



from __future__ import annotations

from math import pow, sqrt





def 							A     (					_UpperCAmelCase    :       float							,       _UpperCAmelCase    :       float							,       _UpperCAmelCase    :       float   )    ->			Dict:







			'''simple docstring'''

			if (resistance, reactance, impedance).count(0   ) != 1:
						raise ValueError('One and only one argument must be 0'   )
			if resistance == 0:
						return {"resistance": sqrt(pow(lowerCamelCase_							,       2   ) - pow(lowerCamelCase_							,       2   )   )}
			elif reactance == 0:
						return {"reactance": sqrt(pow(lowerCamelCase_							,       2   ) - pow(lowerCamelCase_							,       2   )   )}
			elif impedance == 0:
						return {"impedance": sqrt(pow(lowerCamelCase_							,       2   ) + pow(lowerCamelCase_							,       2   )   )}
			else:
						raise ValueError('Exactly one argument must be 0'   )


if __name__ == "__main__":
							import doctest

							doctest.testmod()





def 							A     (					_UpperCAmelCase    :       int   )    ->			"list[int]":







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

			_UpperCAmelCase			=       [0] * (upper_limit + 1)

			# Base case: C(0) = C(1) = 1
			_UpperCAmelCase			=       1
			if upper_limit > 0:
						_UpperCAmelCase			=       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(_UpperCAmelCase   ):
									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:
																					UpperCAmelCase__       =	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()
