




from ..utils import DummyObject, requires_backends




class 		UpperCamelCase__	(metaclass=lowerCAmelCase__     ):

    '''simple docstring'''



    lowerCamelCase_      :	Optional[int]	     =      ["torch", "scipy"]







    def __init__(    self     ,  *UpperCamelCase__     ,  **UpperCamelCase__     )     ->      Optional[int]:
           requires_backends(self     ,  ["torch", "scipy"]     )







    @classmethod
    def     _lowercase     (    cls     ,  *UpperCamelCase__     ,  **UpperCamelCase__     )     ->      Optional[int]:
           requires_backends(cls     ,  ["torch", "scipy"]     )







    @classmethod
    def     _lowercase     (    cls     ,  *UpperCamelCase__     ,  **UpperCamelCase__     )     ->      List[str]:
           requires_backends(cls     ,  ["torch", "scipy"]     )










"""simple docstring"""







def    UpperCAmelCase__       (lowerCAmelCase_   ):




					'''simple docstring'''


					if upper_limit < 0:
										raise ValueError("Limit for the Catalan sequence must be ≥ 0"   )

					__SCREAMING_SNAKE_CASE						   =				[0] * (upper_limit + 1)

					# Base case: C(0) = C(1) = 1
					__SCREAMING_SNAKE_CASE						   =				1
					if upper_limit > 0:
										__SCREAMING_SNAKE_CASE						   =				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:
						a__				:							List[str]						=     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()
