


'''simple docstring'''

import math





def __snake_case					(      UpperCAmelCase_						:						int		):
 lowerCamelCase_      =  math.loga(math.sqrt(4 * positive_integer + 1		) / 2 + 1 / 2		)

 return exponent == int(UpperCAmelCase_		)





def __snake_case					(      UpperCAmelCase_						:						float = 1 / 12345		):
 lowerCamelCase_      =  0
 lowerCamelCase_      =  0

 lowerCamelCase_      =  3
 while True:
  lowerCamelCase_      =  (integer**2 - 1) / 4
  # if candidate is an integer, then there is a partition for k
  if partition_candidate == int(UpperCAmelCase_		):
   lowerCamelCase_      =  int(UpperCAmelCase_		)
   total_partitions += 1
   if check_partition_perfect(UpperCAmelCase_		):
    perfect_partitions += 1
  if perfect_partitions > 0:
   if perfect_partitions / total_partitions < max_proportion:
    return int(UpperCAmelCase_		)
  integer += 1


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








'''simple docstring'''

from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


__lowerCAmelCase									=   {
    '''configuration_bigbird_pegasus''': [
        '''BIGBIRD_PEGASUS_PRETRAINED_CONFIG_ARCHIVE_MAP''',
        '''BigBirdPegasusConfig''',
        '''BigBirdPegasusOnnxConfig''',
    ],
}

try:
							if not is_torch_available():
														raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
							pass
else:
							__lowerCAmelCase									=   [
							    '''BIGBIRD_PEGASUS_PRETRAINED_MODEL_ARCHIVE_LIST''',
							    '''BigBirdPegasusForCausalLM''',
							    '''BigBirdPegasusForConditionalGeneration''',
							    '''BigBirdPegasusForQuestionAnswering''',
							    '''BigBirdPegasusForSequenceClassification''',
							    '''BigBirdPegasusModel''',
							    '''BigBirdPegasusPreTrainedModel''',
							]


if TYPE_CHECKING:
							from .configuration_bigbird_pegasus import (
							    BIGBIRD_PEGASUS_PRETRAINED_CONFIG_ARCHIVE_MAP,
							    BigBirdPegasusConfig,
							    BigBirdPegasusOnnxConfig,
							)

							try:
														if not is_torch_available():
																					raise OptionalDependencyNotAvailable()
							except OptionalDependencyNotAvailable:
														pass
							else:
														from .modeling_bigbird_pegasus import (
														    BIGBIRD_PEGASUS_PRETRAINED_MODEL_ARCHIVE_LIST,
														    BigBirdPegasusForCausalLM,
														    BigBirdPegasusForConditionalGeneration,
														    BigBirdPegasusForQuestionAnswering,
														    BigBirdPegasusForSequenceClassification,
														    BigBirdPegasusModel,
														    BigBirdPegasusPreTrainedModel,
														)


else:
							import sys

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




