import math






def 				__lowerCamelCase		(						lowerCAmelCase__     ):
       lowerCAmelCase__					     = math.loga(math.sqrt(4 * positive_integer + 1     ) / 2 + 1 / 2     )

       return exponent == int(A__     )






def 				__lowerCamelCase		(						lowerCAmelCase__ = 1 / 1_2_3_4_5     ):
       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(A__     ):
                     lowerCAmelCase__					     = int(A__     )
                     total_partitions += 1
                     if check_partition_perfect(A__     ):
                            perfect_partitions += 1
              if perfect_partitions > 0:
                     if perfect_partitions / total_partitions < max_proportion:
                            return int(A__     )
              integer += 1


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


from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


lowerCAmelCase__     						=			{
    'configuration_x_clip': [
        'XCLIP_PRETRAINED_CONFIG_ARCHIVE_MAP',
        'XCLIPConfig',
        'XCLIPTextConfig',
        'XCLIPVisionConfig',
    ],
    'processing_x_clip': ['XCLIPProcessor'],
}

try:
    if not is_torch_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    lowerCAmelCase__     						=			[
        'XCLIP_PRETRAINED_MODEL_ARCHIVE_LIST',
        'XCLIPModel',
        'XCLIPPreTrainedModel',
        'XCLIPTextModel',
        'XCLIPVisionModel',
    ]

if TYPE_CHECKING:
    from .configuration_x_clip import (
        XCLIP_PRETRAINED_CONFIG_ARCHIVE_MAP,
        XCLIPConfig,
        XCLIPTextConfig,
        XCLIPVisionConfig,
    )
    from .processing_x_clip import XCLIPProcessor

    try:
        if not is_torch_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .modeling_x_clip import (
            XCLIP_PRETRAINED_MODEL_ARCHIVE_LIST,
            XCLIPModel,
            XCLIPPreTrainedModel,
            XCLIPTextModel,
            XCLIPVisionModel,
        )

else:
    import sys

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