def 					snake_case    (			snake_case__     :Dict)		->  "list[int]":






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

       _A	  =    [0] * (upper_limit + 1)

       # Base case: C(0) = C(1) = 1
       _A	  =    1
       if upper_limit > 0:
              _A	  =    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:
            _SCREAMING_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()








'''simple docstring'''
from dataclasses import dataclass
from typing import Optional, Tuple

import torch
from torch import nn
from transformers import RobertaPreTrainedModel, XLMRobertaConfig, XLMRobertaModel
from transformers.utils import ModelOutput
@dataclass
class   lowercase      (				A__   ):

		"""simple docstring"""

		_a       					=							None
		_a       					=							None
		_a       					=							None
		_a       					=							None



class   lowercase      (				A__   ):

		"""simple docstring"""

		def __init__(						self       ,  UpperCamelCase_=1       ,  UpperCamelCase_=0       ,  UpperCamelCase_=2       ,  UpperCamelCase_=512       ,  UpperCamelCase_="cls"       ,  UpperCamelCase_=False       ,  UpperCamelCase_=True       ,  **UpperCamelCase_       ,  ):

							'''simple docstring'''


							super().__init__(pad_token_id=UpperCamelCase_       ,  bos_token_id=UpperCamelCase_       ,  eos_token_id=UpperCamelCase_       ,  **UpperCamelCase_				)
							UpperCamelCase__  :Optional[int]				   =					project_dim
							UpperCamelCase__  :List[str]				   =					pooler_fn
							UpperCamelCase__  :Dict				   =					learn_encoder
							UpperCamelCase__  :Any				   =					use_attention_mask



class   lowercase      (				A__   ):

		"""simple docstring"""

		_a       					=							[R'pooler', R'logit_scale']
		_a       					=							[R'position_ids', R'predictions.decoder.bias']
		_a       					=							'roberta'
		_a       					=							RobertaSeriesConfig




		def __init__(						self       ,  UpperCamelCase_				):

							'''simple docstring'''


							super().__init__(UpperCamelCase_				)
							UpperCamelCase__  :Optional[Any]				   =					XLMRobertaModel(UpperCamelCase_				)
							UpperCamelCase__  :Tuple				   =					nn.Linear(config.hidden_size       ,  config.project_dim				)
							UpperCamelCase__  :Union[str, Any]				   =					getattr(UpperCamelCase_       ,  '''has_pre_transformation'''       ,  UpperCamelCase_				)
							if self.has_pre_transformation:
												UpperCamelCase__  :Any				   =					nn.Linear(config.hidden_size       ,  config.project_dim				)
												UpperCamelCase__  :str				   =					nn.LayerNorm(config.hidden_size       ,  eps=config.layer_norm_eps				)
							self.post_init()




		def        lowerCAmelCase__							(						self       ,  UpperCamelCase_ = None       ,  UpperCamelCase_ = None       ,  UpperCamelCase_ = None       ,  UpperCamelCase_ = None       ,  UpperCamelCase_ = None       ,  UpperCamelCase_ = None       ,  UpperCamelCase_ = None       ,  UpperCamelCase_ = None       ,  UpperCamelCase_ = None       ,  UpperCamelCase_ = None       ,  UpperCamelCase_ = None       ,  ):

							'''simple docstring'''


							UpperCamelCase__  :Optional[int]				   =					return_dict if return_dict is not None else self.config.use_return_dict

							UpperCamelCase__  :str				   =					self.base_model(
							    input_ids=UpperCamelCase_       ,  attention_mask=UpperCamelCase_       ,  token_type_ids=UpperCamelCase_       ,  position_ids=UpperCamelCase_       ,  head_mask=UpperCamelCase_       ,  inputs_embeds=UpperCamelCase_       ,  encoder_hidden_states=UpperCamelCase_       ,  encoder_attention_mask=UpperCamelCase_       ,  output_attentions=UpperCamelCase_       ,  output_hidden_states=True if self.has_pre_transformation else output_hidden_states       ,  return_dict=UpperCamelCase_       ,  )

							if self.has_pre_transformation:
												UpperCamelCase__  :Dict				   =					outputs['''hidden_states'''][-2]
												UpperCamelCase__  :Optional[int]				   =					self.pre_LN(UpperCamelCase_				)
												UpperCamelCase__  :Optional[Any]				   =					self.transformation_pre(UpperCamelCase_				)

												return TransformationModelOutput(
												    projection_state=UpperCamelCase_       ,  last_hidden_state=outputs.last_hidden_state       ,  hidden_states=outputs.hidden_states       ,  attentions=outputs.attentions       ,  )
							else:
												UpperCamelCase__  :List[Any]				   =					self.transformation(outputs.last_hidden_state				)
												return TransformationModelOutput(
												    projection_state=UpperCamelCase_       ,  last_hidden_state=outputs.last_hidden_state       ,  hidden_states=outputs.hidden_states       ,  attentions=outputs.attentions       ,  )