





from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_tf_available, is_torch_available


_UpperCAmelCase       : str			     =       {
    """configuration_transfo_xl""": ["""TRANSFO_XL_PRETRAINED_CONFIG_ARCHIVE_MAP""", """TransfoXLConfig"""],
    """tokenization_transfo_xl""": ["""TransfoXLCorpus""", """TransfoXLTokenizer"""],
}

try:
  if not is_torch_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  _UpperCAmelCase       : Optional[int]			     =       [
      """TRANSFO_XL_PRETRAINED_MODEL_ARCHIVE_LIST""",
      """AdaptiveEmbedding""",
      """TransfoXLForSequenceClassification""",
      """TransfoXLLMHeadModel""",
      """TransfoXLModel""",
      """TransfoXLPreTrainedModel""",
      """load_tf_weights_in_transfo_xl""",
  ]

try:
  if not is_tf_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  _UpperCAmelCase       : Optional[int]			     =       [
      """TF_TRANSFO_XL_PRETRAINED_MODEL_ARCHIVE_LIST""",
      """TFAdaptiveEmbedding""",
      """TFTransfoXLForSequenceClassification""",
      """TFTransfoXLLMHeadModel""",
      """TFTransfoXLMainLayer""",
      """TFTransfoXLModel""",
      """TFTransfoXLPreTrainedModel""",
  ]


if TYPE_CHECKING:
  from .configuration_transfo_xl import TRANSFO_XL_PRETRAINED_CONFIG_ARCHIVE_MAP, TransfoXLConfig
  from .tokenization_transfo_xl import TransfoXLCorpus, TransfoXLTokenizer

  try:
    if not is_torch_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .modeling_transfo_xl import (
        TRANSFO_XL_PRETRAINED_MODEL_ARCHIVE_LIST,
        AdaptiveEmbedding,
        TransfoXLForSequenceClassification,
        TransfoXLLMHeadModel,
        TransfoXLModel,
        TransfoXLPreTrainedModel,
        load_tf_weights_in_transfo_xl,
    )

  try:
    if not is_tf_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .modeling_tf_transfo_xl import (
        TF_TRANSFO_XL_PRETRAINED_MODEL_ARCHIVE_LIST,
        TFAdaptiveEmbedding,
        TFTransfoXLForSequenceClassification,
        TFTransfoXLLMHeadModel,
        TFTransfoXLMainLayer,
        TFTransfoXLModel,
        TFTransfoXLPreTrainedModel,
    )

else:
  import sys

  _UpperCAmelCase       : List[Any]			     =       _LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)












from collections import defaultdict
from math import ceil, sqrt


def  SCREAMING_SNAKE_CASE   ( _UpperCAmelCase = 100_0000		,			_UpperCAmelCase = 10				)    ->  int:
    lowerCamelCase__					:   defaultdict      				=	defaultdict(_UpperCAmelCase				)

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

        hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

        for hole_width in range(_UpperCAmelCase		,			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() = }""")





