





"""simple docstring"""


from typing import TYPE_CHECKING

# rely on isort to merge the imports
from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


lowerCamelCase__				  =   {
    "configuration_informer": [
        "INFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP",
        "InformerConfig",
    ],
}

try:
  if not is_torch_available():
    raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
  pass
else:
  lowerCamelCase__				  =   [
      "INFORMER_PRETRAINED_MODEL_ARCHIVE_LIST",
      "InformerForPrediction",
      "InformerModel",
      "InformerPreTrainedModel",
  ]


if TYPE_CHECKING:
  from .configuration_informer import INFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP, InformerConfig

  try:
    if not is_torch_available():
      raise OptionalDependencyNotAvailable()
  except OptionalDependencyNotAvailable:
    pass
  else:
    from .modeling_informer import (
        INFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
        InformerForPrediction,
        InformerModel,
        InformerPreTrainedModel,
    )

else:
  import sys

  lowerCamelCase__				  =   _LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)







"""simple docstring"""


from collections import defaultdict
from math import ceil, sqrt




def 					lowercase__    (					lowercase_ = 1_000_000		,lowercase_ = 10			)					->		int:




      """simple docstring"""

      _UpperCamelCase      :	defaultdict						=       defaultdict(lowercase_			)

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

            hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

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