





"""simple docstring"""


from typing import TYPE_CHECKING

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


__magic_name__       :					List[Any]						=			{
    """configuration_autoformer""": [
        """AUTOFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP""",
        """AutoformerConfig""",
    ],
}

try:
		if not is_torch_available():
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		pass
else:
		__magic_name__       :					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

		__magic_name__       :					Tuple						=			_LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)










"""simple docstring"""


from math import ceil, sqrt

def      UpperCamelCase							(SCREAMING_SNAKE_CASE = 100_0000     ):
						UpperCamelCase				:		int				   =			0

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



