






from __future__ import annotations

from queue import Queue





class        a__      :






		def __init__(      self						)				->				None:
				__A    =							{}






		def 					_lowerCamelCase					(      self						)				->				None:
				for i in self.vertices:
						print(lowercase__							, " : "							, " -> ".join([str(lowercase__						) for j in self.vertices[i]]						)						)






		def 					_lowerCamelCase					(      self							, lowercase__							, lowercase__						)				->				None:
				if from_vertex in self.vertices:
						self.vertices[from_vertex].append(lowercase__						)
				else:
						__A    =							[to_vertex]






		def 					_lowerCamelCase					(      self							, lowercase__						)				->				set[int]:
				__A    =							set()

				# create a first in first out queue to store all the vertices for BFS
				__A    =							Queue()

				# mark the source node as visited and enqueue it
				visited.add(lowercase__						)
				queue.put(lowercase__						)

				while not queue.empty():
						__A    =							queue.get()

						# loop through all adjacent vertex and enqueue it if not yet visited
						for adjacent_vertex in self.vertices[vertex]:
								if adjacent_vertex not in visited:
										queue.put(lowercase__						)
										visited.add(lowercase__						)
				return visited


if __name__ == "__main__":
					from doctest import testmod

					testmod(verbose=True)

					snake_case_   :	List[str]							      =Graph()
					g.add_edge(0, 1)
					g.add_edge(0, 2)
					g.add_edge(1, 2)
					g.add_edge(2, 0)
					g.add_edge(2, 3)
					g.add_edge(3, 3)

					g.print_graph()
					# 0  :  1 -> 2
					# 1  :  2
					# 2  :  0 -> 3
					# 3  :  3

					assert sorted(g.bfs(2)) == [0, 1, 2, 3]



lowerCamelCase__        =						[[0, 1, 1], [0, 0, 1], [1, 0, 0]]







class 	A__				:






				def __init__(		self   : Optional[int]       ,	a   : int  ):






							'''simple docstring'''







							lowerCAmelCase__ : List[str]   =						name
							lowerCAmelCase__ : List[Any]   =						[]
							lowerCAmelCase__ : int   =						[]






				def 				_lowerCamelCase						(		self   : List[str]       ,	a   : Union[str, Any]  ):






							'''simple docstring'''







							self.inbound.append(a  )






				def 				_lowerCamelCase						(		self   : Dict       ,	a   : Union[str, Any]  ):






							'''simple docstring'''







							self.outbound.append(a  )






				def __repr__(		self   : Tuple  ):






							'''simple docstring'''







							return f'''<node={self.name} inbound={self.inbound} outbound={self.outbound}>'''






def 					lowerCAmelCase__     (    SCREAMING_SNAKE_CASE_			,				SCREAMING_SNAKE_CASE_=3			,				SCREAMING_SNAKE_CASE_=0.85	)							->						Optional[Any]:
			lowerCAmelCase__ : Tuple   =						{}
			for node in nodes:
						lowerCAmelCase__ : Union[str, Any]   =						1

			lowerCAmelCase__ : List[str]   =						{}
			for node in nodes:
						lowerCAmelCase__ : str   =						len(node.outbound	)

			for i in range(SCREAMING_SNAKE_CASE_	):
						print(F'''======= Iteration {i + 1} ======='''	)
						for _, node in enumerate(SCREAMING_SNAKE_CASE_	):
									lowerCAmelCase__ : Optional[int]   =						(1 - d) + d * sum(
									    ranks[ib] / outbounds[ib] for ib in node.inbound	)
						print(SCREAMING_SNAKE_CASE_	)
def 					lowerCAmelCase__     (    )							->						Dict:
			lowerCAmelCase__ : List[Any]   =						list(input('Enter Names of the Nodes: '	).split()	)

			lowerCAmelCase__ : Union[str, Any]   =						[Node(SCREAMING_SNAKE_CASE_	) for name in names]

			for ri, row in enumerate(SCREAMING_SNAKE_CASE_	):
						for ci, col in enumerate(SCREAMING_SNAKE_CASE_	):
									if col == 1:
												nodes[ci].add_inbound(names[ri]	)
												nodes[ri].add_outbound(names[ci]	)

			print('======= Nodes ======='	)
			for node in nodes:
						print(SCREAMING_SNAKE_CASE_	)

			page_rank(SCREAMING_SNAKE_CASE_	)


if __name__ == "__main__":
					main()