'''simple docstring'''





from collections import defaultdict
from math import ceil, sqrt


def     __lowerCAmelCase						(       a_ = 100_0000       ,      a_ = 10		)      ->	int:





     '''simple docstring'''





     SCREAMING_SNAKE_CASE					:			List[Any]    	=       defaultdict(a_		)

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




'''simple docstring'''





from typing import TYPE_CHECKING

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


_lowerCAmelCase  :int  				=    {
    """configuration_albert""": ["""ALBERT_PRETRAINED_CONFIG_ARCHIVE_MAP""", """AlbertConfig""", """AlbertOnnxConfig"""],
}

try:
 if not is_sentencepiece_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 _lowerCAmelCase  :str  				=    ["""AlbertTokenizer"""]

try:
 if not is_tokenizers_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 _lowerCAmelCase  :Optional[int]  				=    ["""AlbertTokenizerFast"""]

try:
 if not is_torch_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 _lowerCAmelCase  :List[str]  				=    [
     """ALBERT_PRETRAINED_MODEL_ARCHIVE_LIST""",
     """AlbertForMaskedLM""",
     """AlbertForMultipleChoice""",
     """AlbertForPreTraining""",
     """AlbertForQuestionAnswering""",
     """AlbertForSequenceClassification""",
     """AlbertForTokenClassification""",
     """AlbertModel""",
     """AlbertPreTrainedModel""",
     """load_tf_weights_in_albert""",
 ]

try:
 if not is_tf_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 _lowerCAmelCase  :Any  				=    [
     """TF_ALBERT_PRETRAINED_MODEL_ARCHIVE_LIST""",
     """TFAlbertForMaskedLM""",
     """TFAlbertForMultipleChoice""",
     """TFAlbertForPreTraining""",
     """TFAlbertForQuestionAnswering""",
     """TFAlbertForSequenceClassification""",
     """TFAlbertForTokenClassification""",
     """TFAlbertMainLayer""",
     """TFAlbertModel""",
     """TFAlbertPreTrainedModel""",
 ]

try:
 if not is_flax_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 _lowerCAmelCase  :Optional[int]  				=    [
     """FlaxAlbertForMaskedLM""",
     """FlaxAlbertForMultipleChoice""",
     """FlaxAlbertForPreTraining""",
     """FlaxAlbertForQuestionAnswering""",
     """FlaxAlbertForSequenceClassification""",
     """FlaxAlbertForTokenClassification""",
     """FlaxAlbertModel""",
     """FlaxAlbertPreTrainedModel""",
 ]

if TYPE_CHECKING:
 from .configuration_albert import ALBERT_PRETRAINED_CONFIG_ARCHIVE_MAP, AlbertConfig, AlbertOnnxConfig

 try:
  if not is_sentencepiece_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .tokenization_albert import AlbertTokenizer

 try:
  if not is_tokenizers_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .tokenization_albert_fast import AlbertTokenizerFast

 try:
  if not is_torch_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_albert import (
      ALBERT_PRETRAINED_MODEL_ARCHIVE_LIST,
      AlbertForMaskedLM,
      AlbertForMultipleChoice,
      AlbertForPreTraining,
      AlbertForQuestionAnswering,
      AlbertForSequenceClassification,
      AlbertForTokenClassification,
      AlbertModel,
      AlbertPreTrainedModel,
      load_tf_weights_in_albert,
  )

 try:
  if not is_tf_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_tf_albert import (
      TF_ALBERT_PRETRAINED_MODEL_ARCHIVE_LIST,
      TFAlbertForMaskedLM,
      TFAlbertForMultipleChoice,
      TFAlbertForPreTraining,
      TFAlbertForQuestionAnswering,
      TFAlbertForSequenceClassification,
      TFAlbertForTokenClassification,
      TFAlbertMainLayer,
      TFAlbertModel,
      TFAlbertPreTrainedModel,
  )

 try:
  if not is_flax_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_flax_albert import (
      FlaxAlbertForMaskedLM,
      FlaxAlbertForMultipleChoice,
      FlaxAlbertForPreTraining,
      FlaxAlbertForQuestionAnswering,
      FlaxAlbertForSequenceClassification,
      FlaxAlbertForTokenClassification,
      FlaxAlbertModel,
      FlaxAlbertPreTrainedModel,
  )
else:
 import sys

 _lowerCAmelCase  :Union[str, Any]  				=    _LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)



