(	self			,			lowerCAmelCase			,			lowerCAmelCase = 0 )							->       str:
     assert isinstance(lowerCAmelCase			,			lowerCAmelCase ) and isinstance(lowerCAmelCase			,			lowerCAmelCase )

     SCREAMING_SNAKE_CASE__: Union[str, Any]=   key or self.__key or 1

     # make sure key can be any size
     while key > 255:
      key -= 255

     # This will be returned
     SCREAMING_SNAKE_CASE__: Optional[Any]=   ''''''

     for ch in content:
      ans += chr(ord(lowerCAmelCase ) ^ key )

     return ans
    def     UpperCamelCase_					(	self			,			lowerCAmelCase			,			lowerCAmelCase = 0 )							->       bool:
     assert isinstance(lowerCAmelCase			,			lowerCAmelCase ) and isinstance(lowerCAmelCase			,			lowerCAmelCase )

     try:
      with open(lowerCAmelCase ) as fin, open('''encrypt.out'''			,			'''w+''' ) as fout:
       # actual encrypt-process
       for line in fin:
        fout.write(self.encrypt_string(lowerCAmelCase			,			lowerCAmelCase ) )

     except OSError:
      return False

     return True



    def     UpperCamelCase_					(	self			,			lowerCAmelCase			,			lowerCAmelCase )							->       bool:
     assert isinstance(lowerCAmelCase			,			lowerCAmelCase ) and isinstance(lowerCAmelCase			,			lowerCAmelCase )

     try:
      with open(lowerCAmelCase ) as fin, open('''decrypt.out'''			,			'''w+''' ) as fout:
       # actual encrypt-process
       for line in fin:
        fout.write(self.decrypt_string(lowerCAmelCase			,			lowerCAmelCase ) )

     except OSError:
      return False

     return True


# Tests
# crypt = XORCipher()
# key = 67

# # test encrypt
# print(crypt.encrypt("hallo welt",key))
# # test decrypt
# print(crypt.decrypt(crypt.encrypt("hallo welt",key), key))

# # test encrypt_string
# print(crypt.encrypt_string("hallo welt",key))

# # test decrypt_string
# print(crypt.decrypt_string(crypt.encrypt_string("hallo welt",key),key))

# if (crypt.encrypt_file("test.txt",key)):
#       print("encrypt successful")
# else:
#       print("encrypt unsuccessful")

# if (crypt.decrypt_file("encrypt.out",key)):
#       print("decrypt successful")
# else:
#       print("decrypt unsuccessful")






from __future__ import annotations

from sys import maxsize
from typing import Generic, TypeVar

UpperCAmelCase_		 =					TypeVar("""T""")

def 	SCREAMING_SNAKE_CASE_							(	_snake_case	:int				)  ->     int:
   return (position - 1) // 2

def 	SCREAMING_SNAKE_CASE_							(	_snake_case	:int				)  ->     int:
   return (2 * position) + 1

def 	SCREAMING_SNAKE_CASE_							(	_snake_case	:int				)  ->     int:
   return (2 * position) + 2


class 	lowerCamelCase__	(       Generic[T]):



 """simple docstring"""

 def __init__(    self					:					Optional[int]      )   ->	None:
    _A      =       []
    _A      =       {}
    _A      =       0

 def __len__(    self					:					str      )   ->	int:
    return self.elements

 def __repr__(    self					:					Optional[int]      )   ->	str:
    return str(self.heap      )

 def     snake_case_      (    self					:					str      )   ->	bool:
    # Check if the priority queue is empty
    return self.elements == 0

 def     snake_case_      (    self					:					Optional[int]			,						__lowerCAmelCase					:					T			,						__lowerCAmelCase					:					int      )   ->	None:
    # Add an element with given priority to the queue
    self.heap.append((elem, weight)      )
    _A      =       self.elements
    self.elements += 1
    self._bubble_up(__lowerCAmelCase      )

 def     snake_case_      (    self					:					Tuple      )   ->	T:
    # Remove and return the element with lowest weight (highest priority)
    if self.elements > 1:
       self._swap_nodes(0			,						self.elements - 1      )
    _A  ,    _A      =       self.heap.pop()
    del self.position_map[elem]
    self.elements -= 1
    if self.elements > 0:
       _A  ,    _A      =       self.heap[0]
       self._bubble_down(__lowerCAmelCase      )
    return elem

 def     snake_case_      (    self					:					int			,						__lowerCAmelCase					:					T			,						__lowerCAmelCase					:					int      )   ->	None:
    # Update the weight of the given key
    _A      =       self.position_map[elem]
    _A      =       (elem, weight)
    if position > 0:
       _A      =       get_parent_position(__lowerCAmelCase      )
       _A  ,    _A      =       self.heap[parent_position]
       if parent_weight > weight:
          self._bubble_up(__lowerCAmelCase      )
       else:
          self._bubble_down(__lowerCAmelCase      )
    else:
       self._bubble_down(__lowerCAmelCase      )

