from __future__ import annotations

from sys import maxsize
from typing import Generic, TypeVar

__lowerCamelCase					:	Union[str, Any]       =  TypeVar('''T''')




def       _snake_case	(   lowerCAmelCase							:   int	):
		"""simple docstring"""







		return (position - 1) // 2




def       _snake_case	(   lowerCAmelCase							:   int	):
		"""simple docstring"""







		return (2 * position) + 1




def       _snake_case	(   lowerCAmelCase							:   int	):
		"""simple docstring"""







		return (2 * position) + 2






class 		a__						(					Generic[T]					):

					def __init__(    self      :       str    ):







							"""simple docstring"""






							SCREAMING_SNAKE_CASE_  :		list[tuple[T, int]]				      =    []
							SCREAMING_SNAKE_CASE_  :		dict[T, int]				      =    {}
							SCREAMING_SNAKE_CASE_  :		int				      =    0

					def __len__(    self      :       List[str]    ):







							"""simple docstring"""






							return self.elements

					def __repr__(    self      :       Dict    ):







							"""simple docstring"""






							return str(self.heap    )

					def 				__UpperCamelCase   (    self      :       int    ):







							"""simple docstring"""






							return self.elements == 0

					def 				__UpperCamelCase   (    self      :       str,_A      :       T,_A      :       int    ):







							"""simple docstring"""






							self.heap.append((elem, weight)    )
							SCREAMING_SNAKE_CASE_  :		Union[str, Any]				      =    self.elements
							self.elements += 1
							self._bubble_up(_A    )

					def 				__UpperCamelCase   (    self      :       List[Any]    ):







							"""simple docstring"""






							if self.elements > 1:
									self._swap_nodes(0,self.elements - 1    )
							SCREAMING_SNAKE_CASE_      ,    SCREAMING_SNAKE_CASE_  :		List[Any]				      =    self.heap.pop()
							del self.position_map[elem]
							self.elements -= 1
							if self.elements > 0:
									SCREAMING_SNAKE_CASE_      ,    SCREAMING_SNAKE_CASE_  :		List[str]				      =    self.heap[0]
									self._bubble_down(_A    )
							return elem

					def 				__UpperCamelCase   (    self      :       Union[str, Any],_A      :       T,_A      :       int    ):







							"""simple docstring"""






							SCREAMING_SNAKE_CASE_  :		Tuple				      =    self.position_map[elem]
							SCREAMING_SNAKE_CASE_  :		int				      =    (elem, weight)
							if position > 0:
									SCREAMING_SNAKE_CASE_  :		int				      =    get_parent_position(_A    )
									SCREAMING_SNAKE_CASE_      ,    SCREAMING_SNAKE_CASE_  :		int				      =    self.heap[parent_position]
									if parent_weight > weight:
											self._bubble_up(_A    )
									else:
											self._bubble_down(_A    )
							else:
									self._bubble_down(_A    )

					def 				__UpperCamelCase   (    self      :       List[Any],_A      :       T    ):







							"""simple docstring"""






							SCREAMING_SNAKE_CASE_  :		Dict				      =    self.position_map[elem]
							if curr_pos == 0:
									return None
							SCREAMING_SNAKE_CASE_  :		Tuple				      =    get_parent_position(_A    )
							SCREAMING_SNAKE_CASE_      ,    SCREAMING_SNAKE_CASE_  :		List[Any]				      =    self.heap[curr_pos]
							SCREAMING_SNAKE_CASE_      ,    SCREAMING_SNAKE_CASE_  :		str				      =    self.heap[parent_position]
							if parent_weight > weight:
									self._swap_nodes(_A,_A    )
									return self._bubble_up(_A    )
							return None

					def 				__UpperCamelCase   (    self      :       Optional[Any],_A      :       T    ):







							"""simple docstring"""






							SCREAMING_SNAKE_CASE_  :		List[Any]				      =    self.position_map[elem]
							SCREAMING_SNAKE_CASE_      ,    SCREAMING_SNAKE_CASE_  :		str				      =    self.heap[curr_pos]
							SCREAMING_SNAKE_CASE_  :		Optional[int]				      =    get_child_left_position(_A    )
							SCREAMING_SNAKE_CASE_  :		int				      =    get_child_right_position(_A    )
							if child_left_position < self.elements and child_right_position < self.elements:
									SCREAMING_SNAKE_CASE_      ,    SCREAMING_SNAKE_CASE_  :		str				      =    self.heap[child_left_position]
									SCREAMING_SNAKE_CASE_      ,    SCREAMING_SNAKE_CASE_  :		List[str]				      =    self.heap[child_right_position]
									if child_right_weight < child_left_weight and child_right_weight < weight:
											self._swap_nodes(_A,_A    )
											return self._bubble_down(_A    )
							if child_left_position < self.elements:
									SCREAMING_SNAKE_CASE_      ,    SCREAMING_SNAKE_CASE_  :		Any				      =    self.heap[child_left_position]
									if child_left_weight < weight:
											self._swap_nodes(_A,_A    )
											return self._bubble_down(_A    )
							else:
									return None
							if child_right_position < self.elements:
									SCREAMING_SNAKE_CASE_      ,    SCREAMING_SNAKE_CASE_  :		Optional[int]				      =    self.heap[child_right_position]
									if child_right_weight < weight:
											self._swap_nodes(_A,_A    )
											return self._bubble_down(_A    )
							return None






