


def   _lowerCAmelCase				(   UpperCamelCase__:     int						) ->   "list[int]":





	"""simple docstring"""







	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(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:
			_lowercase       :      Optional[int]	=	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 copy

from ...configuration_utils import PretrainedConfig
from ...utils import logging
from ..auto.configuration_auto import CONFIG_MAPPING


_lowercase       :      int	=	logging.get_logger(__name__)






class       _UpperCamelCase    (					__snake_case				):

				"""simple docstring"""







				lowerCAmelCase 		= 'upernet'

				def __init__(						self				,   a__=None				,   a__=512				,   a__=0.02				,   a__=[1, 2, 3, 6]				,   a__=True				,   a__=0.4				,   a__=384				,   a__=256				,   a__=1				,   a__=False				,   a__=255				,   **a__				,   )	->				Tuple:
					super().__init__(**a__   )

					if backbone_config is None:
						logger.info("""`backbone_config` is `None`. Initializing the config with the default `ResNet` backbone."""   )
						A								=				CONFIG_MAPPING["""resnet"""](out_features=["""stage1""", """stage2""", """stage3""", """stage4"""]   )
					elif isinstance(a__				,   a__   ):
						A								=				backbone_config.get("""model_type"""   )
						A								=				CONFIG_MAPPING[backbone_model_type]
						A								=				config_class.from_dict(a__   )

					A								=				backbone_config
					A								=				hidden_size
					A								=				initializer_range
					A								=				pool_scales
					A								=				use_auxiliary_head
					A								=				auxiliary_loss_weight
					A								=				auxiliary_in_channels
					A								=				auxiliary_channels
					A								=				auxiliary_num_convs
					A								=				auxiliary_concat_input
					A								=				loss_ignore_index

				def      _UpperCAmelCase					(						self   )	->				Dict:
					A								=				copy.deepcopy(self.__dict__   )
					A								=				self.backbone_config.to_dict()
					A								=				self.__class__.model_type
					return output



