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

 SCREAMING_SNAKE_CASE__: List[Any]=   [0] * (upper_limit + 1)

 # Base case: C(0) = C(1) = 1
 SCREAMING_SNAKE_CASE__: List[str]=   1
 if upper_limit > 0:
  SCREAMING_SNAKE_CASE__: List[str]=   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(snake_case_   ):
   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_  : 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()




A_			:					Union[str, Any]    			=     '\n# Installazione di Transformers\n! pip install transformers datasets\n# Per installare dalla fonte invece dell\'ultima versione rilasciata, commenta il comando sopra e\n# rimuovi la modalità commento al comando seguente.\n# ! pip install git+https://github.com/huggingface/transformers.git\n'

A_			:					str    			=     [{'type': 'code', 'content': INSTALL_CONTENT}]
A_			:					Any    			=     {
    '{processor_class}': 'FakeProcessorClass',
    '{model_class}': 'FakeModelClass',
    '{object_class}': 'FakeObjectClass',
}



