



'''simple docstring'''

from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_sentencepiece_available,
    is_tokenizers_available,
    is_torch_available,
)


__lowerCAmelCase									=   {'''configuration_plbart''': ['''PLBART_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''PLBartConfig''']}

try:
							if not is_sentencepiece_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							__lowerCAmelCase									=   ['''PLBartTokenizer''']

try:
							if not is_torch_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							__lowerCAmelCase									=   [
							    '''PLBART_PRETRAINED_MODEL_ARCHIVE_LIST''',
							    '''PLBartForCausalLM''',
							    '''PLBartForConditionalGeneration''',
							    '''PLBartForSequenceClassification''',
							    '''PLBartModel''',
							    '''PLBartPreTrainedModel''',
							]


if TYPE_CHECKING:
							from .configuration_plbart import PLBART_PRETRAINED_CONFIG_ARCHIVE_MAP, PLBartConfig

							try:
														if not is_sentencepiece_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .tokenization_plbart import PLBartTokenizer

							try:
														if not is_torch_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .modeling_plbart import (
														    PLBART_PRETRAINED_MODEL_ARCHIVE_LIST,
														    PLBartForCausalLM,
														    PLBartForConditionalGeneration,
														    PLBartForSequenceClassification,
														    PLBartModel,
														    PLBartPreTrainedModel,
														)


else:
							import sys

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









'''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() = }""")




