





from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


_A :   Tuple  			=  {
    'configuration_jukebox': [
        'JUKEBOX_PRETRAINED_CONFIG_ARCHIVE_MAP',
        'JukeboxConfig',
        'JukeboxPriorConfig',
        'JukeboxVQVAEConfig',
    ],
    'tokenization_jukebox': ['JukeboxTokenizer'],
}

try:
       if not is_torch_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       _A :   str  			=  [
           'JUKEBOX_PRETRAINED_MODEL_ARCHIVE_LIST',
           'JukeboxModel',
           'JukeboxPreTrainedModel',
           'JukeboxVQVAE',
           'JukeboxPrior',
       ]

if TYPE_CHECKING:
       from .configuration_jukebox import (
           JUKEBOX_PRETRAINED_CONFIG_ARCHIVE_MAP,
           JukeboxConfig,
           JukeboxPriorConfig,
           JukeboxVQVAEConfig,
       )
       from .tokenization_jukebox import JukeboxTokenizer

       try:
              if not is_torch_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .modeling_jukebox import (
                  JUKEBOX_PRETRAINED_MODEL_ARCHIVE_LIST,
                  JukeboxModel,
                  JukeboxPreTrainedModel,
                  JukeboxPrior,
                  JukeboxVQVAE,
              )

else:
       import sys

       _A :   List[str]  			=  _LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)










from math import ceil, sqrt



def 	_a						(   UpperCAmelCase = 1000000					)    ->    int:







   """simple docstring"""
   lowerCamelCase__       :						Any        =							0

   for outer_width in range(3      ,  (limit // 4) + 2					):
      if outer_width**2 > limit:
         lowerCamelCase__       :						List[Any]        =							max(ceil(sqrt(outer_width**2 - limit					)					)      ,  1					)
      else:
         lowerCamelCase__       :						Union[str, Any]        =							1
      if (outer_width - hole_width_lower_bound) % 2:
         hole_width_lower_bound += 1

      answer += (outer_width - hole_width_lower_bound - 2) // 2 + 1

   return answer


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



