
class     lowerCamelCase      :







	def __init__(     self      :Union[str, Any]			)		->      int:







				"""simple docstring"""






				SCREAMING_SNAKE_CASE     						= 0
				SCREAMING_SNAKE_CASE     						= 0
				SCREAMING_SNAKE_CASE     						= {}







	def  snake_case__     (     self      :Dict   ,     lowercase      :Tuple			)		->      Any:







				"""simple docstring"""






				if vertex not in self.adjacency:
							SCREAMING_SNAKE_CASE     						= {}
							self.num_vertices += 1







	def  snake_case__     (     self      :Any   ,     lowercase      :Optional[Any]   ,     lowercase      :str   ,     lowercase      :str			)		->      Union[str, Any]:







				"""simple docstring"""






				self.add_vertex(lowercase			)
				self.add_vertex(lowercase			)

				if head == tail:
							return

				SCREAMING_SNAKE_CASE     						= weight
				SCREAMING_SNAKE_CASE     						= weight







	def  snake_case__     (     self      :int			)		->      Tuple:







				"""simple docstring"""






				SCREAMING_SNAKE_CASE     						= self.get_edges()
				for edge in edges:
							SCREAMING_SNAKE_CASE						,							SCREAMING_SNAKE_CASE						,							SCREAMING_SNAKE_CASE     						= edge
							edges.remove((tail, head, weight)			)
				for i in range(len(lowercase			)			):
							SCREAMING_SNAKE_CASE     						= list(edges[i]			)

				edges.sort(key=lambda lowercase			: e[2]			)
				for i in range(len(lowercase			) - 1			):
							if edges[i][2] >= edges[i + 1][2]:
										SCREAMING_SNAKE_CASE     						= edges[i][2] + 1
				for edge in edges:
							SCREAMING_SNAKE_CASE						,							SCREAMING_SNAKE_CASE						,							SCREAMING_SNAKE_CASE     						= edge
							SCREAMING_SNAKE_CASE     						= weight
							SCREAMING_SNAKE_CASE     						= weight







	def __str__(     self      :str			)		->      Optional[int]:







				"""simple docstring"""






				SCREAMING_SNAKE_CASE     						= ''''''
				for tail in self.adjacency:
							for head in self.adjacency[tail]:
										SCREAMING_SNAKE_CASE     						= self.adjacency[head][tail]
										string += f"""{head} -> {tail} == {weight}\n"""
				return string.rstrip('''\n'''			)







	def  snake_case__     (     self      :Optional[Any]			)		->      Tuple:







				"""simple docstring"""






				SCREAMING_SNAKE_CASE     						= []
				for tail in self.adjacency:
							for head in self.adjacency[tail]:
										output.append((tail, head, self.adjacency[head][tail])			)
				return output







	def  snake_case__     (     self      :Union[str, Any]			)		->      Optional[Any]:







				"""simple docstring"""






				return self.adjacency.keys()







	@staticmethod
	def  snake_case__     (     lowercase      :List[Any]=None   ,     lowercase      :int=None			)		->      Optional[int]:







				"""simple docstring"""






				SCREAMING_SNAKE_CASE     						= Graph()
				if vertices is None:
							SCREAMING_SNAKE_CASE     						= []
				if edges is None:
							SCREAMING_SNAKE_CASE     						= []
				for vertex in vertices:
							g.add_vertex(lowercase			)
				for edge in edges:
							g.add_edge(*lowercase			)
				return g





	class     lowerCamelCase      :







		def __init__(     self      :List[str]			)		->      str:







					"""simple docstring"""






					SCREAMING_SNAKE_CASE     						= {}
					SCREAMING_SNAKE_CASE     						= {}







		def __len__(     self      :List[Any]			)		->      Union[str, Any]:







					"""simple docstring"""






					return len(self.parent			)







		def  snake_case__     (     self      :Optional[Any]   ,     lowercase      :Union[str, Any]			)		->      Optional[int]:







					"""simple docstring"""






					if item in self.parent:
								return self.find(lowercase			)

					SCREAMING_SNAKE_CASE     						= item
					SCREAMING_SNAKE_CASE     						= 0
					return item







		def  snake_case__     (     self      :int   ,     lowercase      :Optional[Any]			)		->      int:







					"""simple docstring"""






					if item not in self.parent:
								return self.make_set(lowercase			)
					if item != self.parent[item]:
								SCREAMING_SNAKE_CASE     						= self.find(self.parent[item]			)
					return self.parent[item]







		def  snake_case__     (     self      :Dict   ,     lowercase      :int   ,     lowercase      :int			)		->      List[str]:







					"""simple docstring"""






