






"""simple docstring"""



from __future__ import annotations

from functools import lru_cache
from math import ceil

A_    =							100

A_    =							set(range(3, NUM_PRIMES, 2))
primes.add(2)
A_    =							42

for prime in range(3, ceil(NUM_PRIMES**0.5), 2):
						if prime not in primes:
												continue
						primes.difference_update(set(range(prime * prime, NUM_PRIMES, prime)))




@lru_cache(maxsize=1_0_0      )
def      _lowerCAmelCase		(							UpperCAmelCase__       :					int      )		->set[int]:
						if number_to_partition < 0:
												return set()
						elif number_to_partition == 0:
												return {1}

						A__						:  set[int]		  =  set()
						A__						:  int
						A__						:  int

						for prime in primes:
												if prime > number_to_partition:
																		continue
												for sub in partition(number_to_partition - prime      ):
																		ret.add(sub * prime      )

						return ret




def      _lowerCAmelCase		(							UpperCAmelCase__       :					int = 5_0_0_0      )		->int | None:
						for number_to_partition in range(1,						UpperCAmelCase__      ):
												if len(partition(UpperCAmelCase__      )      ) > number_unique_partitions:
																		return number_to_partition
						return None


if __name__ == "__main__":
						print(F'{solution() = }')














"""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


A_    =							logging.get_logger(__name__)






class 							__SCREAMING_SNAKE_CASE						:
							snake_case_     =							42
							snake_case_     =							None


							@staticmethod
							def 						_UpperCamelCase       (			):
													'''simple docstring'''





													raise NotImplementedError


							def 						_UpperCamelCase       (			self      :						str			,    snake_case      :						int			,    snake_case      :						int			,    snake_case      :						str			,    **snake_case      :						Any							):
													'''simple docstring'''





													raise NotImplementedError


							def 						_UpperCamelCase       (			self      :						Union[str, Any]			,    snake_case      :						Optional[int]							):
													'''simple docstring'''





													raise NotImplementedError


							def 						_UpperCamelCase       (			self      :						Union[str, Any]							):
													'''simple docstring'''





													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 						_UpperCamelCase       (			cls      :						Optional[int]							):
													'''simple docstring'''





													return F'`pip install {cls.pip_package or cls.name}`'






class 							__SCREAMING_SNAKE_CASE						(				UpperCamelCase		):
							snake_case_     =							'optuna'


							@staticmethod
							def 						_UpperCamelCase       (			):
													'''simple docstring'''





													return is_optuna_available()


							def 						_UpperCamelCase       (			self      :						str			,    snake_case      :						str			,    snake_case      :						int			,    snake_case      :						str			,    **snake_case      :						Any							):
													'''simple docstring'''





													return run_hp_search_optuna(snake_case			,    snake_case			,    snake_case			,    **snake_case							)


							def 						_UpperCamelCase       (			self      :						Optional[Any]			,    snake_case      :						int							):
													'''simple docstring'''





													return default_hp_space_optuna(snake_case							)






class 							__SCREAMING_SNAKE_CASE						(				UpperCamelCase		):
							snake_case_     =							'ray'
							snake_case_     =							'\'ray[tune]\''


							@staticmethod
							def 						_UpperCamelCase       (			):
													'''simple docstring'''





													return is_ray_available()


							def 						_UpperCamelCase       (			self      :						Any			,    snake_case      :						Tuple			,    snake_case      :						int			,    snake_case      :						str			,    **snake_case      :						List[Any]							):
													'''simple docstring'''





													return run_hp_search_ray(snake_case			,    snake_case			,    snake_case			,    **snake_case							)


							def 						_UpperCamelCase       (			self      :						Dict			,    snake_case      :						Dict							):
													'''simple docstring'''





													return default_hp_space_ray(snake_case							)






class 							__SCREAMING_SNAKE_CASE						(				UpperCamelCase		):
							snake_case_     =							'sigopt'


							@staticmethod
							def 						_UpperCamelCase       (			):
													'''simple docstring'''





													return is_sigopt_available()


							def 						_UpperCamelCase       (			self      :						str			,    snake_case      :						str			,    snake_case      :						int			,    snake_case      :						str			,    **snake_case      :						Union[str, Any]							):
													'''simple docstring'''





													return run_hp_search_sigopt(snake_case			,    snake_case			,    snake_case			,    **snake_case							)


							def 						_UpperCamelCase       (			self      :						List[str]			,    snake_case      :						Any							):
													'''simple docstring'''





													return default_hp_space_sigopt(snake_case							)






class 							__SCREAMING_SNAKE_CASE						(				UpperCamelCase		):
							snake_case_     =							'wandb'


							@staticmethod
							def 						_UpperCamelCase       (			):
													'''simple docstring'''





													return is_wandb_available()


							def 						_UpperCamelCase       (			self      :						int			,    snake_case      :						int			,    snake_case      :						int			,    snake_case      :						str			,    **snake_case      :						Any							):
													'''simple docstring'''





													return run_hp_search_wandb(snake_case			,    snake_case			,    snake_case			,    **snake_case							)


							def 						_UpperCamelCase       (			self      :						Optional[int]			,    snake_case      :						Union[str, Any]							):
													'''simple docstring'''





													return default_hp_space_wandb(snake_case							)




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




def      _lowerCAmelCase		(							)		->str:
						A__						:  List[Any]		  =  [backend for backend in ALL_HYPERPARAMETER_SEARCH_BACKENDS.values() if backend.is_available()]
						if len(UpperCAmelCase__      ) > 0:
												A__						:  Dict		  =  available_backends[0].name
												if len(UpperCAmelCase__      ) > 1:
																		logger.info(
																		    f'{len(UpperCAmelCase__      )} 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()      )      )






