

from __future__ import annotations

from math import pi

def    A_  (							a					,   a					,   a  ):

      """simple docstring"""



      if (inductance, frequency, reactance).count(0  ) != 1:
            raise ValueError('One and only one argument must be 0'  )
      if inductance < 0:
            raise ValueError('Inductance cannot be negative'  )
      if frequency < 0:
            raise ValueError('Frequency cannot be negative'  )
      if reactance < 0:
            raise ValueError('Inductive reactance cannot be negative'  )
      if inductance == 0:
            return {"inductance": reactance / (2 * pi * frequency)}
      elif frequency == 0:
            return {"frequency": reactance / (2 * pi * inductance)}
      elif reactance == 0:
            return {"reactance": 2 * pi * frequency * inductance}
      else:
            raise ValueError('Exactly one argument must be 0'  )


if __name__ == "__main__":
 import doctest

 doctest.testmod()









def    A_  (							a  ):

      """simple docstring"""



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

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

      # Base case: C(0) = C(1) = 1
      SCREAMING_SNAKE_CASE_				:  Any           =     1
      if upper_limit > 0:
            SCREAMING_SNAKE_CASE_				:  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(a  ):
                  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     :   Union[str, 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()






