



"""simple docstring"""







from collections import deque
from math import floor
from random import random
from time import time






class       UpperCamelCase__			:

			"""simple docstring"""


			def __init__(      self		)      ->	Tuple:
				A__											=					{}


			def   snake_case__	(      self						,	SCREAMING_SNAKE_CASE__						,	SCREAMING_SNAKE_CASE__						,	SCREAMING_SNAKE_CASE__=1		)      ->	Tuple:
				if self.graph.get(SCREAMING_SNAKE_CASE__		):
					if self.graph[u].count([w, v]		) == 0:
						self.graph[u].append([w, v]		)
				else:
					A__											=					[[w, v]]
				if not self.graph.get(SCREAMING_SNAKE_CASE__		):
					A__											=					[]


			def   snake_case__	(      self		)      ->	Optional[Any]:
				return list(self.graph		)


			def   snake_case__	(      self						,	SCREAMING_SNAKE_CASE__						,	SCREAMING_SNAKE_CASE__		)      ->	List[str]:
				if self.graph.get(SCREAMING_SNAKE_CASE__		):
					for _ in self.graph[u]:
						if _[1] == v:
							self.graph[u].remove(SCREAMING_SNAKE_CASE__		)


			def   snake_case__	(      self						,	SCREAMING_SNAKE_CASE__=-2						,	SCREAMING_SNAKE_CASE__=-1		)      ->	List[Any]:
				if s == d:
					return []
				A__											=					[]
				A__											=					[]
				if s == -2:
					A__											=					list(self.graph		)[0]
				stack.append(SCREAMING_SNAKE_CASE__		)
				visited.append(SCREAMING_SNAKE_CASE__		)
				A__											=					s

				while True:
					# check if there is any non isolated nodes
					if len(self.graph[s]		) != 0:
						A__											=					s
						for node in self.graph[s]:
							if visited.count(node[1]		) < 1:
								if node[1] == d:
									visited.append(SCREAMING_SNAKE_CASE__		)
									return visited
								else:
									stack.append(node[1]		)
									visited.append(node[1]		)
									A__											=					node[1]
									break

            # check if all the children are visited
					if s == ss:
						stack.pop()
						if len(SCREAMING_SNAKE_CASE__		) != 0:
							A__											=					stack[len(SCREAMING_SNAKE_CASE__		) - 1]
					else:
						A__											=					ss

					# check if se have reached the starting point
					if len(SCREAMING_SNAKE_CASE__		) == 0:
						return visited


			def   snake_case__	(      self						,	SCREAMING_SNAKE_CASE__=-1		)      ->	Union[str, Any]:
				if c == -1:
					A__											=					floor(random() * 10000		) + 10
				for i in range(SCREAMING_SNAKE_CASE__		):
					# every vertex has max 100 edges
					for _ in range(floor(random() * 102		) + 1		):
						A__											=					floor(random() * c		) + 1
						if n != i:
							self.add_pair(SCREAMING_SNAKE_CASE__						,	SCREAMING_SNAKE_CASE__						,	1		)


			def   snake_case__	(      self						,	SCREAMING_SNAKE_CASE__=-2		)      ->	int:
				A__											=					deque()
				A__											=					[]
				if s == -2:
					A__											=					list(self.graph		)[0]
				d.append(SCREAMING_SNAKE_CASE__		)
				visited.append(SCREAMING_SNAKE_CASE__		)
				while d:
					A__											=					d.popleft()
					if len(self.graph[s]		) != 0:
						for node in self.graph[s]:
							if visited.count(node[1]		) < 1:
								d.append(node[1]		)
								visited.append(node[1]		)
				return visited


			def   snake_case__	(      self						,	SCREAMING_SNAKE_CASE__		)      ->	Optional[Any]:
				A__											=					0
				for x in self.graph:
					for y in self.graph[x]:
						if y[1] == u:
							count += 1
				return count


			def   snake_case__	(      self						,	SCREAMING_SNAKE_CASE__		)      ->	Optional[Any]:
				return len(self.graph[u]		)


			def   snake_case__	(      self						,	SCREAMING_SNAKE_CASE__=-2		)      ->	Optional[int]:
				A__											=					[]
				A__											=					[]
				if s == -2:
					A__											=					list(self.graph		)[0]
				stack.append(SCREAMING_SNAKE_CASE__		)
				visited.append(SCREAMING_SNAKE_CASE__		)
				A__											=					s
				A__											=					[]

				while True:
					# check if there is any non isolated nodes
					if len(self.graph[s]		) != 0:
						A__											=					s
						for node in self.graph[s]:
							if visited.count(node[1]		) < 1:
								stack.append(node[1]		)
								visited.append(node[1]		)
								A__											=					node[1]
								break

