


'''simple docstring'''
def      a (     __a  )    ->      "list[int]":



					'''simple docstring'''






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

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

					# Base case: C(0) = C(1) = 1
					UpperCamelCase__  :Tuple				   =					1
					if upper_limit > 0:
										UpperCamelCase__  :Optional[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:
						__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'''
import logging
from dataclasses import dataclass, field
from typing import Optional

from seqaseq_trainer import arg_to_scheduler

from transformers import TrainingArguments


__snake_case				 =	logging.getLogger(__name__)
@dataclass
class   lowercase      (				A__   ):

		"""simple docstring"""

		_a       					=							field(
		    default=0.0      ,						metadata={'help': 'The label smoothing epsilon to apply (if not zero).'}   )
		_a       					=							field(default=A__      ,						metadata={'help': 'Whether to SortishSamler or not.'}   )
		_a       					=							field(
		    default=A__      ,						metadata={'help': 'Whether to use generate to calculate generative metrics (ROUGE, BLEU).'}   )
		_a       					=							field(default=A__      ,						metadata={'help': 'whether to use adafactor'}   )
		_a       					=							field(
		    default=A__      ,						metadata={'help': 'Encoder layer dropout probability. Goes into model.config.'}   )
		_a       					=							field(
		    default=A__      ,						metadata={'help': 'Decoder layer dropout probability. Goes into model.config.'}   )
		_a       					=							field(default=A__      ,						metadata={'help': 'Dropout probability. Goes into model.config.'}   )
		_a       					=							field(
		    default=A__      ,						metadata={'help': 'Attention dropout probability. Goes into model.config.'}   )
		_a       					=							field(
		    default='linear'      ,						metadata={'help': f'''Which lr scheduler to use. Selected in {sorted(arg_to_scheduler.keys()   )}'''}      ,						)