


from collections import defaultdict
from math import ceil, sqrt







def 	SCREAMING_SNAKE_CASE_						(      __A			:      str = 1_00_00_00  ,   __A			:      Any = 10    )     ->		Optional[Any]:

       """simple docstring"""

       a_ :		int							=  defaultdict(__A    )

       for outer_width in range(3  ,   (t_limit // 4) + 2    ):
              if outer_width * outer_width > t_limit:
                     a_ :		str							=  max(
                         ceil(sqrt(outer_width * outer_width - t_limit    )    )  ,   1    )
              else:
                     a_ :		Optional[Any]							=  1

              hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

              for hole_width in range(__A  ,   outer_width - 1  ,   2    ):
                     count[outer_width * outer_width - hole_width * hole_width] += 1

       return sum(1 for n in count.values() if 1 <= n <= 10    )


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






from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_sentencepiece_available,
    is_tokenizers_available,
    is_torch_available,
)


UpperCAmelCase_				:			Optional[Any]   =	{'configuration_plbart': ['PLBART_PRETRAINED_CONFIG_ARCHIVE_MAP', 'PLBartConfig']}

try:
   if not is_sentencepiece_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   UpperCAmelCase_				:			Union[str, Any]   =	['PLBartTokenizer']

try:
   if not is_torch_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   pass
else:
   UpperCAmelCase_				:			List[str]   =	[
       'PLBART_PRETRAINED_MODEL_ARCHIVE_LIST',
       'PLBartForCausalLM',
       'PLBartForConditionalGeneration',
       'PLBartForSequenceClassification',
       'PLBartModel',
       'PLBartPreTrainedModel',
   ]


if TYPE_CHECKING:
   from .configuration_plbart import PLBART_PRETRAINED_CONFIG_ARCHIVE_MAP, PLBartConfig

   try:
      if not is_sentencepiece_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .tokenization_plbart import PLBartTokenizer

   try:
      if not is_torch_available():
         raise OptionalDependencyNotAvailable()
   except OptionalDependencyNotAvailable:
      pass
   else:
      from .modeling_plbart import (
          PLBART_PRETRAINED_MODEL_ARCHIVE_LIST,
          PLBartForCausalLM,
          PLBartForConditionalGeneration,
          PLBartForSequenceClassification,
          PLBartModel,
          PLBartPreTrainedModel,
      )


else:
   import sys

   UpperCAmelCase_				:			Union[str, Any]   =	_LazyModule(__name__, globals()['__file__'], _import_structure)


