





from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_flax_available,
    is_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


_A :   Any  			=  {
    'configuration_blenderbot_small': [
        'BLENDERBOT_SMALL_PRETRAINED_CONFIG_ARCHIVE_MAP',
        'BlenderbotSmallConfig',
        'BlenderbotSmallOnnxConfig',
    ],
    'tokenization_blenderbot_small': ['BlenderbotSmallTokenizer'],
}

try:
       if not is_tokenizers_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       _A :   Union[str, Any]  			=  ['BlenderbotSmallTokenizerFast']

try:
       if not is_torch_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       _A :   List[str]  			=  [
           'BLENDERBOT_SMALL_PRETRAINED_MODEL_ARCHIVE_LIST',
           'BlenderbotSmallForCausalLM',
           'BlenderbotSmallForConditionalGeneration',
           'BlenderbotSmallModel',
           'BlenderbotSmallPreTrainedModel',
       ]

try:
       if not is_tf_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       _A :   str  			=  [
           'TFBlenderbotSmallForConditionalGeneration',
           'TFBlenderbotSmallModel',
           'TFBlenderbotSmallPreTrainedModel',
       ]

try:
       if not is_flax_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       _A :   Dict  			=  [
           'FlaxBlenderbotSmallForConditionalGeneration',
           'FlaxBlenderbotSmallModel',
           'FlaxBlenderbotSmallPreTrainedModel',
       ]

if TYPE_CHECKING:
       from .configuration_blenderbot_small import (
           BLENDERBOT_SMALL_PRETRAINED_CONFIG_ARCHIVE_MAP,
           BlenderbotSmallConfig,
           BlenderbotSmallOnnxConfig,
       )
       from .tokenization_blenderbot_small import BlenderbotSmallTokenizer

       try:
              if not is_tokenizers_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .tokenization_blenderbot_small_fast import BlenderbotSmallTokenizerFast

       try:
              if not is_torch_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .modeling_blenderbot_small import (
                  BLENDERBOT_SMALL_PRETRAINED_MODEL_ARCHIVE_LIST,
                  BlenderbotSmallForCausalLM,
                  BlenderbotSmallForConditionalGeneration,
                  BlenderbotSmallModel,
                  BlenderbotSmallPreTrainedModel,
              )

       try:
              if not is_tf_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .modeling_tf_blenderbot_small import (
                  TFBlenderbotSmallForConditionalGeneration,
                  TFBlenderbotSmallModel,
                  TFBlenderbotSmallPreTrainedModel,
              )

       try:
              if not is_flax_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .modeling_flax_blenderbot_small import (
                  FlaxBlenderbotSmallForConditionalGeneration,
                  FlaxBlenderbotSmallModel,
                  FlaxBlenderbotSmallPreTrainedModel,
              )

else:
       import sys

       _A :   Optional[int]  			=  _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() = }''')



