






"""simple docstring"""




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    lowercase_    (__UpperCAmelCase     ):
      A__	:		List[str]       			=				['''image_processor''', '''tokenizer''']
      A__	:		Tuple       			=				'''BridgeTowerImageProcessor'''
      A__	:		Optional[Any]       			=				('''RobertaTokenizer''', '''RobertaTokenizerFast''')






      def __init__(    self     ,     a_     ,     a_	)	->Optional[int]:







        '''simple docstring'''


        super().__init__(lowerCAmelCase_     ,     lowerCAmelCase_	)






      def __call__(    self     ,     a_     ,     a_ = None     ,     a_ = True     ,     a_ = False     ,     a_ = None     ,     a_ = None     ,     a_ = 0     ,     a_ = None     ,     a_ = None     ,     a_ = None     ,     a_ = False     ,     a_ = False     ,     a_ = False     ,     a_ = False     ,     a_ = True     ,     a_ = None     ,     **a_     ,     )	->Dict:







        '''simple docstring'''


        _a							=	self.tokenizer(
            text=lowerCAmelCase_     ,     add_special_tokens=lowerCAmelCase_     ,     padding=lowerCAmelCase_     ,     truncation=lowerCAmelCase_     ,     max_length=lowerCAmelCase_     ,     stride=lowerCAmelCase_     ,     pad_to_multiple_of=lowerCAmelCase_     ,     return_token_type_ids=lowerCAmelCase_     ,     return_attention_mask=lowerCAmelCase_     ,     return_overflowing_tokens=lowerCAmelCase_     ,     return_special_tokens_mask=lowerCAmelCase_     ,     return_offsets_mapping=lowerCAmelCase_     ,     return_length=lowerCAmelCase_     ,     verbose=lowerCAmelCase_     ,     return_tensors=lowerCAmelCase_     ,     **lowerCAmelCase_     ,     )
        # add pixel_values + pixel_mask
        _a							=	self.image_processor(
            lowerCAmelCase_     ,     return_tensors=lowerCAmelCase_     ,     do_normalize=lowerCAmelCase_     ,     do_center_crop=lowerCAmelCase_     ,     **lowerCAmelCase_	)
        encoding.update(lowerCAmelCase_	)

        return encoding






      def 			lowerCamelCase__    (    self     ,     *a_     ,     **a_	)	->List[Any]:







        '''simple docstring'''


        return self.tokenizer.batch_decode(*lowerCAmelCase_     ,     **lowerCAmelCase_	)






      def 			lowerCamelCase__    (    self     ,     *a_     ,     **a_	)	->List[Any]:







        '''simple docstring'''


        return self.tokenizer.decode(*lowerCAmelCase_     ,     **lowerCAmelCase_	)






      @property
      def 			lowerCamelCase__    (    self	)	->Any:







        '''simple docstring'''


        _a							=	self.tokenizer.model_input_names
        _a							=	self.image_processor.model_input_names
        return list(dict.fromkeys(tokenizer_input_names + image_processor_input_names	)	)










"""simple docstring"""




import math






def        lowerCAmelCase (      UpperCamelCase_:							int					)       ->							list:







  '''simple docstring'''







  _a							=	[True] * n
  _a							=	False
  _a							=	False
  _a							=	True

  for i in range(3     , int(n**0.5 + 1					)     , 2					):
    _a							=	i * 2
    while index < n:
      _a							=	False
      _a							=	index + i

  _a							=	[2]

  for i in range(3     , UpperCamelCase_     , 2					):
    if is_prime[i]:
      primes.append(UpperCamelCase_					)

  return primes






def        lowerCAmelCase (      UpperCamelCase_:							int = 999966663333					)       ->							int:







  '''simple docstring'''







  _a							=	math.floor(math.sqrt(UpperCamelCase_					)					) + 100
  _a							=	prime_sieve(UpperCamelCase_					)

  _a							=	0
  _a							=	0
  _a							=	primes[prime_index]

  while (last_prime**2) <= limit:
    _a							=	primes[prime_index + 1]

    _a							=	last_prime**2
    _a							=	next_prime**2

    # Get numbers divisible by lps(current)
    _a							=	lower_bound + last_prime
    while upper_bound > current <= limit:
      matches_sum += current
      current += last_prime

    # Reset the upper_bound
    while (upper_bound - next_prime) > limit:
      upper_bound -= next_prime

    # Add the numbers divisible by ups(current)
    _a							=	upper_bound - next_prime
    while current > lower_bound:
      matches_sum += current
      current -= next_prime

    # Remove the numbers divisible by both ups and lps
    _a							=	0
    while upper_bound > current <= limit:
      if current <= lower_bound:
        # Increment the current number
        current += last_prime * next_prime
        continue

      if current > limit:
        break

      # Remove twice since it was added by both ups and lps
      matches_sum -= current * 2

      # Increment the current number
      current += last_prime * next_prime

    # Setup for next pair
    _a							=	next_prime
    prime_index += 1

  return matches_sum


if __name__ == "__main__":
     print(solution())


