





'''simple docstring'''


import math


def 						__a(SCREAMING_SNAKE_CASE_	:       int     ):



    '''simple docstring'''





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

    return exponent == int(SCREAMING_SNAKE_CASE_     )


def 						__a(SCREAMING_SNAKE_CASE_	:       float = 1 / 12345     ):



    '''simple docstring'''





    _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(SCREAMING_SNAKE_CASE_     ):
            _lowerCAmelCase						      =   int(SCREAMING_SNAKE_CASE_     )
            total_partitions += 1
            if check_partition_perfect(SCREAMING_SNAKE_CASE_     ):
                perfect_partitions += 1
        if perfect_partitions > 0:
            if perfect_partitions / total_partitions < max_proportion:
                return int(SCREAMING_SNAKE_CASE_     )
        integer += 1


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









'''simple docstring'''


from typing import TYPE_CHECKING

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


_SCREAMING_SNAKE_CASE									=				{
    "configuration_mctct": ["MCTCT_PRETRAINED_CONFIG_ARCHIVE_MAP", "MCTCTConfig"],
    "feature_extraction_mctct": ["MCTCTFeatureExtractor"],
    "processing_mctct": ["MCTCTProcessor"],
}


try:
       if not is_torch_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       _SCREAMING_SNAKE_CASE									=				[
           "MCTCT_PRETRAINED_MODEL_ARCHIVE_LIST",
           "MCTCTForCTC",
           "MCTCTModel",
           "MCTCTPreTrainedModel",
       ]


if TYPE_CHECKING:
       from .configuration_mctct import MCTCT_PRETRAINED_CONFIG_ARCHIVE_MAP, MCTCTConfig
       from .feature_extraction_mctct import MCTCTFeatureExtractor
       from .processing_mctct import MCTCTProcessor

       try:
              if not is_torch_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .modeling_mctct import MCTCT_PRETRAINED_MODEL_ARCHIVE_LIST, MCTCTForCTC, MCTCTModel, MCTCTPreTrainedModel

else:
       import sys

       _SCREAMING_SNAKE_CASE									=				_LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)