					def 				__UpperCamelCase   (    self      :       Optional[int],_A      :       int,_A      :       int    ):







							"""simple docstring"""






							SCREAMING_SNAKE_CASE_  :		str				      =    self.heap[nodea_pos][0]
							SCREAMING_SNAKE_CASE_  :		List[Any]				      =    self.heap[nodea_pos][0]
							SCREAMING_SNAKE_CASE_      ,    SCREAMING_SNAKE_CASE_  :		Optional[int]				      =    (
							    self.heap[nodea_pos],
							    self.heap[nodea_pos],
							)
							SCREAMING_SNAKE_CASE_  :		Tuple				      =    nodea_pos
							SCREAMING_SNAKE_CASE_  :		List[Any]				      =    nodea_pos







class 		a__						(					Generic[T]					):

					def __init__(    self      :       Any    ):







							"""simple docstring"""






							SCREAMING_SNAKE_CASE_  :		dict[T, dict[T, int]]				      =    {}
							SCREAMING_SNAKE_CASE_  :		int				      =    0

					def __repr__(    self      :       Optional[Any]    ):







							"""simple docstring"""






							return str(self.connections    )

					def __len__(    self      :       str    ):







							"""simple docstring"""






							return self.nodes

					def 				__UpperCamelCase   (    self      :       Tuple,_A      :       T    ):







							"""simple docstring"""






							if node not in self.connections:
									SCREAMING_SNAKE_CASE_  :		Optional[int]				      =    {}
									self.nodes += 1






					def 				__UpperCamelCase   (    self      :       Tuple,_A      :       T,_A      :       T,_A      :       int    ):







							"""simple docstring"""






							self.add_node(_A    )
							self.add_node(_A    )
							SCREAMING_SNAKE_CASE_  :		Union[str, Any]				      =    weight
							SCREAMING_SNAKE_CASE_  :		Union[str, Any]				      =    weight







def       _snake_case	(   lowerCAmelCase							:   GraphUndirectedWeighted[T]   , ):
		"""simple docstring"""







		SCREAMING_SNAKE_CASE_  :		dict[T, int]				      =    {node: maxsize for node in graph.connections}
		SCREAMING_SNAKE_CASE_  :		dict[T, T | None]				      =    {node: None for node in graph.connections}

		SCREAMING_SNAKE_CASE_  :		MinPriorityQueue[T]				      =    MinPriorityQueue()
		for node, weight in dist.items():
				priority_queue.push(lowerCAmelCase   , lowerCAmelCase	)

		if priority_queue.is_empty():
				return dist, parent

		# initialization
		SCREAMING_SNAKE_CASE_  :		Optional[Any]				      =    priority_queue.extract_min()
		SCREAMING_SNAKE_CASE_  :		Dict				      =    0
		for neighbour in graph.connections[node]:
				if dist[neighbour] > dist[node] + graph.connections[node][neighbour]:
						SCREAMING_SNAKE_CASE_  :		int				      =    dist[node] + graph.connections[node][neighbour]
						priority_queue.update_key(lowerCAmelCase   , dist[neighbour]	)
						SCREAMING_SNAKE_CASE_  :		Optional[int]				      =    node

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




import socket
def 			_a (      ):


		"""simple docstring"""




		lowercase__            =      socket.socket(socket.AF_INET						,				socket.SOCK_STREAM     )
		lowercase__            =      socket.gethostname()
		lowercase__            =      1_23_12

		sock.connect((host, port)     )
		sock.send(B'''Hello server!'''     )

		with open('''Received_file'''						,				'''wb'''     ) as out_file:
				print('''File opened'''     )
				print('''Receiving data...'''     )
				while True:
						lowercase__            =      sock.recv(10_24     )
						if not data:
								break
						out_file.write(SCREAMING_SNAKE_CASE     )

		print('''Successfully received the file'''     )
		sock.close()
		print('''Connection closed'''     )


if __name__ == "__main__":
			main()


