


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


						'''simple docstring'''






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

						__snake_case				=		[0] * (upper_limit + 1)

						# Base case: C(0) = C(1) = 1
						__snake_case				=		1
						if upper_limit > 0:
												__snake_case				=		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(_lowerCAmelCase ):
																		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							:					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()









from ...configuration_utils import PretrainedConfig
from ...utils import logging


A							:					str     						=     logging.get_logger(__name__)

A							:					str     						=     {
    'google/fnet-base': 'https://huggingface.co/google/fnet-base/resolve/main/config.json',
    'google/fnet-large': 'https://huggingface.co/google/fnet-large/resolve/main/config.json'
    # See all FNet models at https://huggingface.co/models?filter=fnet
}






class     UpperCamelCase(  _a   ):
					snake_case_		:				List[Any]										=	"""fnet"""


					def __init__(						self	:		Dict     ,    SCREAMING_SNAKE_CASE	:		Dict=3_2_0_0_0     ,    SCREAMING_SNAKE_CASE	:		Optional[int]=7_6_8     ,    SCREAMING_SNAKE_CASE	:		Optional[Any]=1_2     ,    SCREAMING_SNAKE_CASE	:		Any=3_0_7_2     ,    SCREAMING_SNAKE_CASE	:		Tuple="gelu_new"     ,    SCREAMING_SNAKE_CASE	:		Any=0.1     ,    SCREAMING_SNAKE_CASE	:		Dict=5_1_2     ,    SCREAMING_SNAKE_CASE	:		str=4     ,    SCREAMING_SNAKE_CASE	:		Tuple=0.02     ,    SCREAMING_SNAKE_CASE	:		Optional[Any]=1e-1_2     ,    SCREAMING_SNAKE_CASE	:		Dict=False     ,    SCREAMING_SNAKE_CASE	:		int=5_1_2     ,    SCREAMING_SNAKE_CASE	:		str=3     ,    SCREAMING_SNAKE_CASE	:		str=1     ,    SCREAMING_SNAKE_CASE	:		Optional[int]=2     ,    **SCREAMING_SNAKE_CASE	:		List[Any]     ,    )			->	List[Any]:




											'''simple docstring'''

											super().__init__(pad_token_id=SCREAMING_SNAKE_CASE     ,    bos_token_id=SCREAMING_SNAKE_CASE     ,    eos_token_id=SCREAMING_SNAKE_CASE     ,    **SCREAMING_SNAKE_CASE						)

											__snake_case				=		vocab_size
											__snake_case				=		max_position_embeddings
											__snake_case				=		hidden_size
											__snake_case				=		num_hidden_layers
											__snake_case				=		intermediate_size
											__snake_case				=		hidden_act
											__snake_case				=		hidden_dropout_prob
											__snake_case				=		initializer_range
											__snake_case				=		type_vocab_size
											__snake_case				=		layer_norm_eps
											__snake_case				=		use_tpu_fourier_optimizations
											__snake_case				=		tpu_short_seq_length





