


"""simple docstring"""




from copy import deepcopy
class 					__lowerCAmelCase					:


		'''simple docstring'''



		def __init__(  self							, _a = None							, _a = None      ):

				if arr is None and size is not None:
						__a           =			size
						__a           =			[0] * size
				elif arr is not None:
						self.init(_a      )
				else:
						raise ValueError('''Either arr or size must be specified'''      )

		def 			__UpperCAmelCase       (  self							, _a      ):
				__a           =			len(_a      )
				__a           =			deepcopy(_a      )
				for i in range(1							, self.size      ):
						__a           =			self.next_(_a      )
						if j < self.size:
								self.tree[j] += self.tree[i]

		def 			__UpperCAmelCase       (  self      ):
				__a           =			self.tree[:]
				for i in range(self.size - 1							, 0							, -1      ):
						__a           =			self.next_(_a      )
						if j < self.size:
								arr[j] -= arr[i]
				return arr

		@staticmethod
		def 			__UpperCAmelCase       (  _a      ):
				return index + (index & (-index))

		@staticmethod
		def 			__UpperCAmelCase       (  _a      ):
				return index - (index & (-index))

		def 			__UpperCAmelCase       (  self							, _a							, _a      ):
				if index == 0:
						self.tree[0] += value
						return
				while index < self.size:
						self.tree[index] += value
						__a           =			self.next_(_a      )

		def 			__UpperCAmelCase       (  self							, _a							, _a      ):
				self.add(_a							, value - self.get(_a      )      )

		def 			__UpperCAmelCase       (  self							, _a      ):
				if right == 0:
						return 0
				__a           =			self.tree[0]
				right -= 1  # make right inclusive
				while right > 0:
						result += self.tree[right]
						__a           =			self.prev(_a      )
				return result

		def 			__UpperCAmelCase       (  self							, _a							, _a      ):
				return self.prefix(_a      ) - self.prefix(_a      )

		def 			__UpperCAmelCase       (  self							, _a      ):
				return self.query(_a							, index + 1      )





		def 			__UpperCAmelCase       (  self							, _a      ):
				value -= self.tree[0]
				if value < 0:
						return -1

				__a           =			1  # Largest power of 2 <= size
				while j * 2 < self.size:
						j *= 2

				__a           =			0

				while j > 0:
						if i + j < self.size and self.tree[i + j] <= value:
								value -= self.tree[i + j]
								i += j
						j //= 2
				return i


if __name__ == "__main__":
				import doctest

				doctest.testmod()










"""simple docstring"""







class       SCREAMING_SNAKE_CASE__				:
       """simple docstring"""


       def __init__(						self		,     snake_case__ = ""		,     snake_case__ = False						):






         """simple docstring"""





         lowerCAmelCase     :     dict[str, RadixNode]								=							{}

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

         lowerCAmelCase     :     str								=							prefix

       def        lowercase__							(						self		,     snake_case__						):






         """simple docstring"""





         lowerCAmelCase     :     Dict								=							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        lowercase__							(						self		,     snake_case__						):






         """simple docstring"""





         for word in words:
           self.insert(snake_case__						)

       def        lowercase__							(						self		,     snake_case__						):






         """simple docstring"""





         if self.prefix == word:
           lowerCAmelCase     :     Union[str, Any]								=							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:
           lowerCAmelCase     :     Optional[Any]								=							RadixNode(prefix=snake_case__		,     is_leaf=snake_case__						)

         else:
           lowerCAmelCase     :     Tuple								=							self.nodes[word[0]]
           lowerCAmelCase						,  lowerCAmelCase						,  lowerCAmelCase     :     Optional[Any]								=							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:
             lowerCAmelCase     :     Optional[Any]								=							remaining_prefix

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

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

       def        lowercase__							(						self		,     snake_case__						):






         """simple docstring"""





         lowerCAmelCase     :     str								=							self.nodes.get(word[0]		,     snake_case__						)
         if not incoming_node:
           return False
         else:
           lowerCAmelCase						,  lowerCAmelCase						,  lowerCAmelCase     :     int								=							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        lowercase__							(						self		,     snake_case__						):






         """simple docstring"""





         lowerCAmelCase     :     int								=							self.nodes.get(word[0]		,     snake_case__						)
         if not incoming_node:
           return False
         else:
           lowerCAmelCase						,  lowerCAmelCase						,  lowerCAmelCase     :     Union[str, Any]								=							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:
                   lowerCAmelCase     :     List[str]								=							list(self.nodes.values()						)[0]
                   lowerCAmelCase     :     List[str]								=							merging_node.is_leaf
                   self.prefix += merging_node.prefix
                   lowerCAmelCase     :     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:
                 lowerCAmelCase     :     Optional[int]								=							False
               # If there is 1 edge, we merge it with its child
               else:
                 lowerCAmelCase     :     Optional[Any]								=							list(incoming_node.nodes.values()						)[0]
                 lowerCAmelCase     :     int								=							merging_node.is_leaf
                 incoming_node.prefix += merging_node.prefix
                 lowerCAmelCase     :     Tuple								=							merging_node.nodes

               return True







       def        lowercase__							(						self		,     snake_case__ = 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 					a__			(				):


  '''simple docstring'''







  lowerCAmelCase     :     Union[str, Any]								=							"banana bananas bandana band apple all beast".split()
  lowerCAmelCase     :     List[str]								=							RadixNode()
  root.insert_many(SCREAMING_SNAKE_CASE				)

  assert all(root.find(SCREAMING_SNAKE_CASE				) 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 					a__			(				):


  '''simple docstring'''







  assert test_trie()
def 					a__			(				):


  '''simple docstring'''







  lowerCAmelCase     :     Dict								=							RadixNode()
  lowerCAmelCase     :     Optional[Any]								=							"banana bananas bandanas bandana band apple all beast".split()
  root.insert_many(SCREAMING_SNAKE_CASE				)

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


if __name__ == "__main__":
     main()





