





from math import ceil, sqrt





def 	lowerCAmelCase_					(			__a = 1000000						)	->						int:







  """simple docstring"""





  lowerCamelCase__: Any         =0

  for outer_width in range(3      ,       (limit // 4) + 2						):
    if outer_width**2 > limit:
      lowerCamelCase__: Optional[int]         =max(ceil(sqrt(outer_width**2 - limit						)						)      ,       1						)
    else:
      lowerCamelCase__: Tuple         =1
    if (outer_width - hole_width_lower_bound) % 2:
      hole_width_lower_bound += 1

    answer += (outer_width - hole_width_lower_bound - 2) // 2 + 1

  return answer


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






"""simple docstring"""






from typing import TYPE_CHECKING

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


__snake_case				:  Tuple =       {
    'configuration_autoformer': [
        'AUTOFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP',
        'AutoformerConfig',
    ],
}

try:
	if not is_torch_available():
		raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
	pass
else:
	__snake_case				:  Optional[Any] =       [
	    'AUTOFORMER_PRETRAINED_MODEL_ARCHIVE_LIST',
	    'AutoformerForPrediction',
	    'AutoformerModel',
	    'AutoformerPreTrainedModel',
	]


if TYPE_CHECKING:
	from .configuration_autoformer import (
	    AUTOFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP,
	    AutoformerConfig,
	)

	try:
		if not is_torch_available():
			raise OptionalDependencyNotAvailable()
	except OptionalDependencyNotAvailable:
		pass
	else:
		from .modeling_autoformer import (
		    AUTOFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
		    AutoformerForPrediction,
		    AutoformerModel,
		    AutoformerPreTrainedModel,
		)

else:
	import sys

	__snake_case				:  Optional[int] =       _LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)