


class        snake_case_   :
					def __init__(      self   :Union[str, Any]			,__snake_case   :List[Any] = ""			,__snake_case   :Tuple = False      )					->    str:
												# Mapping from the first character of the prefix of the node
												a__             =     {}

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

												a__             =     prefix
					def  lowerCamelCase__(      self   :Dict			,__snake_case   :List[Any]      )					->    int:
												a__             =     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  lowerCamelCase__(      self   :List[Any]			,__snake_case   :Union[str, Any]      )					->    Tuple:
												for word in words:
																			self.insert(__snake_case      )
					def  lowerCamelCase__(      self   :Optional[Any]			,__snake_case   :int      )					->    Dict:
												# Case 1: If the word is the prefix of the node
												# Solution: We set the current node as leaf
												if self.prefix == word:
																			a__             =     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__             =     RadixNode(prefix=__snake_case			,is_leaf=__snake_case      )

												else:
																			a__             =     self.nodes[word[0]]
																			a__             =     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:
																										a__             =     remaining_prefix

																										a__             =     self.nodes[matching_string[0]]
																										a__             =     RadixNode(__snake_case			,__snake_case      )
																										a__             =     aux_node

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

																																	return True



					def  lowerCamelCase__(      self   :Optional[int]			,__snake_case   :int = 0      )					->    int:
												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 							__lowercase   ( ):
							a__             =     """banana bananas bandana band apple all beast""".split()
							a__             =     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 							__lowercase   ( ):
							assert test_trie()






def 							__lowercase   ( ):
							a__             =     RadixNode()
							a__             =     """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()








'''simple docstring'''


from collections import defaultdict
from math import ceil, sqrt







def 			snake_case_   (  SCREAMING_SNAKE_CASE__ = 100_0000							,      SCREAMING_SNAKE_CASE__ = 10     ):







				"""simple docstring"""





				_SCREAMING_SNAKE_CASE :       defaultdict     		=      defaultdict(SCREAMING_SNAKE_CASE__     )

				for outer_width in range(3							,      (t_limit // 4) + 2     ):
								if outer_width * outer_width > t_limit:
												_SCREAMING_SNAKE_CASE :       int     		=      max(
												    ceil(sqrt(outer_width * outer_width - t_limit     )     )							,      1     )
								else:
												_SCREAMING_SNAKE_CASE :       List[str]     		=      1

								hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

								for hole_width in range(SCREAMING_SNAKE_CASE__							,      outer_width - 1							,      2     ):
												count[outer_width * outer_width - hole_width * hole_width] += 1

				return sum(1 for n in count.values() if 1 <= n <= 10     )


if __name__ == "__main__":
				print(F"{solution() = }")




