






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

  UpperCamelCase_: Optional[int]   				=    [0] * (upper_limit + 1)

  # Base case: C(0) = C(1) = 1
  UpperCamelCase_: List[str]   				=    1
  if upper_limit > 0:
    UpperCamelCase_: Dict   				=    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(UpperCAmelCase__  ):
      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:
         A_		:		Dict		     =			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()







import unittest

from transformers import is_torch_available
from transformers.testing_utils import require_sentencepiece, require_tokenizers, require_torch, slow, torch_device


if is_torch_available():
   from transformers import AutoModelForSeqaSeqLM, AutoTokenizer




@require_torch
@require_sentencepiece
@require_tokenizers
class     _lowerCAmelCase(	unittest.TestCase ):





       """simple docstring"""







       @slow
       def       _a   ( self							):
         UpperCamelCase_: Optional[int]   				=    AutoModelForSeqaSeqLM.from_pretrained('google/mt5-small'  ,      return_dict=_lowerCamelCase							).to(_lowerCamelCase							)
         UpperCamelCase_: Dict   				=    AutoTokenizer.from_pretrained('google/mt5-small'							)

         UpperCamelCase_: Dict   				=    tokenizer('Hello there'  ,      return_tensors='pt'							).input_ids
         UpperCamelCase_: Optional[Any]   				=    tokenizer('Hi I am'  ,      return_tensors='pt'							).input_ids

         UpperCamelCase_: int   				=    model(input_ids.to(_lowerCamelCase							)  ,      labels=labels.to(_lowerCamelCase							)							).loss
         UpperCamelCase_: Tuple   				=    -(labels.shape[-1] * loss.item())

         UpperCamelCase_: Any   				=    -8_4.9_1_2_7
         self.assertTrue(abs(mtf_score - EXPECTED_SCORE							) < 1e-4							)