


"""simple docstring"""




def        lowercase							(		lowerCAmelCase__ :     int			) ->      List[Any]:
		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(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:
												lowercase_			     =  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 typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_tf_available,
    is_torch_available,
    is_vision_available,
)


__a  			=					{'configuration_deit': ['DEIT_PRETRAINED_CONFIG_ARCHIVE_MAP', 'DeiTConfig', 'DeiTOnnxConfig']}

try:
						if not is_vision_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						__a  			=					['DeiTFeatureExtractor']
						__a  			=					['DeiTImageProcessor']

try:
						if not is_torch_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						__a  			=					[
						    'DEIT_PRETRAINED_MODEL_ARCHIVE_LIST',
						    'DeiTForImageClassification',
						    'DeiTForImageClassificationWithTeacher',
						    'DeiTForMaskedImageModeling',
						    'DeiTModel',
						    'DeiTPreTrainedModel',
						]

try:
						if not is_tf_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						__a  			=					[
						    'TF_DEIT_PRETRAINED_MODEL_ARCHIVE_LIST',
						    'TFDeiTForImageClassification',
						    'TFDeiTForImageClassificationWithTeacher',
						    'TFDeiTForMaskedImageModeling',
						    'TFDeiTModel',
						    'TFDeiTPreTrainedModel',
						]


if TYPE_CHECKING:
						from .configuration_deit import DEIT_PRETRAINED_CONFIG_ARCHIVE_MAP, DeiTConfig, DeiTOnnxConfig

						try:
												if not is_vision_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .feature_extraction_deit import DeiTFeatureExtractor
												from .image_processing_deit import DeiTImageProcessor

						try:
												if not is_torch_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_deit import (
												    DEIT_PRETRAINED_MODEL_ARCHIVE_LIST,
												    DeiTForImageClassification,
												    DeiTForImageClassificationWithTeacher,
												    DeiTForMaskedImageModeling,
												    DeiTModel,
												    DeiTPreTrainedModel,
												)

						try:
												if not is_tf_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_tf_deit import (
												    TF_DEIT_PRETRAINED_MODEL_ARCHIVE_LIST,
												    TFDeiTForImageClassification,
												    TFDeiTForImageClassificationWithTeacher,
												    TFDeiTForMaskedImageModeling,
												    TFDeiTModel,
												    TFDeiTPreTrainedModel,
												)


else:
						import sys

						__a  			=					_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)




