






"""simple docstring"""


def     snake_case						(A_   :int   ):







  '''simple docstring'''

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

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

  # Base case: C(0) = C(1) = 1
  a  :    Optional[int]       =     1
  if upper_limit > 0:
    a  :    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(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:
         _UpperCamelCase       :					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()












"""simple docstring"""


_UpperCamelCase       :					Tuple									=		'\n# Transformers installation\n! pip install transformers datasets\n# To install from source instead of the last release, comment the command above and uncomment the following one.\n# ! pip install git+https://github.com/huggingface/transformers.git\n'

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




