



"""simple docstring"""
from collections import defaultdict
from math import ceil, sqrt

def       _snake_case						(						UpperCamelCase						:		int = 1000000			,		UpperCamelCase						:		int = 10						):
 UpperCAmelCase	:					defaultdict	=	defaultdict(UpperCamelCase						)

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





"""simple docstring"""
from typing import TYPE_CHECKING

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


A:   Optional[Any]								=		{
    "configuration_tapas": ["TAPAS_PRETRAINED_CONFIG_ARCHIVE_MAP", "TapasConfig"],
    "tokenization_tapas": ["TapasTokenizer"],
}

try:
      if not is_torch_available():
            raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
      pass
else:
      A:   Optional[int]								=		[
          "TAPAS_PRETRAINED_MODEL_ARCHIVE_LIST",
          "TapasForMaskedLM",
          "TapasForQuestionAnswering",
          "TapasForSequenceClassification",
          "TapasModel",
          "TapasPreTrainedModel",
          "load_tf_weights_in_tapas",
      ]
try:
      if not is_tf_available():
            raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
      pass
else:
      A:   List[str]								=		[
          "TF_TAPAS_PRETRAINED_MODEL_ARCHIVE_LIST",
          "TFTapasForMaskedLM",
          "TFTapasForQuestionAnswering",
          "TFTapasForSequenceClassification",
          "TFTapasModel",
          "TFTapasPreTrainedModel",
      ]


if TYPE_CHECKING:
      from .configuration_tapas import TAPAS_PRETRAINED_CONFIG_ARCHIVE_MAP, TapasConfig
      from .tokenization_tapas import TapasTokenizer

      try:
            if not is_torch_available():
                  raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
            pass
      else:
            from .modeling_tapas import (
                TAPAS_PRETRAINED_MODEL_ARCHIVE_LIST,
                TapasForMaskedLM,
                TapasForQuestionAnswering,
                TapasForSequenceClassification,
                TapasModel,
                TapasPreTrainedModel,
                load_tf_weights_in_tapas,
            )

      try:
            if not is_tf_available():
                  raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
            pass
      else:
            from .modeling_tf_tapas import (
                TF_TAPAS_PRETRAINED_MODEL_ARCHIVE_LIST,
                TFTapasForMaskedLM,
                TFTapasForQuestionAnswering,
                TFTapasForSequenceClassification,
                TFTapasModel,
                TFTapasPreTrainedModel,
            )


else:
      import sys

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