


import math



def       _lowerCAmelCase    (				lowerCAmelCase_				:int				)->list:
   '''simple docstring'''






   snake_case_            =       [True] * n
   snake_case_            =       False
   snake_case_            =       False
   snake_case_            =       True

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

   snake_case_            =       [2]

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

   return primes



def       _lowerCAmelCase    (				lowerCAmelCase_				:int = 999_966_663_333				)->int:
   '''simple docstring'''






   snake_case_            =       math.floor(math.sqrt(lowerCAmelCase_				)				) + 100
   snake_case_            =       prime_sieve(lowerCAmelCase_				)

   snake_case_            =       0
   snake_case_            =       0
   snake_case_            =       primes[prime_index]

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

      snake_case_            =       last_prime**2
      snake_case_            =       next_prime**2

      # Get numbers divisible by lps(current)
      snake_case_            =       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)
      snake_case_            =       upper_bound - next_prime
      while current > lower_bound:
         matches_sum += current
         current -= next_prime

      # Remove the numbers divisible by both ups and lps
      snake_case_            =       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
      snake_case_            =       next_prime
      prime_index += 1

   return matches_sum


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








import logging
import os

from .state import PartialState


class      __lowerCAmelCase  (			logging.LoggerAdapter       ):






  """simple docstring"""





  @staticmethod
  def        lowerCAmelCase__	(  _lowerCAmelCase							:							int	) ->			Tuple:




     """simple docstring"""
     snake_case_            =       PartialState()
     return not main_process_only or (main_process_only and state.is_main_process)



  def        lowerCAmelCase__	(  self							:							Union[str, Any]     ,					_lowerCAmelCase							:							List[Any]     ,					_lowerCAmelCase							:							Tuple     ,					*_lowerCAmelCase							:							List[Any]     ,					**_lowerCAmelCase							:							Any	) ->			Optional[int]:




     """simple docstring"""
     if PartialState._shared_state == {}:
        raise RuntimeError(
            "You must initialize the accelerate state by calling either `PartialState()` or `Accelerator()` before using the logging utility."	)
     snake_case_            =       kwargs.pop("main_process_only"     ,					_lowerCAmelCase	)
     snake_case_            =       kwargs.pop("in_order"     ,					_lowerCAmelCase	)

     if self.isEnabledFor(_lowerCAmelCase	):
        if self._should_log(_lowerCAmelCase	):
           snake_case_     ,     snake_case_            =       self.process(_lowerCAmelCase     ,					_lowerCAmelCase	)
           self.logger.log(_lowerCAmelCase     ,					_lowerCAmelCase     ,					*_lowerCAmelCase     ,					**_lowerCAmelCase	)

        elif in_order:
           snake_case_            =       PartialState()
           for i in range(state.num_processes	):
              if i == state.process_index:
                 snake_case_     ,     snake_case_            =       self.process(_lowerCAmelCase     ,					_lowerCAmelCase	)
                 self.logger.log(_lowerCAmelCase     ,					_lowerCAmelCase     ,					*_lowerCAmelCase     ,					**_lowerCAmelCase	)
              state.wait_for_everyone()






def       _lowerCAmelCase    (				lowerCAmelCase_				:str		,    lowerCAmelCase_				:str = None				)->Any:
   '''simple docstring'''






   if log_level is None:
      snake_case_            =       os.environ.get("ACCELERATE_LOG_LEVEL"		,    lowerCAmelCase_				)
   snake_case_            =       logging.getLogger(lowerCAmelCase_				)
   if log_level is not None:
      logger.setLevel(log_level.upper()				)
      logger.root.setLevel(log_level.upper()				)
   return MultiProcessAdapter(lowerCAmelCase_		,    {}				)




