

"""simple docstring"""





from .integrations import (
    is_optuna_available,
    is_ray_available,
    is_sigopt_available,
    is_wandb_available,
    run_hp_search_optuna,
    run_hp_search_ray,
    run_hp_search_sigopt,
    run_hp_search_wandb,
)
from .trainer_utils import (
    HPSearchBackend,
    default_hp_space_optuna,
    default_hp_space_ray,
    default_hp_space_sigopt,
    default_hp_space_wandb,
)
from .utils import logging


__UpperCamelCase  :      Optional[Any]							      =		logging.get_logger(__name__)







class 				SCREAMING_SNAKE_CASE					:






					"""simple docstring"""



					lowercase__				 =       42
					lowercase__				 =       None







					@staticmethod
					def        __lowerCAmelCase (       ):
						raise NotImplementedError







					def        __lowerCAmelCase (       self			:				List[Any]   ,lowercase_			:				List[Any]   ,lowercase_			:				int   ,lowercase_			:				str   ,**lowercase_			:				List[str]		):
						raise NotImplementedError







					def        __lowerCAmelCase (       self			:				int   ,lowercase_			:				int		):
						raise NotImplementedError







					def        __lowerCAmelCase (       self			:				List[str]		):
						if not self.is_available():
							raise RuntimeError(
							    F'You picked the {self.name} backend, but it is not installed. Run {self.pip_install()}.'		)







					@classmethod
					def        __lowerCAmelCase (       cls			:				str		):
						return F'`pip install {cls.pip_package or cls.name}`'







class 				SCREAMING_SNAKE_CASE					(		a_       ):






					"""simple docstring"""



					lowercase__				 =       "optuna"







					@staticmethod
					def        __lowerCAmelCase (       ):
						return is_optuna_available()







					def        __lowerCAmelCase (       self			:				Any   ,lowercase_			:				List[str]   ,lowercase_			:				int   ,lowercase_			:				str   ,**lowercase_			:				Any		):
						return run_hp_search_optuna(lowercase_   ,lowercase_   ,lowercase_   ,**lowercase_		)







					def        __lowerCAmelCase (       self			:				int   ,lowercase_			:				List[Any]		):
						return default_hp_space_optuna(lowercase_		)







class 				SCREAMING_SNAKE_CASE					(		a_       ):






					"""simple docstring"""



					lowercase__				 =       "ray"
					lowercase__				 =       "'ray[tune]'"







					@staticmethod
					def        __lowerCAmelCase (       ):
						return is_ray_available()







					def        __lowerCAmelCase (       self			:				str   ,lowercase_			:				int   ,lowercase_			:				int   ,lowercase_			:				str   ,**lowercase_			:				str		):
						return run_hp_search_ray(lowercase_   ,lowercase_   ,lowercase_   ,**lowercase_		)







					def        __lowerCAmelCase (       self			:				Dict   ,lowercase_			:				Tuple		):
						return default_hp_space_ray(lowercase_		)







class 				SCREAMING_SNAKE_CASE					(		a_       ):






					"""simple docstring"""



					lowercase__				 =       "sigopt"







					@staticmethod
					def        __lowerCAmelCase (       ):
						return is_sigopt_available()







					def        __lowerCAmelCase (       self			:				Tuple   ,lowercase_			:				List[str]   ,lowercase_			:				int   ,lowercase_			:				str   ,**lowercase_			:				List[Any]		):
						return run_hp_search_sigopt(lowercase_   ,lowercase_   ,lowercase_   ,**lowercase_		)







					def        __lowerCAmelCase (       self			:				str   ,lowercase_			:				Union[str, Any]		):
						return default_hp_space_sigopt(lowercase_		)







class 				SCREAMING_SNAKE_CASE					(		a_       ):






					"""simple docstring"""



					lowercase__				 =       "wandb"







					@staticmethod
					def        __lowerCAmelCase (       ):
						return is_wandb_available()







					def        __lowerCAmelCase (       self			:				str   ,lowercase_			:				Optional[int]   ,lowercase_			:				int   ,lowercase_			:				str   ,**lowercase_			:				List[Any]		):
						return run_hp_search_wandb(lowercase_   ,lowercase_   ,lowercase_   ,**lowercase_		)







					def        __lowerCAmelCase (       self			:				Any   ,lowercase_			:				Optional[int]		):
						return default_hp_space_wandb(lowercase_		)

__UpperCamelCase  :      Dict							      =		{
    HPSearchBackend(backend.name): backend for backend in [OptunaBackend, RayTuneBackend, SigOptBackend, WandbBackend]
}

def   __SCREAMING_SNAKE_CASE  (      ):
	lowerCAmelCase__	:						Tuple  				=	[backend for backend in ALL_HYPERPARAMETER_SEARCH_BACKENDS.values() if backend.is_available()]
	if len(A_ ) > 0:
		lowerCAmelCase__	:						Optional[int]  				=	available_backends[0].name
		if len(A_ ) > 1:
			logger.info(
			    f'{len(A_ )} hyperparameter search backends available. Using {name} as the default.' )
		return name
	raise RuntimeError(
	    '''No hyperparameter search backend available.\n'''
	    + '''\n'''.join(
	        f' - To install {backend.name} run {backend.pip_install()}'
	        for backend in ALL_HYPERPARAMETER_SEARCH_BACKENDS.values() ) )





from math import isqrt, loga






def  snake_case  (       snake_case__			:int)						->   list[int]:
       _A        =  [True] * max_number
       for i in range(2   ,	isqrt(max_number - 1) + 1):
              if is_prime[i]:
                     for j in range(i**2   ,	snake_case__   ,	snake_case__):
                            _A        =  False

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






def  snake_case  (       snake_case__			:int = 800_800   ,	snake_case__			:int = 800_800)						->   int:
       _A        =  degree * loga(snake_case__)
       _A        =  int(snake_case__)
       _A        =  calculate_prime_numbers(snake_case__)

       _A        =  0
       _A        =  0
       _A        =  len(snake_case__) - 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() = }''')