					SCREAMING_SNAKE_CASE     						= self.find(lowercase			)
					SCREAMING_SNAKE_CASE     						= self.find(lowercase			)

					if roota == roota:
								return roota

					if self.rank[roota] > self.rank[roota]:
								SCREAMING_SNAKE_CASE     						= roota
								return roota

					if self.rank[roota] < self.rank[roota]:
								SCREAMING_SNAKE_CASE     						= roota
								return roota

					if self.rank[roota] == self.rank[roota]:
								self.rank[roota] += 1
								SCREAMING_SNAKE_CASE     						= roota
								return roota
					return None







	@staticmethod
	def  snake_case__     (     lowercase      :str			)		->      List[Any]:







				"""simple docstring"""






				SCREAMING_SNAKE_CASE     						= graph.num_vertices

				SCREAMING_SNAKE_CASE     						= Graph.UnionFind()
				SCREAMING_SNAKE_CASE     						= []
				while num_components > 1:
							SCREAMING_SNAKE_CASE     						= {}
							for vertex in graph.get_vertices():
										SCREAMING_SNAKE_CASE     						= -1

							SCREAMING_SNAKE_CASE     						= graph.get_edges()
							for edge in edges:
										SCREAMING_SNAKE_CASE						,							SCREAMING_SNAKE_CASE						,							SCREAMING_SNAKE_CASE     						= edge
										edges.remove((tail, head, weight)			)
							for edge in edges:
										SCREAMING_SNAKE_CASE						,							SCREAMING_SNAKE_CASE						,							SCREAMING_SNAKE_CASE     						= edge
										SCREAMING_SNAKE_CASE     						= union_find.find(lowercase			)
										SCREAMING_SNAKE_CASE     						= union_find.find(lowercase			)
										if seta != seta:
													if cheap_edge[seta] == -1 or cheap_edge[seta][2] > weight:
																SCREAMING_SNAKE_CASE     						= [head, tail, weight]

													if cheap_edge[seta] == -1 or cheap_edge[seta][2] > weight:
																SCREAMING_SNAKE_CASE     						= [head, tail, weight]
							for vertex in cheap_edge:
										if cheap_edge[vertex] != -1:
													SCREAMING_SNAKE_CASE						,							SCREAMING_SNAKE_CASE						,							SCREAMING_SNAKE_CASE     						= cheap_edge[vertex]
													if union_find.find(lowercase			) != union_find.find(lowercase			):
																union_find.union(lowercase   ,     lowercase			)
																mst_edges.append(cheap_edge[vertex]			)
																SCREAMING_SNAKE_CASE     						= num_components - 1
				SCREAMING_SNAKE_CASE     						= Graph.build(edges=lowercase			)
				return mst





class       a_       :





	def __init__(							self      ,     SCREAMING_SNAKE_CASE = ""      ,     SCREAMING_SNAKE_CASE = False      )  ->					None:




				"""simple docstring"""



				SCREAMING_SNAKE_CASE_								=						{}

				# A node will be a leaf if the tree contains its word
				SCREAMING_SNAKE_CASE_								=						is_leaf

				SCREAMING_SNAKE_CASE_								=						prefix





	def 						A_(							self      ,     SCREAMING_SNAKE_CASE      )  ->					tuple[str, str, str]:




				"""simple docstring"""



				SCREAMING_SNAKE_CASE_								=						0
				for q, w in zip(self.prefix      ,     SCREAMING_SNAKE_CASE      ):
							if q != w:
										break

							x += 1

				return self.prefix[:x], self.prefix[x:], word[x:]





	def 						A_(							self      ,     SCREAMING_SNAKE_CASE      )  ->					None:




				"""simple docstring"""



				for word in words:
							self.insert(SCREAMING_SNAKE_CASE      )





	def 						A_(							self      ,     SCREAMING_SNAKE_CASE      )  ->					None:




				"""simple docstring"""



				if self.prefix == word:
							SCREAMING_SNAKE_CASE_								=						True

				# Case 2: The node has no edges that have a prefix to the word
				# Solution: We create an edge from the current node to a new one
				# containing the word
				elif word[0] not in self.nodes:
							SCREAMING_SNAKE_CASE_								=						RadixNode(prefix=SCREAMING_SNAKE_CASE      ,     is_leaf=SCREAMING_SNAKE_CASE      )

				else:
							SCREAMING_SNAKE_CASE_								=						self.nodes[word[0]]
							SCREAMING_SNAKE_CASE_						,		SCREAMING_SNAKE_CASE_						,		SCREAMING_SNAKE_CASE_								=						incoming_node.match(
							    SCREAMING_SNAKE_CASE      )

							# Case 3: The node prefix is equal to the matching
							# Solution: We insert remaining word on the next node
							if remaining_prefix == "":
										self.nodes[matching_string[0]].insert(SCREAMING_SNAKE_CASE      )

							# Case 4: The word is greater equal to the matching
							# Solution: Create a node in between both nodes, change
							# prefixes and add the new node for the remaining word
							else:
										SCREAMING_SNAKE_CASE_								=						remaining_prefix

