


class  snake_case_     :
					def __init__(   self     :List[Any]    ,__snake_case     :str = ""    ,__snake_case     :bool = False   )      ->					None:
												# 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     :List[str]    ,__snake_case     :str   )      ->					tuple[str, str, str]:
												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     :Union[str, Any]    ,__snake_case     :list[str]   )      ->					None:
												for word in words:
																			self.insert(__snake_case   )
					def 				lowerCamelCase__(   self     :str    ,__snake_case     :str   )      ->					None:
												# 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__   ,      a__   ,      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     :Dict    ,__snake_case     :str   )      ->					bool:
												a__    =  self.nodes.get(word[0]    ,__snake_case   )
												if not incoming_node:
																			return False
												else:
																			a__   ,      a__   ,      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     :List[str]    ,__snake_case     :str   )      ->					bool:
												a__    =  self.nodes.get(word[0]    ,__snake_case   )
												if not incoming_node:
																			return False
												else:
																			a__   ,      a__   ,      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     :str    ,__snake_case     :int = 0   )      ->					None:
												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(__lowerCAmelCase     )

							assert all(root.find(__lowerCAmelCase     ) 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(__lowerCAmelCase     )

							print('Words:'      ,					__lowerCAmelCase     )
							print('Tree:'     )
							root.print_tree()


if __name__ == "__main__":
						main()








def 							__lowercase     (				__lowerCAmelCase							:       int = 2_0_0     ):
							a__    =  [1, 2, 5, 1_0, 2_0, 5_0, 1_0_0, 2_0_0]
							a__    =  [0] * (pence + 1)
							a__    =  1  # base case: 1 way to make 0 pence

							for coin in coins:
														for i in range(__lowerCAmelCase      ,					pence + 1      ,					1     ):
																					number_of_ways[i] += number_of_ways[i - coin]
							return number_of_ways[pence]


if __name__ == "__main__":
						assert solution(2_00) == 7_36_82




