






'''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    :      Union[str, Any]  			=		logging.get_logger(__name__)




class 		UpperCamelCase__    :




		'''simple docstring'''





		_UpperCamelCase				  =					42
		_UpperCamelCase				  =					None






		@staticmethod
		def 			UpperCamelCase_					(      ):
								raise NotImplementedError






		def 			UpperCamelCase_					(      self   ,_lowerCAmelCase   ,_lowerCAmelCase   ,_lowerCAmelCase   ,**_lowerCAmelCase       ):
								raise NotImplementedError






		def 			UpperCamelCase_					(      self   ,_lowerCAmelCase       ):
								raise NotImplementedError






		def 			UpperCamelCase_					(      self       ):
								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       ):
								return F'''`pip install {cls.pip_package or cls.name}`'''




class 		UpperCamelCase__    (a			):




		'''simple docstring'''





		_UpperCamelCase				  =					'optuna'






		@staticmethod
		def 			UpperCamelCase_					(      ):
								return is_optuna_available()






		def 			UpperCamelCase_					(      self   ,_lowerCAmelCase   ,_lowerCAmelCase   ,_lowerCAmelCase   ,**_lowerCAmelCase       ):
								return run_hp_search_optuna(_lowerCAmelCase   ,_lowerCAmelCase   ,_lowerCAmelCase   ,**_lowerCAmelCase       )






		def 			UpperCamelCase_					(      self   ,_lowerCAmelCase       ):
								return default_hp_space_optuna(_lowerCAmelCase       )




class 		UpperCamelCase__    (a			):




		'''simple docstring'''





		_UpperCamelCase				  =					'ray'
		_UpperCamelCase				  =					'\'ray[tune]\''






		@staticmethod
		def 			UpperCamelCase_					(      ):
								return is_ray_available()






		def 			UpperCamelCase_					(      self   ,_lowerCAmelCase   ,_lowerCAmelCase   ,_lowerCAmelCase   ,**_lowerCAmelCase       ):
								return run_hp_search_ray(_lowerCAmelCase   ,_lowerCAmelCase   ,_lowerCAmelCase   ,**_lowerCAmelCase       )






		def 			UpperCamelCase_					(      self   ,_lowerCAmelCase       ):
								return default_hp_space_ray(_lowerCAmelCase       )




class 		UpperCamelCase__    (a			):




		'''simple docstring'''





		_UpperCamelCase				  =					'sigopt'






		@staticmethod
		def 			UpperCamelCase_					(      ):
								return is_sigopt_available()






		def 			UpperCamelCase_					(      self   ,_lowerCAmelCase   ,_lowerCAmelCase   ,_lowerCAmelCase   ,**_lowerCAmelCase       ):
								return run_hp_search_sigopt(_lowerCAmelCase   ,_lowerCAmelCase   ,_lowerCAmelCase   ,**_lowerCAmelCase       )






		def 			UpperCamelCase_					(      self   ,_lowerCAmelCase       ):
								return default_hp_space_sigopt(_lowerCAmelCase       )




class 		UpperCamelCase__    (a			):




		'''simple docstring'''





		_UpperCamelCase				  =					'wandb'






		@staticmethod
		def 			UpperCamelCase_					(      ):
								return is_wandb_available()






		def 			UpperCamelCase_					(      self   ,_lowerCAmelCase   ,_lowerCAmelCase   ,_lowerCAmelCase   ,**_lowerCAmelCase       ):
								return run_hp_search_wandb(_lowerCAmelCase   ,_lowerCAmelCase   ,_lowerCAmelCase   ,**_lowerCAmelCase       )






		def 			UpperCamelCase_					(      self   ,_lowerCAmelCase       ):
								return default_hp_space_wandb(_lowerCAmelCase       )



UpperCamelCase    :      Union[str, Any]  			=		{
    HPSearchBackend(backend.name): backend for backend in [OptunaBackend, RayTuneBackend, SigOptBackend, WandbBackend]
}
def 						A__			(				):
						lowerCamelCase__         =  [backend for backend in ALL_HYPERPARAMETER_SEARCH_BACKENDS.values() if backend.is_available()]
						if len(__lowerCAmelCase						) > 0:
												lowerCamelCase__         =  available_backends[0].name
												if len(__lowerCAmelCase						) > 1:
																		logger.info(
																		    F'''{len(__lowerCAmelCase						)} 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()						)						)









'''simple docstring'''







from math import factorial

UpperCamelCase    :      dict[str, int]  			=		{str(digit): factorial(digit) for digit in range(10)}
def 						A__			(				__lowerCAmelCase		:			int						):
						if not isinstance(__lowerCAmelCase   ,    __lowerCAmelCase						):
												raise TypeError("""Parameter number must be int"""						)

						if number < 0:
												raise ValueError("""Parameter number must be greater than or equal to 0"""						)

						# Converts number in string to iterate on its digits and adds its factorial.
						return sum(DIGIT_FACTORIAL[digit] for digit in str(__lowerCAmelCase						)						)
def 						A__			(				__lowerCAmelCase		:			int = 60   ,    __lowerCAmelCase		:			int = 100_0000						):

						if not isinstance(__lowerCAmelCase   ,    __lowerCAmelCase						) or not isinstance(__lowerCAmelCase   ,    __lowerCAmelCase						):
												raise TypeError("""Parameters chain_length and number_limit must be int"""						)

						if chain_length <= 0 or number_limit <= 0:
												raise ValueError(
												    """Parameters chain_length and number_limit must be greater than 0"""						)

						# the counter for the chains with the exact desired length
						lowerCamelCase__         =  0
						# the cached sizes of the previous chains
						lowerCamelCase__         =  {}

						for start_chain_element in range(1   ,    __lowerCAmelCase						):
												# The temporary set will contain the elements of the chain
												lowerCamelCase__         =  set()
												lowerCamelCase__         =  0

												# Stop computing the chain when you find a cached size, a repeating item or the
												# length is greater then the desired one.
												lowerCamelCase__         =  start_chain_element
												while (
												    chain_element not in chain_sets_lengths
												    and chain_element not in chain_set
												    and chain_set_length <= chain_length
												):
																		chain_set.add(__lowerCAmelCase						)
																		chain_set_length += 1
																		lowerCamelCase__         =  digit_factorial_sum(__lowerCAmelCase						)

												if chain_element in chain_sets_lengths:
																		chain_set_length += chain_sets_lengths[chain_element]

												lowerCamelCase__         =  chain_set_length

												# If chain contains the exact amount of elements increase the counter
												if chain_set_length == chain_length:
																		chains_counter += 1

						return chains_counter


if __name__ == "__main__":
							import doctest

							doctest.testmod()
							print(F'{solution()}')

