




from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


SCREAMING_SNAKE_CASE__       :      int  =   {
    'configuration_pegasus_x': ['PEGASUS_X_PRETRAINED_CONFIG_ARCHIVE_MAP', 'PegasusXConfig'],
}

try:
       if not is_torch_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       SCREAMING_SNAKE_CASE__       :      Optional[Any]  =   [
           'PEGASUS_X_PRETRAINED_MODEL_ARCHIVE_LIST',
           'PegasusXForConditionalGeneration',
           'PegasusXModel',
           'PegasusXPreTrainedModel',
       ]


if TYPE_CHECKING:
       from .configuration_pegasus_x import PEGASUS_X_PRETRAINED_CONFIG_ARCHIVE_MAP, PegasusXConfig

       try:
              if not is_torch_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .modeling_pegasus_x import (
                  PEGASUS_X_PRETRAINED_MODEL_ARCHIVE_LIST,
                  PegasusXForConditionalGeneration,
                  PegasusXModel,
                  PegasusXPreTrainedModel,
              )


else:
       import sys

       SCREAMING_SNAKE_CASE__       :      Any  =   _LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)












from math import sqrt

def      A      (      _SCREAMING_SNAKE_CASE = 100_0000    )	-> int:
       lowerCamelCase   :      int			 =					0
       lowerCamelCase   :      int			 =					0
       lowerCamelCase   :      int

       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(_SCREAMING_SNAKE_CASE ,sum_shortest_sides // 2    )
                                - max(1 ,sum_shortest_sides - max_cuboid_size    )
                                + 1
                            )

       return max_cuboid_size


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