            # check if all the children are visited
					if s == ss:
						sorted_nodes.append(stack.pop()		)
						if len(SCREAMING_SNAKE_CASE__		) != 0:
							A__											=					stack[len(SCREAMING_SNAKE_CASE__		) - 1]
					else:
						A__											=					ss

					# check if se have reached the starting point
					if len(SCREAMING_SNAKE_CASE__		) == 0:
						return sorted_nodes


			def   snake_case__	(      self		)      ->	int:
				A__											=					[]
				A__											=					[]
				A__											=					list(self.graph		)[0]
				stack.append(SCREAMING_SNAKE_CASE__		)
				visited.append(SCREAMING_SNAKE_CASE__		)
				A__											=					-2
				A__											=					[]
				A__											=					s
				A__											=					False
				A__											=					set()

				while True:
					# check if there is any non isolated nodes
					if len(self.graph[s]		) != 0:
						A__											=					s
						for node in self.graph[s]:
							if (
							    visited.count(node[1]		) > 0
							    and node[1] != parent
							    and indirect_parents.count(node[1]		) > 0
							    and not on_the_way_back
							):
								A__											=					len(SCREAMING_SNAKE_CASE__		) - 1
								while len_stack >= 0:
									if stack[len_stack] == node[1]:
										anticipating_nodes.add(node[1]		)
										break
									else:
										anticipating_nodes.add(stack[len_stack]		)
										len_stack -= 1
							if visited.count(node[1]		) < 1:
								stack.append(node[1]		)
								visited.append(node[1]		)
								A__											=					node[1]
								break

            # check if all the children are visited
					if s == ss:
						stack.pop()
						A__											=					True
						if len(SCREAMING_SNAKE_CASE__		) != 0:
							A__											=					stack[len(SCREAMING_SNAKE_CASE__		) - 1]
					else:
						A__											=					False
						indirect_parents.append(SCREAMING_SNAKE_CASE__		)
						A__											=					s
						A__											=					ss

					# check if se have reached the starting point
					if len(SCREAMING_SNAKE_CASE__		) == 0:
						return list(SCREAMING_SNAKE_CASE__		)


			def   snake_case__	(      self		)      ->	int:
				A__											=					[]
				A__											=					[]
				A__											=					list(self.graph		)[0]
				stack.append(SCREAMING_SNAKE_CASE__		)
				visited.append(SCREAMING_SNAKE_CASE__		)
				A__											=					-2
				A__											=					[]
				A__											=					s
				A__											=					False
				A__											=					set()

				while True:
					# check if there is any non isolated nodes
					if len(self.graph[s]		) != 0:
						A__											=					s
						for node in self.graph[s]:
							if (
							    visited.count(node[1]		) > 0
							    and node[1] != parent
							    and indirect_parents.count(node[1]		) > 0
							    and not on_the_way_back
							):
								A__											=					len(SCREAMING_SNAKE_CASE__		) - 1
								while len_stack_minus_one >= 0:
									if stack[len_stack_minus_one] == node[1]:
										anticipating_nodes.add(node[1]		)
										break
									else:
										return True
							if visited.count(node[1]		) < 1:
								stack.append(node[1]		)
								visited.append(node[1]		)
								A__											=					node[1]
								break

            # check if all the children are visited
					if s == ss:
						stack.pop()
						A__											=					True
						if len(SCREAMING_SNAKE_CASE__		) != 0:
							A__											=					stack[len(SCREAMING_SNAKE_CASE__		) - 1]
					else:
						A__											=					False
						indirect_parents.append(SCREAMING_SNAKE_CASE__		)
						A__											=					s
						A__											=					ss

