





from __future__ import annotations

from sys import maxsize
from typing import Generic, TypeVar

snake_case__					:							Tuple													=     TypeVar('T')



def _a				(	lowerCamelCase:   Optional[Any] )	->						Tuple:







      '''simple docstring'''






      return (position - 1) // 2



def _a				(	lowerCamelCase:   Optional[int] )	->						List[Any]:







      '''simple docstring'''






      return (2 * position) + 1



def _a				(	lowerCamelCase:   int )	->						Optional[Any]:







      '''simple docstring'''






      return (2 * position) + 2





class A_					(			Generic[T]   ):




   def __init__(self	:Union[str, Any] )->					List[Any]:
         __A          =				[]
         __A          =				{}
         __A          =				0




   def __len__(self	:Optional[Any] )->					Any:
         return self.elements




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




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




   def _lowerCAmelCase      (self	:str    ,   _UpperCamelCase	:T    ,   _UpperCamelCase	:int )->					Tuple:
         # Add an element with given priority to the queue
         self.heap.append((elem, weight) )
         __A          =				self.elements
         self.elements += 1
         self._bubble_up(lowercase__ )




   def _lowerCAmelCase      (self	:int )->					Union[str, Any]:
         # 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(lowercase__ )
         return elem




   def _lowerCAmelCase      (self	:Optional[Any]    ,   _UpperCamelCase	:T    ,   _UpperCamelCase	:int )->					Union[str, Any]:
         # Update the weight of the given key
         __A          =				self.position_map[elem]
         __A          =				(elem, weight)
         if position > 0:
               __A          =				get_parent_position(lowercase__ )
               __A   ,						__A          =				self.heap[parent_position]
               if parent_weight > weight:
                     self._bubble_up(lowercase__ )
               else:
                     self._bubble_down(lowercase__ )
         else:
               self._bubble_down(lowercase__ )




   def _lowerCAmelCase      (self	:Dict    ,   _UpperCamelCase	:T )->					str:
         # 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(lowercase__ )
         __A   ,						__A          =				self.heap[curr_pos]
         __A   ,						__A          =				self.heap[parent_position]
         if parent_weight > weight:
               self._swap_nodes(lowercase__    ,   lowercase__ )
               return self._bubble_up(lowercase__ )
         return None




   def _lowerCAmelCase      (self	:List[str]    ,   _UpperCamelCase	:T )->					List[str]:
         # 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(lowercase__ )
         __A          =				get_child_right_position(lowercase__ )
         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(lowercase__    ,   lowercase__ )
                     return self._bubble_down(lowercase__ )
         if child_left_position < self.elements:
               __A   ,						__A          =				self.heap[child_left_position]
               if child_left_weight < weight:
                     self._swap_nodes(lowercase__    ,   lowercase__ )
                     return self._bubble_down(lowercase__ )
         else:
               return None
         if child_right_position < self.elements:
               __A   ,						__A          =				self.heap[child_right_position]
               if child_right_weight < weight:
                     self._swap_nodes(lowercase__    ,   lowercase__ )
                     return self._bubble_down(lowercase__ )
         return None






   def _lowerCAmelCase      (self	:Optional[int]    ,   _UpperCamelCase	:int    ,   _UpperCamelCase	:int )->					Tuple:
         # 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 A_					(			Generic[T]   ):




   def __init__(self	:Any )->					List[str]:
         __A          =				{}
         __A          =				0




   def __repr__(self	:Any )->					Union[str, Any]:
         return str(self.connections )




   def __len__(self	:Any )->					str:
         return self.nodes




   def _lowerCAmelCase      (self	:Dict    ,   _UpperCamelCase	:T )->					Tuple:
         # Add a node in the graph if it is not in the graph
         if node not in self.connections:
               __A          =				{}
               self.nodes += 1






   def _lowerCAmelCase      (self	:Optional[Any]    ,   _UpperCamelCase	:T    ,   _UpperCamelCase	:T    ,   _UpperCamelCase	:int )->					List[Any]:
         # Add an edge between 2 nodes in the graph
         self.add_node(lowercase__ )
         self.add_node(lowercase__ )
         __A          =				weight
         __A          =				weight





def _a				(	lowerCamelCase:   Optional[int]					,				)	->						Optional[int]:







      '''simple docstring'''






      __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(A__					,				A__ )

      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(A__					,				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(A__					,				dist[neighbour] )
                        __A          =				node
      return dist, parent








'''simple docstring'''






lowerCAmelCase__											=	'''Input must be a string of 8 numbers plus letter'''
lowerCAmelCase__											=	'''TRWAGMYFPDXBNJZSQVHLCKE'''


def 		_A     (    A__      ):






 """simple docstring"""



 if not isinstance(A__     ,				A__      ):
  __lowercase							  = F"Expected string as input, found {type(A__      ).__name__}"
  raise TypeError(A__      )

 __lowercase							  = spanish_id.replace('''-'''     ,				''''''      ).upper()
 if len(A__      ) != 9:
  raise ValueError(A__      )

 try:
  __lowercase							  = int(spanish_id_clean[0:8]      )
  __lowercase							  = spanish_id_clean[8]
 except ValueError as ex:
  raise ValueError(A__      ) from ex

 if letter.isdigit():
  raise ValueError(A__      )

 return letter == LOOKUP_LETTERS[number % 23]


if __name__ == "__main__":
 import doctest

 doctest.testmod()