 def     snake_case_      (    self					:					Optional[Any]			,						__lowerCAmelCase					:					T      )   ->	None:
    # Place a node at the proper position (upward movement) [to be used internally
    # only]
    _A      =       self.position_map[elem]
    if curr_pos == 0:
       return None
    _A      =       get_parent_position(__lowerCAmelCase      )
    _A  ,    _A      =       self.heap[curr_pos]
    _A  ,    _A      =       self.heap[parent_position]
    if parent_weight > weight:
       self._swap_nodes(__lowerCAmelCase			,						__lowerCAmelCase      )
       return self._bubble_up(__lowerCAmelCase      )
    return None

 def     snake_case_      (    self					:					Dict			,						__lowerCAmelCase					:					T      )   ->	None:
    # Place a node at the proper position (downward movement) [to be used
    # internally only]
    _A      =       self.position_map[elem]
    _A  ,    _A      =       self.heap[curr_pos]
    _A      =       get_child_left_position(__lowerCAmelCase      )
    _A      =       get_child_right_position(__lowerCAmelCase      )
    if child_left_position < self.elements and child_right_position < self.elements:
       _A  ,    _A      =       self.heap[child_left_position]
       _A  ,    _A      =       self.heap[child_right_position]
       if child_right_weight < child_left_weight and child_right_weight < weight:
          self._swap_nodes(__lowerCAmelCase			,						__lowerCAmelCase      )
          return self._bubble_down(__lowerCAmelCase      )
    if child_left_position < self.elements:
       _A  ,    _A      =       self.heap[child_left_position]
       if child_left_weight < weight:
          self._swap_nodes(__lowerCAmelCase			,						__lowerCAmelCase      )
          return self._bubble_down(__lowerCAmelCase      )
    else:
       return None
    if child_right_position < self.elements:
       _A  ,    _A      =       self.heap[child_right_position]
       if child_right_weight < weight:
          self._swap_nodes(__lowerCAmelCase			,						__lowerCAmelCase      )
          return self._bubble_down(__lowerCAmelCase      )
    return None

 def     snake_case_      (    self					:					List[str]			,						__lowerCAmelCase					:					int			,						__lowerCAmelCase					:					int      )   ->	None:
    # Swap the nodes at the given positions
    _A      =       self.heap[nodea_pos][0]
    _A      =       self.heap[nodea_pos][0]
    _A  ,    _A      =       (
        self.heap[nodea_pos],
        self.heap[nodea_pos],
    )
    _A      =       nodea_pos
    _A      =       nodea_pos


class 	lowerCamelCase__	(       Generic[T]):



 """simple docstring"""

 def __init__(    self					:					str      )   ->	None:
    _A      =       {}
    _A      =       0

 def __repr__(    self					:					str      )   ->	str:
    return str(self.connections      )

 def __len__(    self					:					Dict      )   ->	int:
    return self.nodes

 def     snake_case_      (    self					:					Any			,						__lowerCAmelCase					:					T      )   ->	None:
    # Add a node in the graph if it is not in the graph
    if node not in self.connections:
       _A      =       {}
       self.nodes += 1

 def     snake_case_      (    self					:					str			,						__lowerCAmelCase					:					T			,						__lowerCAmelCase					:					T			,						__lowerCAmelCase					:					int      )   ->	None:
    # Add an edge between 2 nodes in the graph
    self.add_node(__lowerCAmelCase      )
    self.add_node(__lowerCAmelCase      )
    _A      =       weight
    _A      =       weight

def 	SCREAMING_SNAKE_CASE_							(	_snake_case	:GraphUndirectedWeighted[T]	,   )  ->     tuple[dict[T, int], dict[T, T | None]]:
   _A      =       {node: maxsize for node in graph.connections}
   _A      =       {node: None for node in graph.connections}

   _A      =       MinPriorityQueue()
   for node, weight in dist.items():
      priority_queue.push(_snake_case	,   _snake_case				)

   if priority_queue.is_empty():
      return dist, parent

   # initialization
   _A      =       priority_queue.extract_min()
   _A      =       0
   for neighbour in graph.connections[node]:
      if dist[neighbour] > dist[node] + graph.connections[node][neighbour]:
         _A      =       dist[node] + graph.connections[node][neighbour]
         priority_queue.update_key(_snake_case	,   dist[neighbour]				)
         _A      =       node

    # running prim's algorithm
   while not priority_queue.is_empty():
      _A      =       priority_queue.extract_min()
      for neighbour in graph.connections[node]:
         if dist[neighbour] > dist[node] + graph.connections[node][neighbour]:
            _A      =       dist[node] + graph.connections[node][neighbour]
            priority_queue.update_key(_snake_case	,   dist[neighbour]				)
            _A      =       node
   return dist, parent



