



class 							lowerCAmelCase__  :







     def __init__(       self      :     int			,		_A      :     Optional[int] = ""			,		_A      :     Union[str, Any] = False):
           A__	:							List[Any]						    = {}

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

           A__	:							Dict						    = prefix







     def  _lowercase			(       self      :     Optional[Any]			,		_A      :     Tuple):
           A__	:							Tuple						    = 0
           for q, w in zip(self.prefix			,		_A):
                 if q != w:
                       break

                 x += 1

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







     def  _lowercase			(       self      :     Optional[int]			,		_A      :     Tuple):

           for word in words:
                 self.insert(_A)







     def  _lowercase			(       self      :     Any			,		_A      :     Tuple):

           if self.prefix == word:
                 A__	:							Optional[int]						    = 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=_A			,		is_leaf=_A)

           else:
                 A__	:							str						    = self.nodes[word[0]]
                 A__    ,       A__    ,       A__	:							Optional[int]						    = incoming_node.match(
                     _A)

                 # 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(_A)

                 # 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__	:							Dict						    = remaining_prefix

                       A__	:							Any						    = self.nodes[matching_string[0]]
                       A__	:							Optional[int]						    = RadixNode(_A			,		_A)
                       A__	:							List[Any]						    = aux_node

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







     def  _lowercase			(       self      :     Optional[Any]			,		_A      :     List[Any]):
           A__	:							List[Any]						    = self.nodes.get(word[0]			,		_A)
           if not incoming_node:
                 return False
           else:
                 A__    ,       A__    ,       A__	:							Union[str, Any]						    = incoming_node.match(
                     _A)
                 # 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(_A)







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

                             return True







     def  _lowercase			(       self      :     str			,		_A      :     Tuple = 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 	snake_case__       (					)		->		str:







      """simple docstring"""

      A__	:							Optional[int]						    = "banana bananas bandana band apple all beast".split()
      A__	:							Optional[Any]						    = RadixNode()
      root.insert_many(__lowercase       )

      assert all(root.find(__lowercase       ) 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 	snake_case__       (					)		->		Tuple:







      """simple docstring"""

      assert test_trie()
def 	snake_case__       (					)		->		Union[str, Any]:







      """simple docstring"""

      A__	:							Any						    = RadixNode()
      A__	:							Tuple						    = "banana bananas bandanas bandana band apple all beast".split()
      root.insert_many(__lowercase       )

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


if __name__ == "__main__":
  main()




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







						"""simple docstring"""

						A__	:							Tuple						    = []
						A__	:							Optional[int]						    = 1

						while len(__lowercase       ) < 1E6:
												constant.append(str(__lowercase       )       )
												i += 1

						A__	:							Any						    = "".join(__lowercase       )

						return (
						    int(constant[0]       )
						    * int(constant[9]       )
						    * int(constant[9_9]       )
						    * int(constant[9_9_9]       )
						    * int(constant[9_9_9_9]       )
						    * int(constant[9_9_9_9_9]       )
						    * int(constant[9_9_9_9_9_9]       )
						)


if __name__ == "__main__":
		print(solution())