






from math import isqrt, loga

def      lowerCAmelCase__	(    _a       :			int    ):
  snake_case_				:							Dict						 =       [True] * max_number
  for i in range(2  ,      isqrt(max_number - 1    ) + 1    ):
    if is_prime[i]:
      for j in range(i**2  ,      __lowercase  ,      __lowercase    ):
        snake_case_				:							List[str]						 =       False

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

def      lowerCAmelCase__	(    _a       :			int = 80_08_00  ,      _a       :			int = 80_08_00    ):
  snake_case_				:							str						 =       degree * loga(__lowercase    )
  snake_case_				:							Dict						 =       int(__lowercase    )
  snake_case_				:							Dict						 =       calculate_prime_numbers(__lowercase    )

  snake_case_				:							Any						 =       0
  snake_case_				:							Optional[Any]						 =       0
  snake_case_				:							List[Any]						 =       len(__lowercase    ) - 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() = }""")








import warnings
from typing import List, Optional, Union

from ...processing_utils import ProcessorMixin
from ...tokenization_utils_base import BatchEncoding, PaddingStrategy, PreTokenizedInput, TextInput, TruncationStrategy
from ...utils import TensorType




class 		UpperCAmelCase_						(	SCREAMING_SNAKE_CASE__					):


						'''simple docstring'''




						A     :   Tuple						=					['image_processor', 'tokenizer']
						A     :   List[Any]						=					'ViltImageProcessor'
						A     :   Optional[Any]						=					('BertTokenizer', 'BertTokenizerFast')






						def __init__(	self		,				_SCREAMING_SNAKE_CASE=None		,				_SCREAMING_SNAKE_CASE=None		,				**_SCREAMING_SNAKE_CASE				) ->				int:
								snake_case_				:							str						 =       None
								if "feature_extractor" in kwargs:
										warnings.warn(
										    "The `feature_extractor` argument is deprecated and will be removed in v5, use `image_processor`"
										    " instead."		,				_SCREAMING_SNAKE_CASE		,				)
										snake_case_				:							str						 =       kwargs.pop("feature_extractor"				)

								snake_case_				:							Tuple						 =       image_processor if image_processor is not None else feature_extractor
								if image_processor is None:
										raise ValueError("You need to specify an `image_processor`."				)
								if tokenizer is None:
										raise ValueError("You need to specify a `tokenizer`."				)

								super().__init__(_SCREAMING_SNAKE_CASE		,				_SCREAMING_SNAKE_CASE				)
								snake_case_				:							str						 =       self.image_processor






						def __call__(	self		,				_SCREAMING_SNAKE_CASE		,				_SCREAMING_SNAKE_CASE = None		,				_SCREAMING_SNAKE_CASE = True		,				_SCREAMING_SNAKE_CASE = False		,				_SCREAMING_SNAKE_CASE = None		,				_SCREAMING_SNAKE_CASE = None		,				_SCREAMING_SNAKE_CASE = 0		,				_SCREAMING_SNAKE_CASE = None		,				_SCREAMING_SNAKE_CASE = None		,				_SCREAMING_SNAKE_CASE = None		,				_SCREAMING_SNAKE_CASE = False		,				_SCREAMING_SNAKE_CASE = False		,				_SCREAMING_SNAKE_CASE = False		,				_SCREAMING_SNAKE_CASE = False		,				_SCREAMING_SNAKE_CASE = True		,				_SCREAMING_SNAKE_CASE = None		,				**_SCREAMING_SNAKE_CASE		,				) ->				BatchEncoding:
								snake_case_				:							List[Any]						 =       self.tokenizer(
								    text=_SCREAMING_SNAKE_CASE		,				add_special_tokens=_SCREAMING_SNAKE_CASE		,				padding=_SCREAMING_SNAKE_CASE		,				truncation=_SCREAMING_SNAKE_CASE		,				max_length=_SCREAMING_SNAKE_CASE		,				stride=_SCREAMING_SNAKE_CASE		,				pad_to_multiple_of=_SCREAMING_SNAKE_CASE		,				return_token_type_ids=_SCREAMING_SNAKE_CASE		,				return_attention_mask=_SCREAMING_SNAKE_CASE		,				return_overflowing_tokens=_SCREAMING_SNAKE_CASE		,				return_special_tokens_mask=_SCREAMING_SNAKE_CASE		,				return_offsets_mapping=_SCREAMING_SNAKE_CASE		,				return_length=_SCREAMING_SNAKE_CASE		,				verbose=_SCREAMING_SNAKE_CASE		,				return_tensors=_SCREAMING_SNAKE_CASE		,				**_SCREAMING_SNAKE_CASE		,				)
								# add pixel_values + pixel_mask
								snake_case_				:							str						 =       self.image_processor(_SCREAMING_SNAKE_CASE		,				return_tensors=_SCREAMING_SNAKE_CASE				)
								encoding.update(_SCREAMING_SNAKE_CASE				)

								return encoding






						def       _lowerCAmelCase       (	self		,				*_SCREAMING_SNAKE_CASE		,				**_SCREAMING_SNAKE_CASE				) ->				List[str]:
								return self.tokenizer.batch_decode(*_SCREAMING_SNAKE_CASE		,				**_SCREAMING_SNAKE_CASE				)






						def       _lowerCAmelCase       (	self		,				*_SCREAMING_SNAKE_CASE		,				**_SCREAMING_SNAKE_CASE				) ->				Dict:
								return self.tokenizer.decode(*_SCREAMING_SNAKE_CASE		,				**_SCREAMING_SNAKE_CASE				)






						@property
						def       _lowerCAmelCase       (	self				) ->				Tuple:
								snake_case_				:							List[Any]						 =       self.tokenizer.model_input_names
								snake_case_				:							Tuple						 =       self.image_processor.model_input_names
								return list(dict.fromkeys(tokenizer_input_names + image_processor_input_names				)				)






						@property
						def       _lowerCAmelCase       (	self				) ->				Optional[Any]:
								warnings.warn(
								    "`feature_extractor_class` is deprecated and will be removed in v5. Use `image_processor_class` instead."		,				_SCREAMING_SNAKE_CASE		,				)
								return self.image_processor_class






						@property
						def       _lowerCAmelCase       (	self				) ->				Optional[int]:
								warnings.warn(
								    "`feature_extractor` is deprecated and will be removed in v5. Use `image_processor` instead."		,				_SCREAMING_SNAKE_CASE		,				)
								return self.image_processor
