





def 				SCREAMING_SNAKE_CASE__							(	snake_case__	:int  )   ->    "list[int]":
  if upper_limit < 0:
    raise ValueError('Limit for the Catalan sequence must be ≥ 0'  )

  _lowercase						    =			[0] * (upper_limit + 1)

  # Base case: C(0) = C(1) = 1
  _lowercase						    =			1
  if upper_limit > 0:
    _lowercase						    =			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:
                  snake_case								=							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()




from ...configuration_utils import PretrainedConfig
from ...utils import logging


__snake_case     :Optional[Any]			       =logging.get_logger(__name__)

__snake_case     :Tuple			       ={
    'transfo-xl-wt103': 'https://huggingface.co/transfo-xl-wt103/resolve/main/config.json',
}



class        lowerCAmelCase__					(  _lowerCamelCase       ):
				A_   :     Any								=     'transfo-xl'
				A_   :     Dict								=     ['mems']
				A_   :     int								=     {
				    'n_token': 'vocab_size',
				    'hidden_size': 'd_model',
				    'num_attention_heads': 'n_head',
				    'num_hidden_layers': 'n_layer',
				}


				def __init__(							self      :  Optional[Any]						, __UpperCamelCase      :  str=267_735						, __UpperCamelCase      :  int=[20_000, 40_000, 200_000]						, __UpperCamelCase      :  List[str]=1_024						, __UpperCamelCase      :  Union[str, Any]=1_024						, __UpperCamelCase      :  Optional[Any]=16						, __UpperCamelCase      :  Dict=64						, __UpperCamelCase      :  Optional[Any]=4_096						, __UpperCamelCase      :  int=4						, __UpperCamelCase      :  List[str]=False						, __UpperCamelCase      :  Optional[int]=18						, __UpperCamelCase      :  int=1_600						, __UpperCamelCase      :  Dict=1_000						, __UpperCamelCase      :  Optional[Any]=True						, __UpperCamelCase      :  Optional[Any]=True						, __UpperCamelCase      :  Optional[Any]=0						, __UpperCamelCase      :  Any=-1						, __UpperCamelCase      :  Any=True						, __UpperCamelCase      :  List[Any]=0.1						, __UpperCamelCase      :  str=0.0						, __UpperCamelCase      :  Dict=True						, __UpperCamelCase      :  int="normal"						, __UpperCamelCase      :  List[Any]=0.0_1						, __UpperCamelCase      :  str=0.0_1						, __UpperCamelCase      :  Any=0.0_2						, __UpperCamelCase      :  str=1e-5						, __UpperCamelCase      :  Optional[int]=0						, **__UpperCamelCase      :  Any						, )		->     int:
											A      						=    vocab_size
											A      						=    []
											self.cutoffs.extend(__UpperCamelCase       )
											if proj_share_all_but_first:
																		A      						=    [False] + [True] * len(self.cutoffs       )
											else:
																		A      						=    [False] + [False] * len(self.cutoffs       )
											A      						=    d_model
											A      						=    d_embed
											A      						=    d_head
											A      						=    d_inner
											A      						=    div_val
											A      						=    pre_lnorm
											A      						=    n_layer
											A      						=    n_head
											A      						=    mem_len
											A      						=    same_length
											A      						=    attn_type
											A      						=    clamp_len
											A      						=    sample_softmax
											A      						=    adaptive
											A      						=    dropout
											A      						=    dropatt
											A      						=    untie_r
											A      						=    init
											A      						=    init_range
											A      						=    proj_init_std
											A      						=    init_std
											A      						=    layer_norm_epsilon
											super().__init__(eos_token_id=__UpperCamelCase						, **__UpperCamelCase       )


				@property
				def __UpperCamelCase						(							self      :  Any       )		->     Optional[int]:
											# Message copied from Transformer-XL documentation
											logger.info(f'''The model {self.model_type} is one of the few models that has no sequence length limit.'''       )
											return -1


				@max_position_embeddings.setter
				def __UpperCamelCase						(							self      :  List[Any]						, __UpperCamelCase      :  List[Any]       )		->     List[Any]:
											# Message copied from Transformer-XL documentation
											raise NotImplementedError(
											    f'''The model {self.model_type} is one of the few models that has no sequence length limit.'''       )