






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

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

							# Base case: C(0) = C(1) = 1
							__lowercase      :							Tuple				=     1
							if upper_limit > 0:
														__lowercase      :							Dict				=     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:
			lowerCamelCase : Dict						   =       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()







def       snake_case_		(     lowerCAmelCase_       :						int       ,       lowerCAmelCase_       :						int      ):
							return int((input_a, input_a).count(0      ) == 0      )
def       snake_case_		(     ):
							assert and_gate(0       ,       0      ) == 0
							assert and_gate(0       ,       1      ) == 0
							assert and_gate(1       ,       0      ) == 0
							assert and_gate(1       ,       1      ) == 1


if __name__ == "__main__":
	test_and_gate()
	print(and_gate(1, 0))
	print(and_gate(0, 0))
	print(and_gate(0, 1))
	print(and_gate(1, 1))