



"""simple docstring"""






from math import isqrt, loga






def        snake_case_  (      A_					:		int						):


       '''simple docstring'''





       _lowerCamelCase						:				Optional[Any]    			= [True] * max_number
       for i in range(2,				isqrt(max_number - 1						) + 1						):
              if is_prime[i]:
                     for j in range(i**2,				A_,				A_						):
                            _lowerCamelCase						:				str    			= False

       return [i for i in range(2,				A_						) if is_prime[i]]






def        snake_case_  (      A_					:		int = 80_08_00,				A_					:		int = 80_08_00						):


       '''simple docstring'''





       _lowerCamelCase						:				Dict    			= degree * loga(A_						)
       _lowerCamelCase						:				Any    			= int(A_						)
       _lowerCamelCase						:				List[Any]    			= calculate_prime_numbers(A_						)

       _lowerCamelCase						:				Dict    			= 0
       _lowerCamelCase						:				Dict    			= 0
       _lowerCamelCase						:				str    			= len(A_						) - 1
       while left < right:
              while (
                  prime_numbers[right] * loga(prime_numbers[left]						)
                  + prime_numbers[left] * loga(prime_numbers[right]						)
                  > upper_bound
              ):
                     right -= 1
              hybrid_integers_count += right - left
              left += 1

       return hybrid_integers_count


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









"""simple docstring"""





from collections import OrderedDict
from typing import TYPE_CHECKING, Any, Mapping, Optional

from ...configuration_utils import PretrainedConfig
from ...onnx import OnnxConfig
from ...utils import logging


if TYPE_CHECKING:
       from ... import FeatureExtractionMixin, TensorType

SCREAMING_SNAKE_CASE__					=   logging.get_logger(__name__)

SCREAMING_SNAKE_CASE__					=   {
    "openai/imagegpt-small": "",
    "openai/imagegpt-medium": "",
    "openai/imagegpt-large": "",
}

class 		lowercase					(					_UpperCAmelCase					):
      _SCREAMING_SNAKE_CASE					=      'imagegpt'
      _SCREAMING_SNAKE_CASE					=      ['past_key_values']
      _SCREAMING_SNAKE_CASE					=      {
          'hidden_size': 'n_embd',
          'max_position_embeddings': 'n_positions',
          'num_attention_heads': 'n_head',
          'num_hidden_layers': 'n_layer',
      }





      def __init__(       self      ,						lowercase=512 + 1      ,						lowercase=32 * 32      ,						lowercase=512      ,						lowercase=24      ,						lowercase=8      ,						lowercase=None      ,						lowercase="quick_gelu"      ,						lowercase=0.1      ,						lowercase=0.1      ,						lowercase=0.1      ,						lowercase=1e-5      ,						lowercase=0.02      ,						lowercase=True      ,						lowercase=True      ,						lowercase=False      ,						lowercase=False      ,						lowercase=False      ,						**lowercase      ,						)		->     Any:
            lowerCAmelCase  						=       vocab_size
            lowerCAmelCase  						=       n_positions
            lowerCAmelCase  						=       n_embd
            lowerCAmelCase  						=       n_layer
            lowerCAmelCase  						=       n_head
            lowerCAmelCase  						=       n_inner
            lowerCAmelCase  						=       activation_function
            lowerCAmelCase  						=       resid_pdrop
            lowerCAmelCase  						=       embd_pdrop
            lowerCAmelCase  						=       attn_pdrop
            lowerCAmelCase  						=       layer_norm_epsilon
            lowerCAmelCase  						=       initializer_range
            lowerCAmelCase  						=       scale_attn_weights
            lowerCAmelCase  						=       use_cache
            lowerCAmelCase  						=       scale_attn_by_inverse_layer_idx
            lowerCAmelCase  						=       reorder_and_upcast_attn
            lowerCAmelCase  						=       tie_word_embeddings

            super().__init__(tie_word_embeddings=lowercase      ,						**lowercase )







class 		lowercase					(					_UpperCAmelCase					):





      @property
      def     _snake_case			(       self )		->     Mapping[str, Mapping[int, str]]:
            return OrderedDict(
                [
                    ("""input_ids""", {0: """batch""", 1: """sequence"""}),
                ] )





      def     _snake_case			(       self      ,						lowercase      ,						lowercase = 1      ,						lowercase = -1      ,						lowercase = False      ,						lowercase = None      ,						lowercase = 3      ,						lowercase = 32      ,						lowercase = 32      ,						)		->     Mapping[str, Any]:
            lowerCAmelCase  						=       self._generate_dummy_images(lowercase      ,						lowercase      ,						lowercase      ,						lowercase )
            lowerCAmelCase  						=       dict(preprocessor(images=lowercase      ,						return_tensors=lowercase ) )

            return inputs






