


'''simple docstring'''




class 			_lowercase :
   def __init__(						self       :      Optional[int]      ) ->							None:
        __snake_case           =						{}  # Mapping from char to TrieNode
        __snake_case           =						False
   def a  (						self       :      List[str]       ,   SCREAMING_SNAKE_CASE_       :      list[str]      ) ->							None:
        for word in words:
             self.insert(UpperCamelCase__      )
   def a  (						self       :      Optional[int]       ,   SCREAMING_SNAKE_CASE_       :      str      ) ->							None:
        __snake_case           =						self
        for char in word:
             if char not in curr.nodes:
                  __snake_case           =						TrieNode()
             __snake_case           =						curr.nodes[char]
        __snake_case           =						True
   def a  (						self       :      str       ,   SCREAMING_SNAKE_CASE_       :      str      ) ->							bool:
        __snake_case           =						self
        for char in word:
             if char not in curr.nodes:
                  return False
             __snake_case           =						curr.nodes[char]
        return curr.is_leaf





   def a  (						self       :      Union[str, Any]       ,   SCREAMING_SNAKE_CASE_       :      str      ) ->							None:

        def _delete(SCREAMING_SNAKE_CASE_       :      TrieNode       ,   SCREAMING_SNAKE_CASE_       :      str       ,   SCREAMING_SNAKE_CASE_       :      int      ) -> bool:
             if index == len(UpperCamelCase__      ):
                  # If word does not exist
                  if not curr.is_leaf:
                       return False
                  __snake_case           =						False
                  return len(curr.nodes      ) == 0
             __snake_case           =						word[index]
             __snake_case           =						curr.nodes.get(UpperCamelCase__      )
             # If char not in current trie node
             if not char_node:
                  return False
             # Flag to check if node can be deleted
             __snake_case           =						_delete(UpperCamelCase__       ,   UpperCamelCase__       ,   index + 1      )
             if delete_curr:
                  del curr.nodes[char]
                  return len(curr.nodes      ) == 0
             return delete_curr

        _delete(self       ,   UpperCamelCase__       ,   0      )





def   _a		(lowercase__			:   TrieNode							,   lowercase__			:   str						)			->			Any:






     """simple docstring"""
     if node.is_leaf:
          print(__snake_case							,   end=' '						)

     for key, value in node.nodes.items():
          print_words(__snake_case							,   word + key						)





def   _a		()			->			List[Any]:






     """simple docstring"""
     __snake_case           =						'banana bananas bandana band apple all beast'.split()
     __snake_case           =						TrieNode()
     root.insert_many(__snake_case						)
     # print_words(root, "")
     assert all(root.find(__snake_case						) for word in words						)
     assert root.find('banana'						)
     assert not root.find('bandanas'						)
     assert not root.find('apps'						)
     assert root.find('apple'						)
     assert root.find('all'						)
     root.delete('all'						)
     assert not root.find('all'						)
     root.delete('banana'						)
     assert not root.find('banana'						)
     assert root.find('bananas'						)
     return True





def   _a		(lowercase__			:   str							,   lowercase__			:   bool						)			->			Any:






     """simple docstring"""
     print(str(__snake_case						)							,   'works!' if passes else 'doesn\'t work :('						)





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






     """simple docstring"""
     assert test_trie()





def   _a		()			->			Optional[Any]:






     """simple docstring"""
     print_results('Testing trie functionality'							,   test_trie()						)


if __name__ == "__main__":
       main()





'''simple docstring'''






import math





def  _SCREAMING_SNAKE_CASE		(      __snake_case							:			int				):
     _A    		=  []
     _A    		=  2
     _A    		=  int(math.sqrt(__snake_case				)				)  # Size of every segment
     _A    		=  [True] * (end + 1)
     _A    		=  []

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

     _A    		=  end + 1
     _A    		=  min(2 * end   ,		__snake_case				)

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

               for j in range(__snake_case   ,		high + 1   ,		__snake_case				):
                    _A    		=  False

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

          _A    		=  high + 1
          _A    		=  min(high + end   ,		__snake_case				)

     return prime
print(sieve(10**6))



