



"""simple docstring"""
import logging
import os

from .state import PartialState



class    SCREAMING_SNAKE_CASE__						(      logging.LoggerAdapter				):

   @staticmethod
   def 			SCREAMING_SNAKE_CASE  (     _SCREAMING_SNAKE_CASE		)						->   List[str]:





    '''simple docstring'''




    UpperCAmelCase			:      Optional[int]			=			PartialState()
    return not main_process_only or (main_process_only and state.is_main_process)




   def 			SCREAMING_SNAKE_CASE  (     self   ,  _SCREAMING_SNAKE_CASE   ,  _SCREAMING_SNAKE_CASE   ,  *_SCREAMING_SNAKE_CASE   ,  **_SCREAMING_SNAKE_CASE		)						->   List[str]:





    '''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."""		)
    UpperCAmelCase			:      Union[str, Any]			=			kwargs.pop("""main_process_only"""   ,  _SCREAMING_SNAKE_CASE		)
    UpperCAmelCase			:      List[Any]			=			kwargs.pop("""in_order"""   ,  _SCREAMING_SNAKE_CASE		)

    if self.isEnabledFor(_SCREAMING_SNAKE_CASE		):
     if self._should_log(_SCREAMING_SNAKE_CASE		):
      UpperCAmelCase			,	UpperCAmelCase			:      List[str]			=			self.process(_SCREAMING_SNAKE_CASE   ,  _SCREAMING_SNAKE_CASE		)
      self.logger.log(_SCREAMING_SNAKE_CASE   ,  _SCREAMING_SNAKE_CASE   ,  *_SCREAMING_SNAKE_CASE   ,  **_SCREAMING_SNAKE_CASE		)

     elif in_order:
      UpperCAmelCase			:      List[str]			=			PartialState()
      for i in range(state.num_processes		):
       if i == state.process_index:
        UpperCAmelCase			,	UpperCAmelCase			:      Optional[Any]			=			self.process(_SCREAMING_SNAKE_CASE   ,  _SCREAMING_SNAKE_CASE		)
        self.logger.log(_SCREAMING_SNAKE_CASE   ,  _SCREAMING_SNAKE_CASE   ,  *_SCREAMING_SNAKE_CASE   ,  **_SCREAMING_SNAKE_CASE		)
       state.wait_for_everyone()

def    _snake_case		(		UpperCamelCase		:	str    ,	UpperCamelCase		:	str = None		):
 if log_level is None:
  UpperCAmelCase			:      Union[str, Any]			=			os.environ.get("""ACCELERATE_LOG_LEVEL"""    ,	UpperCamelCase		)
 UpperCAmelCase			:      List[str]			=			logging.getLogger(UpperCamelCase		)
 if log_level is not None:
  logger.setLevel(log_level.upper()		)
  logger.root.setLevel(log_level.upper()		)
 return MultiProcessAdapter(UpperCamelCase    ,	{}		)





"""simple docstring"""
from __future__ import annotations

from collections.abc import Generator

def    _snake_case		(		):
 UpperCAmelCase			:      dict[int, int]			=			{}
 UpperCAmelCase			:      str			=			2
 while True:
  UpperCAmelCase			:      List[str]			=			factor_map.pop(UpperCamelCase    ,	UpperCamelCase		)
  if factor:
   UpperCAmelCase			:      Dict			=			factor + prime
   while x in factor_map:
    x += factor
   UpperCAmelCase			:      Tuple			=			factor
  else:
   UpperCAmelCase			:      Optional[int]			=			prime
   yield prime
  prime += 1

def    _snake_case		(		UpperCamelCase		:	float = 1e1_0		):
 UpperCAmelCase			:      Tuple			=			sieve()

 UpperCAmelCase			:      Optional[Any]			=			1
 while True:
  UpperCAmelCase			:      List[str]			=			next(UpperCamelCase		)
  if (2 * prime * n) > limit:
   return n
  # Ignore the next prime as the reminder will be 2.
  next(UpperCamelCase		)
  n += 2


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