					# check if se have reached the starting point
					if len(SCREAMING_SNAKE_CASE__		) == 0:
						return False


			def   snake_case__	(      self						,	SCREAMING_SNAKE_CASE__=-2						,	SCREAMING_SNAKE_CASE__=-1		)      ->	Union[str, Any]:
				A__											=					time()
				self.dfs(SCREAMING_SNAKE_CASE__						,	SCREAMING_SNAKE_CASE__		)
				A__											=					time()
				return end - begin







			def   snake_case__	(      self						,	SCREAMING_SNAKE_CASE__=-2		)      ->	Dict:
				A__											=					time()
				self.bfs(SCREAMING_SNAKE_CASE__		)
				A__											=					time()
				return end - begin






class       UpperCamelCase__			:

			"""simple docstring"""


			def __init__(      self		)      ->	Tuple:
				A__											=					{}


			def   snake_case__	(      self						,	SCREAMING_SNAKE_CASE__						,	SCREAMING_SNAKE_CASE__						,	SCREAMING_SNAKE_CASE__=1		)      ->	Dict:
				# check if the u exists
				if self.graph.get(SCREAMING_SNAKE_CASE__		):
					# if there already is a edge
					if self.graph[u].count([w, v]		) == 0:
						self.graph[u].append([w, v]		)
				else:
					# if u does not exist
					A__											=					[[w, v]]
				# add the other way
				if self.graph.get(SCREAMING_SNAKE_CASE__		):
					# if there already is a edge
					if self.graph[v].count([w, u]		) == 0:
						self.graph[v].append([w, u]		)
				else:
					# if u does not exist
					A__											=					[[w, u]]


			def   snake_case__	(      self						,	SCREAMING_SNAKE_CASE__						,	SCREAMING_SNAKE_CASE__		)      ->	Optional[int]:
				if self.graph.get(SCREAMING_SNAKE_CASE__		):
					for _ in self.graph[u]:
						if _[1] == v:
							self.graph[u].remove(SCREAMING_SNAKE_CASE__		)
        # the other way round
				if self.graph.get(SCREAMING_SNAKE_CASE__		):
					for _ in self.graph[v]:
						if _[1] == u:
							self.graph[v].remove(SCREAMING_SNAKE_CASE__		)


			def   snake_case__	(      self						,	SCREAMING_SNAKE_CASE__=-2						,	SCREAMING_SNAKE_CASE__=-1		)      ->	List[str]:
				if s == d:
					return []
				A__											=					[]
				A__											=					[]
				if s == -2:
					A__											=					list(self.graph		)[0]
				stack.append(SCREAMING_SNAKE_CASE__		)
				visited.append(SCREAMING_SNAKE_CASE__		)
				A__											=					s

				while True:
					# check if there is any non isolated nodes
					if len(self.graph[s]		) != 0:
						A__											=					s
						for node in self.graph[s]:
							if visited.count(node[1]		) < 1:
								if node[1] == d:
									visited.append(SCREAMING_SNAKE_CASE__		)
									return visited
								else:
									stack.append(node[1]		)
									visited.append(node[1]		)
									A__											=					node[1]
									break

            # check if all the children are visited
					if s == ss:
						stack.pop()
						if len(SCREAMING_SNAKE_CASE__		) != 0:
							A__											=					stack[len(SCREAMING_SNAKE_CASE__		) - 1]
					else:
						A__											=					ss

					# check if se have reached the starting point
					if len(SCREAMING_SNAKE_CASE__		) == 0:
						return visited


			def   snake_case__	(      self						,	SCREAMING_SNAKE_CASE__=-1		)      ->	Optional[int]:
				if c == -1:
					A__											=					floor(random() * 10000		) + 10
				for i in range(SCREAMING_SNAKE_CASE__		):
					# every vertex has max 100 edges
					for _ in range(floor(random() * 102		) + 1		):
						A__											=					floor(random() * c		) + 1
						if n != i:
							self.add_pair(SCREAMING_SNAKE_CASE__						,	SCREAMING_SNAKE_CASE__						,	1		)