										SCREAMING_SNAKE_CASE_								=						self.nodes[matching_string[0]]
										SCREAMING_SNAKE_CASE_								=						RadixNode(SCREAMING_SNAKE_CASE      ,     SCREAMING_SNAKE_CASE      )
										SCREAMING_SNAKE_CASE_								=						aux_node

										if remaining_word == "":
													SCREAMING_SNAKE_CASE_								=						True
										else:
													self.nodes[matching_string[0]].insert(SCREAMING_SNAKE_CASE      )





	def 						A_(							self      ,     SCREAMING_SNAKE_CASE      )  ->					bool:




				"""simple docstring"""



				SCREAMING_SNAKE_CASE_								=						self.nodes.get(word[0]      ,     SCREAMING_SNAKE_CASE      )
				if not incoming_node:
							return False
				else:
							SCREAMING_SNAKE_CASE_						,		SCREAMING_SNAKE_CASE_						,		SCREAMING_SNAKE_CASE_								=						incoming_node.match(
							    SCREAMING_SNAKE_CASE      )
							# If there is remaining prefix, the word can't be on the tree
							if remaining_prefix != "":
										return False
							# This applies when the word and the prefix are equal
							elif remaining_word == "":
										return incoming_node.is_leaf
							# We have word remaining so we check the next node
							else:
										return incoming_node.find(SCREAMING_SNAKE_CASE      )





	def 						A_(							self      ,     SCREAMING_SNAKE_CASE      )  ->					bool:




				"""simple docstring"""



				SCREAMING_SNAKE_CASE_								=						self.nodes.get(word[0]      ,     SCREAMING_SNAKE_CASE      )
				if not incoming_node:
							return False
				else:
							SCREAMING_SNAKE_CASE_						,		SCREAMING_SNAKE_CASE_						,		SCREAMING_SNAKE_CASE_								=						incoming_node.match(
							    SCREAMING_SNAKE_CASE      )
							# If there is remaining prefix, the word can't be on the tree
							if remaining_prefix != "":
										return False
							# We have word remaining so we check the next node
							elif remaining_word != "":
										return incoming_node.delete(SCREAMING_SNAKE_CASE      )
							else:
										# If it is not a leaf, we don't have to delete
										if not incoming_node.is_leaf:
													return False
										else:
													# We delete the nodes if no edges go from it
													if len(incoming_node.nodes      ) == 0:
																del self.nodes[word[0]]
																# We merge the current node with its only child
																if len(self.nodes      ) == 1 and not self.is_leaf:
																			SCREAMING_SNAKE_CASE_								=						list(self.nodes.values()      )[0]
																			SCREAMING_SNAKE_CASE_								=						merging_node.is_leaf
																			self.prefix += merging_node.prefix
																			SCREAMING_SNAKE_CASE_								=						merging_node.nodes
                    # If there is more than 1 edge, we just mark it as non-leaf
													elif len(incoming_node.nodes      ) > 1:
																SCREAMING_SNAKE_CASE_								=						False
													# If there is 1 edge, we merge it with its child
													else:
																SCREAMING_SNAKE_CASE_								=						list(incoming_node.nodes.values()      )[0]
																SCREAMING_SNAKE_CASE_								=						merging_node.is_leaf
																incoming_node.prefix += merging_node.prefix
																SCREAMING_SNAKE_CASE_								=						merging_node.nodes

													return True





	def 						A_(							self      ,     SCREAMING_SNAKE_CASE = 0      )  ->					None:




				"""simple docstring"""



				if self.prefix != "":
							print('-' * height      ,     self.prefix      ,     '  (leaf)' if self.is_leaf else ''      )

				for value in self.nodes.values():
							value.print_tree(height + 1      )




def lowercase    (  )			->							bool:


			'''simple docstring'''







			SCREAMING_SNAKE_CASE_								=						'banana bananas bandana band apple all beast'.split()
			SCREAMING_SNAKE_CASE_								=						RadixNode()
			root.insert_many(SCREAMING_SNAKE_CASE )

			assert all(root.find(SCREAMING_SNAKE_CASE ) for word in words )
			assert not root.find('bandanas' )
			assert not root.find('apps' )
			root.delete('all' )
			assert not root.find('all' )
			root.delete('banana' )
			assert not root.find('banana' )
			assert root.find('bananas' )

			return True

def lowercase    (  )			->							None:


			'''simple docstring'''







			assert test_trie()

def lowercase    (  )			->							None:


			'''simple docstring'''







			SCREAMING_SNAKE_CASE_								=						RadixNode()
			SCREAMING_SNAKE_CASE_								=						'banana bananas bandanas bandana band apple all beast'.split()
			root.insert_many(SCREAMING_SNAKE_CASE )

			print('Words:'       ,    SCREAMING_SNAKE_CASE )
			print('Tree:' )
			root.print_tree()


if __name__ == "__main__":
				main()
