



class SCREAMING_SNAKE_CASE__					:




				'''simple docstring'''






				def __init__(	self,		lowerCamelCase__ = "",		lowerCamelCase__ = False		):
								# Mapping from the first character of the prefix of the node
								A			:	Tuple										=       {}

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

								A			:	str										=       prefix






				def       _lowerCAmelCase (	self,		lowerCamelCase__		):
								A			:	Optional[int]										=       0
								for q, w in zip(self.prefix,		__lowerCamelCase		):
												if q != w:
																break

												x += 1

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






				def       _lowerCAmelCase (	self,		lowerCamelCase__		):
								for word in words:
												self.insert(__lowerCamelCase		)






				def       _lowerCAmelCase (	self,		lowerCamelCase__		):
								# Case 1: If the word is the prefix of the node
								# Solution: We set the current node as leaf
								if self.prefix == word:
												A			:	List[str]										=       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			:	List[str]										=       RadixNode(prefix=__lowerCamelCase,		is_leaf=__lowerCamelCase		)

								else:
												A			:	Optional[Any]										=       self.nodes[word[0]]
												A					,							A					,							A			:	List[str]										=       incoming_node.match(
												    __lowerCamelCase		)

												# 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(__lowerCamelCase		)

												# 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			:	Optional[int]										=       remaining_prefix

																A			:	Optional[Any]										=       self.nodes[matching_string[0]]
																A			:	Optional[int]										=       RadixNode(__lowerCamelCase,		__lowerCamelCase		)
																A			:	Tuple										=       aux_node

																if remaining_word == "":
																				A			:	Any										=       True
																else:
																				self.nodes[matching_string[0]].insert(__lowerCamelCase		)






				def       _lowerCAmelCase (	self,		lowerCamelCase__		):
								A			:	Tuple										=       self.nodes.get(word[0],		__lowerCamelCase		)
								if not incoming_node:
												return False
								else:
												A					,							A					,							A			:	Optional[Any]										=       incoming_node.match(
												    __lowerCamelCase		)
												# 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(__lowerCamelCase		)






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

																				return True






				def       _lowerCAmelCase (	self,		lowerCamelCase__ = 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:



				"""simple docstring"""






				A			:	str										=       """banana bananas bandana band apple all beast""".split()
				A			:	Union[str, Any]										=       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      __UpperCamelCase     (  )	->  None:



				"""simple docstring"""






				assert test_trie()




def      __UpperCamelCase     (  )	->  None:



				"""simple docstring"""






				A			:	Optional[Any]										=       RadixNode()
				A			:	Tuple										=       """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()







from __future__ import annotations




def      __UpperCamelCase     (  _lowerCAmelCase		)	->  list[int]:



    """simple docstring"""






    A			:	Tuple										=       2
    A			:	List[Any]										=       []
    while i * i <= n:
        if n % i:
            i += 1
        else:
            n //= i
            factors.append(_lowerCAmelCase		)
    if n > 1:
        factors.append(_lowerCAmelCase		)
    return factors


if __name__ == "__main__":
     import doctest

     doctest.testmod()


