




import math



def 						lowerCAmelCase		(		_lowerCAmelCase							:   int	):




 """simple docstring"""







 UpperCAmelCase__							 =						math.loga(math.sqrt(4 * positive_integer + 1	) / 2 + 1 / 2	)

 return exponent == int(_lowerCAmelCase	)



def 						lowerCAmelCase		(		_lowerCAmelCase							:   float = 1 / 1_2345	):




 """simple docstring"""







 UpperCAmelCase__							 =						0
 UpperCAmelCase__							 =						0

 UpperCAmelCase__							 =						3
 while True:
  UpperCAmelCase__							 =						(integer**2 - 1) / 4
  # if candidate is an integer, then there is a partition for k
  if partition_candidate == int(_lowerCAmelCase	):
   UpperCAmelCase__							 =						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() = }''')











from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_flax_available, is_torch_available


_lowerCAmelCase						:   Optional[int]		=   {
    "configuration_gpt_neo": ["GPT_NEO_PRETRAINED_CONFIG_ARCHIVE_MAP", "GPTNeoConfig", "GPTNeoOnnxConfig"],
}

try:
  if not is_torch_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  _lowerCAmelCase						:   List[str]		=   [
      "GPT_NEO_PRETRAINED_MODEL_ARCHIVE_LIST",
      "GPTNeoForCausalLM",
      "GPTNeoForQuestionAnswering",
      "GPTNeoForSequenceClassification",
      "GPTNeoForTokenClassification",
      "GPTNeoModel",
      "GPTNeoPreTrainedModel",
      "load_tf_weights_in_gpt_neo",
  ]

try:
  if not is_flax_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  _lowerCAmelCase						:   Tuple		=   [
      "FlaxGPTNeoForCausalLM",
      "FlaxGPTNeoModel",
      "FlaxGPTNeoPreTrainedModel",
  ]


if TYPE_CHECKING:
  from .configuration_gpt_neo import GPT_NEO_PRETRAINED_CONFIG_ARCHIVE_MAP, GPTNeoConfig, GPTNeoOnnxConfig

  try:
    if not is_torch_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .modeling_gpt_neo import (
        GPT_NEO_PRETRAINED_MODEL_ARCHIVE_LIST,
        GPTNeoForCausalLM,
        GPTNeoForQuestionAnswering,
        GPTNeoForSequenceClassification,
        GPTNeoForTokenClassification,
        GPTNeoModel,
        GPTNeoPreTrainedModel,
        load_tf_weights_in_gpt_neo,
    )

  try:
    if not is_flax_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .modeling_flax_gpt_neo import FlaxGPTNeoForCausalLM, FlaxGPTNeoModel, FlaxGPTNeoPreTrainedModel


else:
  import sys

  _lowerCAmelCase						:   Union[str, Any]		=   _LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)





