


class A__     :



  """simple docstring"""



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

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

        a__	:  Optional[Any]     =   prefix

  def    _UpperCamelCase( self			:  List[Any]				,				lowerCamelCase__			:  str       ):
        a__	:  List[str]     =   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    _UpperCamelCase( self			:  str				,				lowerCamelCase__			:  list[str]       ):
        for word in words:
              self.insert(lowerCamelCase__       )

  def    _UpperCamelCase( self			:  Dict				,				lowerCamelCase__			:  str       ):
        # Case 1: If the word is the prefix of the node
        # Solution: We set the current node as leaf
        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__	:  Optional[int]     =   RadixNode(prefix=lowerCamelCase__				,				is_leaf=lowerCamelCase__       )

        else:
              a__	:  List[str]     =   self.nodes[word[0]]
              a__,	a__,	a__	:  Dict     =   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[Any]     =   remaining_prefix

                    a__	:  str     =   self.nodes[matching_string[0]]
                    a__	:  Union[str, Any]     =   RadixNode(lowerCamelCase__				,				lowerCamelCase__       )
                    a__	:  int     =   aux_node

                    if remaining_word == "":
                          a__	:  Union[str, Any]     =   True
                    else:
                          self.nodes[matching_string[0]].insert(lowerCamelCase__       )

  def    _UpperCamelCase( self			:  Optional[int]				,				lowerCamelCase__			:  str       ):
        a__	:  List[Any]     =   self.nodes.get(word[0]				,				lowerCamelCase__       )
        if not incoming_node:
              return False
        else:
              a__,	a__,	a__	:  List[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    _UpperCamelCase( self			:  int				,				lowerCamelCase__			:  str       ):
        a__	:  Any     =   self.nodes.get(word[0]				,				lowerCamelCase__       )
        if not incoming_node:
              return False
        else:
              a__,	a__,	a__	:  Tuple     =   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__	:  Any     =   list(self.nodes.values()       )[0]
                                      a__	:  List[str]     =   merging_node.is_leaf
                                      self.prefix += merging_node.prefix
                                      a__	:  List[str]     =   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__	:  Union[str, Any]     =   list(incoming_node.nodes.values()       )[0]
                                a__	:  Optional[Any]     =   merging_node.is_leaf
                                incoming_node.prefix += merging_node.prefix
                                a__	:  Dict     =   merging_node.nodes

                          return True

  def    _UpperCamelCase( self			:  Optional[int]				,				lowerCamelCase__			:  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:
      a__	:  Tuple     =   "banana bananas bandana band apple all beast".split()
      a__	:  Union[str, Any]     =   RadixNode()
      root.insert_many(__a      )

      assert all(root.find(__a      ) 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:
      a__	:  Tuple     =   RadixNode()
      a__	:  int     =   "banana bananas bandanas bandana band apple all beast".split()
      root.insert_many(__a      )

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


if __name__ == "__main__":
    main()





'''simple docstring'''






from maths.is_square_free import is_square_free
from maths.prime_factors import prime_factors







def 							UpperCamelCase_     (       A__   :  int   ):
  '''simple docstring'''





  lowerCAmelCase_     : Any     =  prime_factors(A__   )
  if is_square_free(A__   ):
    return -1 if len(A__   ) % 2 else 1
  return 0


if __name__ == "__main__":
  import doctest

  doctest.testmod()



