






'''simple docstring'''



from math import sqrt


def 							lowercase_				(    __A :       Optional[int] = 1_0_0_0_0_0_0			)       ->      int:



 """simple docstring"""




 lowercase					:   Union[str, Any]				  =0
 lowercase					:   Tuple				  =0
 lowercase					:   List[str]				  =4_2

 while num_cuboids <= limit:
  max_cuboid_size += 1
  for sum_shortest_sides in range(2					,      2 * max_cuboid_size + 1			):
   if sqrt(sum_shortest_sides**2 + max_cuboid_size**2			).is_integer():
    num_cuboids += (
        min(lowercase__					,      sum_shortest_sides // 2			)
        - max(1					,      sum_shortest_sides - max_cuboid_size			)
        + 1
    )

 return max_cuboid_size


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_mega': ['MEGA_PRETRAINED_CONFIG_ARCHIVE_MAP', 'MegaConfig', 'MegaOnnxConfig'],
}

try:
      if not is_torch_available():
            raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
      pass
else:
      SCREAMING_SNAKE_CASE						=	[
          'MEGA_PRETRAINED_MODEL_ARCHIVE_LIST',
          'MegaForCausalLM',
          'MegaForMaskedLM',
          'MegaForMultipleChoice',
          'MegaForQuestionAnswering',
          'MegaForSequenceClassification',
          'MegaForTokenClassification',
          'MegaModel',
          'MegaPreTrainedModel',
      ]

if TYPE_CHECKING:
      from .configuration_mega import MEGA_PRETRAINED_CONFIG_ARCHIVE_MAP, MegaConfig, MegaOnnxConfig

      try:
            if not is_torch_available():
                  raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
            pass
      else:
            from .modeling_mega import (
                MEGA_PRETRAINED_MODEL_ARCHIVE_LIST,
                MegaForCausalLM,
                MegaForMaskedLM,
                MegaForMultipleChoice,
                MegaForQuestionAnswering,
                MegaForSequenceClassification,
                MegaForTokenClassification,
                MegaModel,
                MegaPreTrainedModel,
            )

else:
      import sys

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



