
def 			UpperCamelCase					(    __lowerCamelCase     : int				,					__lowerCamelCase     : int    ):
       snake_case       :   Any							=      1  # To kept the Calculated Value
       # Since C(n, k) = C(n, n-k)
       if k > (n - k):
              snake_case       :   int							=      n - k
       # Calculate C(n,k)
       for i in range(_lowerCamelCase    ):
              result *= n - i
              result //= i + 1
       return result


def 			UpperCamelCase					(    __lowerCamelCase     : int    ):
       return binomial_coefficient(2 * node_count				,					_lowerCamelCase    ) // (node_count + 1)


def 			UpperCamelCase					(    __lowerCamelCase     : int    ):





       if n < 0:
              raise ValueError("factorial() not defined for negative values"    )
       snake_case       :   Tuple							=      1
       for i in range(1				,					n + 1    ):
              result *= i
       return result


def 			UpperCamelCase					(    __lowerCamelCase     : int    ):
       return catalan_number(_lowerCamelCase    ) * factorial(_lowerCamelCase    )


if __name__ == "__main__":
   __lowerCamelCase							=       int(input("""Enter the number of nodes: """).strip() or 0)
   if node_count <= 0:
      raise ValueError("""We need some nodes to work with.""")
   print(
       F'Given {node_count} nodes, there are {binary_tree_count(node_count)} '
       F'binary trees and {catalan_number(node_count)} binary search trees.'
   )







class  lowerCamelCase__							:




	'''simple docstring'''




	def __init__(					self		:Union[str, Any]						)		-> None:
								__UpperCamelCase	:   dict[str, TrieNode]			   =					{}  # Mapping from char to TrieNode
								__UpperCamelCase	:   List[str]			   =					False







	def    _lowerCamelCase				(					self		:Any     ,   a		:list[str]						)		-> None:
								for word in words:
															self.insert(a						)







	def    _lowerCamelCase				(					self		:List[str]     ,   a		:str						)		-> None:
								__UpperCamelCase	:   Dict			   =					self
								for char in word:
															if char not in curr.nodes:
																						__UpperCamelCase	:   List[Any]			   =					TrieNode()
															__UpperCamelCase	:   List[Any]			   =					curr.nodes[char]
								__UpperCamelCase	:   Union[str, Any]			   =					True







	def    _lowerCamelCase				(					self		:Optional[int]     ,   a		:str						)		-> bool:
								__UpperCamelCase	:   Union[str, Any]			   =					self
								for char in word:
															if char not in curr.nodes:
																						return False
															__UpperCamelCase	:   Union[str, Any]			   =					curr.nodes[char]
								return curr.is_leaf







	def    _lowerCamelCase				(					self		:Any     ,   a		:str						)		-> None:

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

								_delete(self     ,   a     ,   0						)




def 	_SCREAMING_SNAKE_CASE					(		_lowerCamelCase :			TrieNode						,  _lowerCamelCase :			str)					->    None:






							'''simple docstring'''





							if node.is_leaf:
														print(_lowerCamelCase						,  end=" ")

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




def 	_SCREAMING_SNAKE_CASE					(		)					->    bool:






							'''simple docstring'''





							__UpperCamelCase	:   int			   =					"banana bananas bandana band apple all beast".split()
							__UpperCamelCase	:   Union[str, Any]			   =					TrieNode()
							root.insert_many(_lowerCamelCase)
							# print_words(root, "")
							assert all(root.find(_lowerCamelCase) 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 	_SCREAMING_SNAKE_CASE					(		_lowerCamelCase :			str						,  _lowerCamelCase :			bool)					->    None:






							'''simple docstring'''





							print(str(_lowerCamelCase)						,  "works!" if passes else "doesn't work :(")




def 	_SCREAMING_SNAKE_CASE					(		)					->    None:






							'''simple docstring'''





							assert test_trie()




def 	_SCREAMING_SNAKE_CASE					(		)					->    None:






							'''simple docstring'''





							print_results("Testing trie functionality"						,  test_trie())


if __name__ == "__main__":
		main()