			def   snake_case__	(      self						,	SCREAMING_SNAKE_CASE__=-2		)      ->	Any:
				A__											=					deque()
				A__											=					[]
				if s == -2:
					A__											=					list(self.graph		)[0]
				d.append(SCREAMING_SNAKE_CASE__		)
				visited.append(SCREAMING_SNAKE_CASE__		)
				while d:
					A__											=					d.popleft()
					if len(self.graph[s]		) != 0:
						for node in self.graph[s]:
							if visited.count(node[1]		) < 1:
								d.append(node[1]		)
								visited.append(node[1]		)
				return visited


			def   snake_case__	(      self						,	SCREAMING_SNAKE_CASE__		)      ->	Dict:
				return len(self.graph[u]		)


			def   snake_case__	(      self		)      ->	Any:
				A__											=					[]
				A__											=					[]
				A__											=					list(self.graph		)[0]
				stack.append(SCREAMING_SNAKE_CASE__		)
				visited.append(SCREAMING_SNAKE_CASE__		)
				A__											=					-2
				A__											=					[]
				A__											=					s
				A__											=					False
				A__											=					set()

				while True:
					# check if there is any non isolated nodes
					if len(self.graph[s]		) != 0:
						A__											=					s
						for node in self.graph[s]:
							if (
							    visited.count(node[1]		) > 0
							    and node[1] != parent
							    and indirect_parents.count(node[1]		) > 0
							    and not on_the_way_back
							):
								A__											=					len(SCREAMING_SNAKE_CASE__		) - 1
								while len_stack >= 0:
									if stack[len_stack] == node[1]:
										anticipating_nodes.add(node[1]		)
										break
									else:
										anticipating_nodes.add(stack[len_stack]		)
										len_stack -= 1
							if visited.count(node[1]		) < 1:
								stack.append(node[1]		)
								visited.append(node[1]		)
								A__											=					node[1]
								break

            # check if all the children are visited
					if s == ss:
						stack.pop()
						A__											=					True
						if len(SCREAMING_SNAKE_CASE__		) != 0:
							A__											=					stack[len(SCREAMING_SNAKE_CASE__		) - 1]
					else:
						A__											=					False
						indirect_parents.append(SCREAMING_SNAKE_CASE__		)
						A__											=					s
						A__											=					ss

					# check if se have reached the starting point
					if len(SCREAMING_SNAKE_CASE__		) == 0:
						return list(SCREAMING_SNAKE_CASE__		)


			def   snake_case__	(      self		)      ->	Any:
				A__											=					[]
				A__											=					[]
				A__											=					list(self.graph		)[0]
				stack.append(SCREAMING_SNAKE_CASE__		)
				visited.append(SCREAMING_SNAKE_CASE__		)
				A__											=					-2
				A__											=					[]
				A__											=					s
				A__											=					False
				A__											=					set()

				while True:
					# check if there is any non isolated nodes
					if len(self.graph[s]		) != 0:
						A__											=					s
						for node in self.graph[s]:
							if (
							    visited.count(node[1]		) > 0
							    and node[1] != parent
							    and indirect_parents.count(node[1]		) > 0
							    and not on_the_way_back
							):
								A__											=					len(SCREAMING_SNAKE_CASE__		) - 1
								while len_stack_minus_one >= 0:
									if stack[len_stack_minus_one] == node[1]:
										anticipating_nodes.add(node[1]		)
										break
									else:
										return True
							if visited.count(node[1]		) < 1:
								stack.append(node[1]		)
								visited.append(node[1]		)
								A__											=					node[1]
								break

            # check if all the children are visited
					if s == ss:
						stack.pop()
						A__											=					True
						if len(SCREAMING_SNAKE_CASE__		) != 0:
							A__											=					stack[len(SCREAMING_SNAKE_CASE__		) - 1]
					else:
						A__											=					False
						indirect_parents.append(SCREAMING_SNAKE_CASE__		)
						A__											=					s
						A__											=					ss

