

lowerCAmelCase     :   List[Any]						     =  {
    """Pillow""": """Pillow""",
    """accelerate""": """accelerate>=0.11.0""",
    """compel""": """compel==0.1.8""",
    """black""": """black~=23.1""",
    """datasets""": """datasets""",
    """filelock""": """filelock""",
    """flax""": """flax>=0.4.1""",
    """hf-doc-builder""": """hf-doc-builder>=0.3.0""",
    """huggingface-hub""": """huggingface-hub>=0.13.2""",
    """requests-mock""": """requests-mock==1.10.0""",
    """importlib_metadata""": """importlib_metadata""",
    """invisible-watermark""": """invisible-watermark""",
    """isort""": """isort>=5.5.4""",
    """jax""": """jax>=0.2.8,!=0.3.2""",
    """jaxlib""": """jaxlib>=0.1.65""",
    """Jinja2""": """Jinja2""",
    """k-diffusion""": """k-diffusion>=0.0.12""",
    """torchsde""": """torchsde""",
    """note_seq""": """note_seq""",
    """librosa""": """librosa""",
    """numpy""": """numpy""",
    """omegaconf""": """omegaconf""",
    """parameterized""": """parameterized""",
    """protobuf""": """protobuf>=3.20.3,<4""",
    """pytest""": """pytest""",
    """pytest-timeout""": """pytest-timeout""",
    """pytest-xdist""": """pytest-xdist""",
    """ruff""": """ruff>=0.0.241""",
    """safetensors""": """safetensors""",
    """sentencepiece""": """sentencepiece>=0.1.91,!=0.1.92""",
    """scipy""": """scipy""",
    """onnx""": """onnx""",
    """regex""": """regex!=2019.12.17""",
    """requests""": """requests""",
    """tensorboard""": """tensorboard""",
    """torch""": """torch>=1.4""",
    """torchvision""": """torchvision""",
    """transformers""": """transformers>=4.25.1""",
    """urllib3""": """urllib3<=2.0.0""",
}









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()






