


import math
from collections.abc import Iterator
from itertools import takewhile






def   _lowercase(					__a				:						int     ):

							if 1 < number < 4:
														# 2 and 3 are primes
														return True
							elif number < 2 or number % 2 == 0 or number % 3 == 0:
														# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
														return False

							# All primes number are in format of 6k +/- 1
							for i in range(5    ,     int(math.sqrt(__a     ) + 1     )    ,     6     ):
														if number % i == 0 or number % (i + 2) == 0:
																					return False
							return True






def   _lowercase(					):
							a__      =2
							while True:
														if is_prime(__a     ):
																					yield num
														num += 1






def   _lowercase(					__a				:						int = 200_0000     ):
							return sum(takewhile(lambda __a     : x < n    ,     prime_generator()     )     )


if __name__ == "__main__":
	print(F"""{solution() = }""")





from typing import List, Optional

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


_lowerCAmelCase:						List[Any]   				=       logging.get_logger(__name__)

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




class       lowercase_					(lowercase__   ):
				snake_case	    ='autoformer'
				snake_case	    ={
				    'hidden_size': 'd_model',
				    'num_attention_heads': 'encoder_attention_heads',
				    'num_hidden_layers': 'encoder_layers',
				}





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

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

											a__      =dropout
											a__      =attention_dropout
											a__      =activation_dropout
											a__      =encoder_layerdrop
											a__      =decoder_layerdrop

											a__      =activation_function
											a__      =init_std

											a__      =use_cache

											# Autoformer
											a__      =label_length
											a__      =moving_average
											a__      =autocorrelation_factor

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





				@property
				def 						__UpperCamelCase    (				self)  -> int:
											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
											)

