



'''simple docstring'''

from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


__lowerCAmelCase									=   {
    '''configuration_jukebox''': [
        '''JUKEBOX_PRETRAINED_CONFIG_ARCHIVE_MAP''',
        '''JukeboxConfig''',
        '''JukeboxPriorConfig''',
        '''JukeboxVQVAEConfig''',
    ],
    '''tokenization_jukebox''': ['''JukeboxTokenizer'''],
}

try:
							if not is_torch_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							__lowerCAmelCase									=   [
							    '''JUKEBOX_PRETRAINED_MODEL_ARCHIVE_LIST''',
							    '''JukeboxModel''',
							    '''JukeboxPreTrainedModel''',
							    '''JukeboxVQVAE''',
							    '''JukeboxPrior''',
							]

if TYPE_CHECKING:
							from .configuration_jukebox import (
							    JUKEBOX_PRETRAINED_CONFIG_ARCHIVE_MAP,
							    JukeboxConfig,
							    JukeboxPriorConfig,
							    JukeboxVQVAEConfig,
							)
							from .tokenization_jukebox import JukeboxTokenizer

							try:
														if not is_torch_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .modeling_jukebox import (
														    JUKEBOX_PRETRAINED_MODEL_ARCHIVE_LIST,
														    JukeboxModel,
														    JukeboxPreTrainedModel,
														    JukeboxPrior,
														    JukeboxVQVAE,
														)

else:
							import sys

							__lowerCAmelCase									=   _LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)









'''simple docstring'''

import math



def      __lowerCamelCase     (      lowerCAmelCase_  )			->      bool:
		_a     :      Optional[int]        =							math.loga(math.sqrt(4 * positive_integer + 1  ) / 2 + 1 / 2  )

		return exponent == int(lowerCAmelCase_  )



def      __lowerCamelCase     (      lowerCAmelCase_ = 1 / 12345  )			->      int:
		_a     :      int        =							0
		_a     :      Optional[Any]        =							0

		_a     :      int        =							3
		while True:
				_a     :      Tuple        =							(integer**2 - 1) / 4
				# if candidate is an integer, then there is a partition for k
				if partition_candidate == int(lowerCAmelCase_  ):
						_a     :      Union[str, Any]        =							int(lowerCAmelCase_  )
						total_partitions += 1
						if check_partition_perfect(lowerCAmelCase_  ):
								perfect_partitions += 1
				if perfect_partitions > 0:
						if perfect_partitions / total_partitions < max_proportion:
								return int(lowerCAmelCase_  )
				integer += 1


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




