




"""simple docstring"""







import math





def 							lowercase					(snake_case__   : int )     ->  list[int]:


				'''simple docstring'''






				lowerCAmelCase  =				[]
				lowerCAmelCase  =				2
				lowerCAmelCase  =				int(math.sqrt(snake_case__ ) )  # Size of every segment
				lowerCAmelCase  =				[True] * (end + 1)
				lowerCAmelCase  =				[]

				while start <= end:
								if temp[start] is True:
												in_prime.append(snake_case__ )
												for i in range(start * start      ,       end + 1      ,       snake_case__ ):
																lowerCAmelCase  =				False
								start += 1
				prime += in_prime

				lowerCAmelCase  =				end + 1
				lowerCAmelCase  =				min(2 * end      ,       snake_case__ )

				while low <= n:
								lowerCAmelCase  =				[True] * (high - low + 1)
								for each in in_prime:
												lowerCAmelCase  =				math.floor(low / each ) * each
												if t < low:
																t += each

												for j in range(snake_case__      ,       high + 1      ,       snake_case__ ):
																lowerCAmelCase  =				False

								for j in range(len(snake_case__ ) ):
												if temp[j] is True:
																prime.append(j + low )

								lowerCAmelCase  =				high + 1
								lowerCAmelCase  =				min(high + end      ,       snake_case__ )

				return prime






print(sieve(1_0**6))











"""simple docstring"""







from typing import List, Optional

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


a      =							logging.get_logger(__name__)

a      =							{
    'huggingface/autoformer-tourism-monthly': 'https://huggingface.co/huggingface/autoformer-tourism-monthly/resolve/main/config.json',
}






class       SCREAMING_SNAKE_CASE__					(					_a					):
						_a    						=						'autoformer'
						_a    						=						{
						    'hidden_size': 'd_model',
						    'num_attention_heads': 'encoder_attention_heads',
						    'num_hidden_layers': 'encoder_layers',
						}


						def __init__(							self				:			Dict						,						lowerCAmelCase				:			Optional[int] = None						,						lowerCAmelCase				:			Optional[int] = None						,						lowerCAmelCase				:			str = "student_t"						,						lowerCAmelCase				:			str = "nll"						,						lowerCAmelCase				:			int = 1						,						lowerCAmelCase				:			List[int] = [1, 2, 3, 4, 5, 6, 7]						,						lowerCAmelCase				:			bool = True						,						lowerCAmelCase				:			int = 0						,						lowerCAmelCase				:			int = 0						,						lowerCAmelCase				:			int = 0						,						lowerCAmelCase				:			int = 0						,						lowerCAmelCase				:			Optional[List[int]] = None						,						lowerCAmelCase				:			Optional[List[int]] = None						,						lowerCAmelCase				:			int = 64						,						lowerCAmelCase				:			int = 2						,						lowerCAmelCase				:			int = 2						,						lowerCAmelCase				:			int = 2						,						lowerCAmelCase				:			int = 2						,						lowerCAmelCase				:			int = 32						,						lowerCAmelCase				:			int = 32						,						lowerCAmelCase				:			str = "gelu"						,						lowerCAmelCase				:			float = 0.1						,						lowerCAmelCase				:			float = 0.1						,						lowerCAmelCase				:			float = 0.1						,						lowerCAmelCase				:			float = 0.1						,						lowerCAmelCase				:			float = 0.1						,						lowerCAmelCase				:			int = 100						,						lowerCAmelCase				:			float = 0.02						,						lowerCAmelCase				:			bool = True						,						lowerCAmelCase				:			Tuple=True						,						lowerCAmelCase				:			int = 10						,						lowerCAmelCase				:			int = 25						,						lowerCAmelCase				:			int = 3						,						**lowerCAmelCase				:			Tuple						,						):
										# time series specific configuration
										lowerCAmelCase  =				prediction_length
										lowerCAmelCase  =				context_length if context_length is not None else prediction_length
										lowerCAmelCase  =				distribution_output
										lowerCAmelCase  =				loss
										lowerCAmelCase  =				input_size
										lowerCAmelCase  =				num_time_features
										lowerCAmelCase  =				lags_sequence
										lowerCAmelCase  =				scaling
										lowerCAmelCase  =				num_dynamic_real_features
										lowerCAmelCase  =				num_static_real_features
										lowerCAmelCase  =				num_static_categorical_features
										if cardinality is not None and num_static_categorical_features > 0:
														if len(lowerCAmelCase					) != num_static_categorical_features:
																		raise ValueError(
																		    """The cardinality should be a list of the same length as `num_static_categorical_features`"""					)
														lowerCAmelCase  =				cardinality
										else:
														lowerCAmelCase  =				[0]
										if embedding_dimension is not None and num_static_categorical_features > 0:
														if len(lowerCAmelCase					) != num_static_categorical_features:
																		raise ValueError(
																		    """The embedding dimension should be a list of the same length as `num_static_categorical_features`"""					)
														lowerCAmelCase  =				embedding_dimension
										else:
														lowerCAmelCase  =				[min(50						,						(cat + 1) // 2					) for cat in self.cardinality]
										lowerCAmelCase  =				num_parallel_samples

										# Transformer architecture configuration
										lowerCAmelCase  =				input_size * len(self.lags_sequence					) + self._number_of_features
										lowerCAmelCase  =				d_model
										lowerCAmelCase  =				encoder_attention_heads
										lowerCAmelCase  =				decoder_attention_heads
										lowerCAmelCase  =				encoder_ffn_dim
										lowerCAmelCase  =				decoder_ffn_dim
										lowerCAmelCase  =				encoder_layers
										lowerCAmelCase  =				decoder_layers

										lowerCAmelCase  =				dropout
										lowerCAmelCase  =				attention_dropout
										lowerCAmelCase  =				activation_dropout
										lowerCAmelCase  =				encoder_layerdrop
										lowerCAmelCase  =				decoder_layerdrop

										lowerCAmelCase  =				activation_function
										lowerCAmelCase  =				init_std

										lowerCAmelCase  =				use_cache

										# Autoformer
										lowerCAmelCase  =				label_length
										lowerCAmelCase  =				moving_average
										lowerCAmelCase  =				autocorrelation_factor

										super().__init__(is_encoder_decoder=lowerCAmelCase						,						**lowerCAmelCase					)




						@property
						def   __lowercase (							self				:			Tuple					):
										return (
										    sum(self.embedding_dimension					)
										    + self.num_dynamic_real_features
										    + self.num_time_features
										    + self.num_static_real_features
										    + self.input_size * 2  # the log1p(abs(loc)) and log(scale) features
										)





