






'''simple docstring'''




def       __UpperCAmelCase						(  lowerCamelCase_)							->     int:

		if not isinstance(__UpperCamelCase     ,      __UpperCamelCase):
				raise TypeError('only integers accepted as input')
		else:
				UpperCamelCase__				:					List[str]					=					str(abs(__UpperCamelCase))
				UpperCamelCase__				:					Dict					=					[list(__UpperCamelCase) for char in range(len(__UpperCamelCase))]
				for index in range(len(__UpperCamelCase)):
						num_transpositions[index].pop(__UpperCamelCase)
				return max(
				    int(''.join(list(__UpperCamelCase))) for transposition in num_transpositions)


if __name__ == "__main__":
		__import__('doctest').testmod()







'''simple docstring'''




class       __lowercase					:

	def __init__(      self   :						List[str]  ,					UpperCAmelCase_   :						str = ""  ,					UpperCAmelCase_   :						bool = False):
			# Mapping from the first character of the prefix of the node
			UpperCamelCase__				:					dict[str, RadixNode]					=					{}

			# A node will be a leaf if the tree contains its word
			UpperCamelCase__				:					List[Any]					=					is_leaf

			UpperCamelCase__				:					Optional[Any]					=					prefix

	def      __UpperCamelCase							(      self   :						List[Any]  ,					UpperCAmelCase_   :						str):
			UpperCamelCase__				:					Optional[int]					=					0
			for q, w in zip(self.prefix  ,					UpperCAmelCase_):
					if q != w:
							break

					x += 1

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

	def      __UpperCamelCase							(      self   :						str  ,					UpperCAmelCase_   :						list[str]):
			for word in words:
					self.insert(UpperCAmelCase_)

	def      __UpperCamelCase							(      self   :						Optional[int]  ,					UpperCAmelCase_   :						str):
			# Case 1: If the word is the prefix of the node
			# Solution: We set the current node as leaf
			if self.prefix == word:
					UpperCamelCase__				:					Optional[Any]					=					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:
					UpperCamelCase__				:					Optional[Any]					=					RadixNode(prefix=UpperCAmelCase_  ,					is_leaf=UpperCAmelCase_)

			else:
					UpperCamelCase__				:					int					=					self.nodes[word[0]]
					UpperCamelCase__,	UpperCamelCase__,	UpperCamelCase__				:					List[Any]					=					incoming_node.match(
					    UpperCAmelCase_)

					# 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(UpperCAmelCase_)

					# 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:
							UpperCamelCase__				:					Tuple					=					remaining_prefix

							UpperCamelCase__				:					str					=					self.nodes[matching_string[0]]
							UpperCamelCase__				:					Optional[Any]					=					RadixNode(UpperCAmelCase_  ,					UpperCAmelCase_)
							UpperCamelCase__				:					str					=					aux_node

							if remaining_word == "":
									UpperCamelCase__				:					int					=					True
							else:
									self.nodes[matching_string[0]].insert(UpperCAmelCase_)

	def      __UpperCamelCase							(      self   :						Union[str, Any]  ,					UpperCAmelCase_   :						str):
			UpperCamelCase__				:					Optional[Any]					=					self.nodes.get(word[0]  ,					UpperCAmelCase_)
			if not incoming_node:
					return False
			else:
					UpperCamelCase__,	UpperCamelCase__,	UpperCamelCase__				:					int					=					incoming_node.match(
					    UpperCAmelCase_)
					# 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(UpperCAmelCase_)

	def      __UpperCamelCase							(      self   :						str  ,					UpperCAmelCase_   :						str):
			UpperCamelCase__				:					Optional[int]					=					self.nodes.get(word[0]  ,					UpperCAmelCase_)
			if not incoming_node:
					return False
			else:
					UpperCamelCase__,	UpperCamelCase__,	UpperCamelCase__				:					Union[str, Any]					=					incoming_node.match(
					    UpperCAmelCase_)
					# 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(UpperCAmelCase_)
					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:
													UpperCamelCase__				:					List[str]					=					list(self.nodes.values())[0]
													UpperCamelCase__				:					Tuple					=					merging_node.is_leaf
													self.prefix += merging_node.prefix
													UpperCamelCase__				:					Tuple					=					merging_node.nodes
                    # If there is more than 1 edge, we just mark it as non-leaf
									elif len(incoming_node.nodes) > 1:
											UpperCamelCase__				:					str					=					False
									# If there is 1 edge, we merge it with its child
									else:
											UpperCamelCase__				:					List[Any]					=					list(incoming_node.nodes.values())[0]
											UpperCamelCase__				:					Optional[Any]					=					merging_node.is_leaf
											incoming_node.prefix += merging_node.prefix
											UpperCamelCase__				:					Union[str, Any]					=					merging_node.nodes

									return True





	def      __UpperCamelCase							(      self   :						str  ,					UpperCAmelCase_   :						int = 0):
			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       __UpperCAmelCase						(  )							->     bool:
		UpperCamelCase__				:					Union[str, Any]					=					'banana bananas bandana band apple all beast'.split()
		UpperCamelCase__				:					List[Any]					=					RadixNode()
		root.insert_many(lowerCamelCase_)

		assert all(root.find(lowerCamelCase_) 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       __UpperCAmelCase						(  )							->     None:
		assert test_trie()







def       __UpperCAmelCase						(  )							->     None:
		UpperCamelCase__				:					List[Any]					=					RadixNode()
		UpperCamelCase__				:					List[str]					=					'banana bananas bandanas bandana band apple all beast'.split()
		root.insert_many(lowerCamelCase_)

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


if __name__ == "__main__":
		main()




