



"""simple docstring"""






def   snake_case__     (	__lowerCamelCase       :					int			):
			"""simple docstring"""
			if upper_limit < 0:
						raise ValueError('''Limit for the Catalan sequence must be ≥ 0'''			)

			lowerCamelCase__	:	List[str]				=[0] * (upper_limit + 1)

			# Base case: C(0) = C(1) = 1
			lowerCamelCase__	:	str				=1
			if upper_limit > 0:
						lowerCamelCase__	:	Optional[int]				=1

			# Recurrence relation: C(i) = sum(C(j).C(i-j-1)), from j = 0 to i
			for i in range(2							,	upper_limit + 1			):
						for j in range(__lowerCamelCase			):
									catalan_list[i] += catalan_list[j] * catalan_list[i - j - 1]

			return catalan_list


if __name__ == "__main__":
		print("\n********* Catalan Numbers Using Dynamic Programming ************\n")
		print("\n*** Enter -1 at any time to quit ***")
		print("\nEnter the upper limit (≥ 0) for the Catalan number sequence: ", end="")
		try:
				while True:
						_lowercase				:				List[Any]   		=		int(input().strip())
						if N < 0:
								print("\n********* Goodbye!! ************")
								break
						else:
								print(f'The Catalan numbers from 0 through {N} are:')
								print(catalan_numbers(N))
								print("Try another upper limit for the sequence: ", end="")
		except (NameError, ValueError):
				print("\n********* Invalid input, goodbye! ************\n")

		import doctest

		doctest.testmod()









"""simple docstring"""






from __future__ import annotations

from collections.abc import Iterator

class  __SCREAMING_SNAKE_CASE			:


					'''simple docstring'''





					def __init__( self							:						str,						lowerCamelCase							:						int  )->      None:
								lowerCamelCase__	:	str				=value
								lowerCamelCase__	:	Node | None				=None
								lowerCamelCase__	:	Node | None				=None





class  __SCREAMING_SNAKE_CASE			:


					'''simple docstring'''





					def __init__( self							:						int,						lowerCamelCase							:						Node  )->      None:
								lowerCamelCase__	:	Any				=tree



					def 	snake_case ( self							:						str,						lowerCamelCase							:						Node | None  )->      int:
								if node is None:
											return 0
								return node.value + (
								    self.depth_first_search(node.left  ) + self.depth_first_search(node.right  )
								)




					def __iter__( self							:						Dict  )->      Iterator[int]:
								yield self.depth_first_search(self.tree  )


if __name__ == "__main__":
		import doctest

		doctest.testmod()




