'''simple docstring'''






def   __UpperCAmelCase     (    a_:			List[str]				):

   if p < 2:
      raise ValueError("p should not be less than 2!"				)
   elif p == 2:
      return True

   _UpperCAmelCase				:      Dict				=  4
   _UpperCAmelCase				:      int				=  (1 << p) - 1
   for _ in range(p - 2				):
      _UpperCAmelCase				:      Union[str, Any]				=  ((s * s) - 2) % m
   return s == 0


if __name__ == "__main__":
     print(lucas_lehmer_test(7))
     print(lucas_lehmer_test(11))







"""simple docstring"""
from typing import List, Optional, Union

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


_lowerCAmelCase       =				logging.get_logger(__name__)

_lowerCAmelCase       =				{
    "huggingface/informer-tourism-monthly": (
        "https://huggingface.co/huggingface/informer-tourism-monthly/resolve/main/config.json"
    ),
    # See all Informer models at https://huggingface.co/models?filter=informer
}



class   SCREAMING_SNAKE_CASE	(					_SCREAMING_SNAKE_CASE    ):





	"""simple docstring"""




	_A							:					Optional[Any] 			=					"""informer"""
	_A							:					Dict 			=					{
	    """hidden_size""": """d_model""",
	    """num_attention_heads""": """encoder_attention_heads""",
	    """num_hidden_layers""": """encoder_layers""",
	}





	def __init__(self  ,  lowerCAmelCase_ = None  ,  lowerCAmelCase_ = None  ,  lowerCAmelCase_ = "student_t"  ,  lowerCAmelCase_ = "nll"  ,  lowerCAmelCase_ = 1  ,  lowerCAmelCase_ = None  ,  lowerCAmelCase_ = "mean"  ,  lowerCAmelCase_ = 0  ,  lowerCAmelCase_ = 0  ,  lowerCAmelCase_ = 0  ,  lowerCAmelCase_ = 0  ,  lowerCAmelCase_ = None  ,  lowerCAmelCase_ = None  ,  lowerCAmelCase_ = 64  ,  lowerCAmelCase_ = 32  ,  lowerCAmelCase_ = 32  ,  lowerCAmelCase_ = 2  ,  lowerCAmelCase_ = 2  ,  lowerCAmelCase_ = 2  ,  lowerCAmelCase_ = 2  ,  lowerCAmelCase_ = True  ,  lowerCAmelCase_ = "gelu"  ,  lowerCAmelCase_ = 0.05  ,  lowerCAmelCase_ = 0.1  ,  lowerCAmelCase_ = 0.1  ,  lowerCAmelCase_ = 0.1  ,  lowerCAmelCase_ = 0.1  ,  lowerCAmelCase_ = 100  ,  lowerCAmelCase_ = 0.02  ,  lowerCAmelCase_=True  ,  lowerCAmelCase_ = "prob"  ,  lowerCAmelCase_ = 5  ,  lowerCAmelCase_ = True  ,  **lowerCAmelCase_  ,  ):
		# time series specific configuration
		A_		:    Optional[Any]						     = prediction_length
		A_		:    Dict						     = context_length or prediction_length
		A_		:    Dict						     = distribution_output
		A_		:    Tuple						     = loss
		A_		:    Dict						     = input_size
		A_		:    Union[str, Any]						     = num_time_features
		A_		:    List[str]						     = lags_sequence if lags_sequence is not None else [1, 2, 3, 4, 5, 6, 7]
		A_		:    Optional[int]						     = scaling
		A_		:    Optional[Any]						     = num_dynamic_real_features
		A_		:    Tuple						     = num_static_real_features
		A_		:    Tuple						     = num_static_categorical_features

		# set cardinality
		if cardinality 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`"""				)
			A_		:    List[str]						     = cardinality
		else:
			A_		:    List[Any]						     = [0]

		# set embedding_dimension
		if embedding_dimension 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`"""				)
			A_		:    int						     = embedding_dimension
		else:
			A_		:    Optional[int]						     = [min(50  ,  (cat + 1) // 2				) for cat in self.cardinality]

		A_		:    Optional[int]						     = num_parallel_samples

		# Transformer architecture configuration
		A_		:    Union[str, Any]						     = input_size * len(self.lags_sequence				) + self._number_of_features
		A_		:    Dict						     = d_model
		A_		:    Dict						     = encoder_attention_heads
		A_		:    Dict						     = decoder_attention_heads
		A_		:    Any						     = encoder_ffn_dim
		A_		:    Tuple						     = decoder_ffn_dim
		A_		:    Tuple						     = encoder_layers
		A_		:    Optional[int]						     = decoder_layers

		A_		:    List[str]						     = dropout
		A_		:    List[str]						     = attention_dropout
		A_		:    Any						     = activation_dropout
		A_		:    Any						     = encoder_layerdrop
		A_		:    List[Any]						     = decoder_layerdrop

		A_		:    str						     = activation_function
		A_		:    Optional[Any]						     = init_std

		A_		:    Optional[int]						     = use_cache

		# Informer
		A_		:    Dict						     = attention_type
		A_		:    List[Any]						     = sampling_factor
		A_		:    List[Any]						     = distil

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





	@property
	def  lowerCamelCase(self				):
		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
		)