					# check if se have reached the starting point
					if len(SCREAMING_SNAKE_CASE__		) == 0:
						return False


			def   snake_case__	(      self		)      ->	Any:
				return list(self.graph		)


			def   snake_case__	(      self						,	SCREAMING_SNAKE_CASE__=-2						,	SCREAMING_SNAKE_CASE__=-1		)      ->	Tuple:
				A__											=					time()
				self.dfs(SCREAMING_SNAKE_CASE__						,	SCREAMING_SNAKE_CASE__		)
				A__											=					time()
				return end - begin







			def   snake_case__	(      self						,	SCREAMING_SNAKE_CASE__=-2		)      ->	str:
				A__											=					time()
				self.bfs(SCREAMING_SNAKE_CASE__		)
				A__											=					time()
				return end - begin









"""simple docstring"""







class       UpperCamelCase__			:

			"""simple docstring"""


			def __init__(      self						,	SCREAMING_SNAKE_CASE__ = ""						,	SCREAMING_SNAKE_CASE__ = False		)      ->	None:
				# Mapping from the first character of the prefix of the node
				A__											=					{}

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

				A__											=					prefix


			def   snake_case__	(      self						,	SCREAMING_SNAKE_CASE__		)      ->	tuple[str, str, str]:
				A__											=					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   snake_case__	(      self						,	SCREAMING_SNAKE_CASE__		)      ->	None:
				for word in words:
					self.insert(SCREAMING_SNAKE_CASE__		)


			def   snake_case__	(      self						,	SCREAMING_SNAKE_CASE__		)      ->	None:
				# Case 1: If the word is the prefix of the node
				# Solution: We set the current node as leaf
				if self.prefix == word:
					A__											=					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:
					A__											=					RadixNode(prefix=SCREAMING_SNAKE_CASE__						,	is_leaf=SCREAMING_SNAKE_CASE__		)

				else:
					A__											=					self.nodes[word[0]]
					A__							,							A__							,							A__											=					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:
						A__											=					remaining_prefix

						A__											=					self.nodes[matching_string[0]]
						A__											=					RadixNode(SCREAMING_SNAKE_CASE__						,	SCREAMING_SNAKE_CASE__		)
						A__											=					aux_node

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


			def   snake_case__	(      self						,	SCREAMING_SNAKE_CASE__		)      ->	bool:
				A__											=					self.nodes.get(word[0]						,	SCREAMING_SNAKE_CASE__		)
				if not incoming_node:
					return False
				else:
					A__							,							A__							,							A__											=					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   snake_case__	(      self						,	SCREAMING_SNAKE_CASE__		)      ->	bool:
				A__											=					self.nodes.get(word[0]						,	SCREAMING_SNAKE_CASE__		)
				if not incoming_node:
					return False
				else:
					A__							,							A__							,							A__											=					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:
									A__											=					list(self.nodes.values()		)[0]
									A__											=					merging_node.is_leaf
									self.prefix += merging_node.prefix
									A__											=					merging_node.nodes
                    # If there is more than 1 edge, we just mark it as non-leaf
							elif len(incoming_node.nodes		) > 1:
								A__											=					False
							# If there is 1 edge, we merge it with its child
							else:
								A__											=					list(incoming_node.nodes.values()		)[0]
								A__											=					merging_node.is_leaf
								incoming_node.prefix += merging_node.prefix
								A__											=					merging_node.nodes

							return True







			def   snake_case__	(      self						,	SCREAMING_SNAKE_CASE__ = 0		)      ->	None:
				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       _lowerCamelCase				(							)	-> bool:






	"""simple docstring"""





	A__											=					"banana bananas bandana band apple all beast".split()
	A__											=					RadixNode()
	root.insert_many(UpperCAmelCase_     )

	assert all(root.find(UpperCAmelCase_     ) 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       _lowerCamelCase				(							)	-> None:






	"""simple docstring"""





	assert test_trie()

def       _lowerCamelCase				(							)	-> None:






	"""simple docstring"""





	A__											=					RadixNode()
	A__											=					"banana bananas bandanas bandana band apple all beast".split()
	root.insert_many(UpperCAmelCase_     )

	print("Words:",	UpperCAmelCase_     )
	print("Tree:"     )
	root.print_tree()


if __name__ == "__main__":
			main()




