

class   UpperCamelCase			:

    def __init__(      self			:   Optional[Any]				,     snake_case__			:   str = ""				,     snake_case__			:   bool = False     ):

     """simple docstring"""






     SCREAMING_SNAKE_CASE		    =      {}

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

     SCREAMING_SNAKE_CASE		    =      prefix

    def UpperCamelCase      (      self			:   List[str]				,     snake_case__			:   str     ):

     """simple docstring"""






     SCREAMING_SNAKE_CASE		    =      0
     for q, w in zip(self.prefix				,     snake_case__     ):
      if q != w:
       break

      x += 1

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

    def UpperCamelCase      (      self			:   Tuple				,     snake_case__			:   list[str]     ):

     """simple docstring"""






     for word in words:
      self.insert(snake_case__     )

    def UpperCamelCase      (      self			:   Optional[int]				,     snake_case__			:   str     ):

     """simple docstring"""






     if self.prefix == word:
      SCREAMING_SNAKE_CASE		    =      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:
      SCREAMING_SNAKE_CASE		    =      RadixNode(prefix=snake_case__				,     is_leaf=snake_case__     )

     else:
      SCREAMING_SNAKE_CASE		    =      self.nodes[word[0]]
      SCREAMING_SNAKE_CASE    ,						SCREAMING_SNAKE_CASE    ,						SCREAMING_SNAKE_CASE		    =      incoming_node.match(
          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(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:
       SCREAMING_SNAKE_CASE		    =      remaining_prefix

       SCREAMING_SNAKE_CASE		    =      self.nodes[matching_string[0]]
       SCREAMING_SNAKE_CASE		    =      RadixNode(snake_case__				,     snake_case__     )
       SCREAMING_SNAKE_CASE		    =      aux_node

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

    def UpperCamelCase      (      self			:   str				,     snake_case__			:   str     ):

     """simple docstring"""






     SCREAMING_SNAKE_CASE		    =      self.nodes.get(word[0]				,     snake_case__     )
     if not incoming_node:
      return False
     else:
      SCREAMING_SNAKE_CASE    ,						SCREAMING_SNAKE_CASE    ,						SCREAMING_SNAKE_CASE		    =      incoming_node.match(
          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(snake_case__     )

    def UpperCamelCase      (      self			:   List[str]				,     snake_case__			:   str     ):

     """simple docstring"""






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

        return True




    def UpperCamelCase      (      self			:   str				,     snake_case__			:   int = 0     ):

     """simple docstring"""






     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'''


 SCREAMING_SNAKE_CASE		    =      'banana bananas bandana band apple all beast'.split()
 SCREAMING_SNAKE_CASE		    =      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'''


 SCREAMING_SNAKE_CASE		    =      RadixNode()
 SCREAMING_SNAKE_CASE		    =      '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()




import math


def 							__lowerCAmelCase     (							_UpperCamelCase		:	int						)		->				list[int]:
 '''simple docstring'''


 SCREAMING_SNAKE_CASE		    =      []
 SCREAMING_SNAKE_CASE		    =      2
 SCREAMING_SNAKE_CASE		    =      int(math.sqrt(_UpperCamelCase						)						)  # Size of every segment
 SCREAMING_SNAKE_CASE		    =      [True] * (end + 1)
 SCREAMING_SNAKE_CASE		    =      []

 while start <= end:
  if temp[start] is True:
   in_prime.append(_UpperCamelCase						)
   for i in range(start * start		,				end + 1		,				_UpperCamelCase						):
    SCREAMING_SNAKE_CASE		    =      False
  start += 1
 prime += in_prime

 SCREAMING_SNAKE_CASE		    =      end + 1
 SCREAMING_SNAKE_CASE		    =      min(2 * end		,				_UpperCamelCase						)

 while low <= n:
  SCREAMING_SNAKE_CASE		    =      [True] * (high - low + 1)
  for each in in_prime:
   SCREAMING_SNAKE_CASE		    =      math.floor(low / each						) * each
   if t < low:
    t += each

   for j in range(_UpperCamelCase		,				high + 1		,				_UpperCamelCase						):
    SCREAMING_SNAKE_CASE		    =      False

  for j in range(len(_UpperCamelCase						)						):
   if temp[j] is True:
    prime.append(j + low						)

  SCREAMING_SNAKE_CASE		    =      high + 1
  SCREAMING_SNAKE_CASE		    =      min(high + end		,				_UpperCamelCase						)

 return prime




print(sieve(10**6))

