






from math import ceil, sqrt






def    __magic_name__    (	SCREAMING_SNAKE_CASE = 1_000_000				)     ->    int:
							_lowercase							:   str 							=   0

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








from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


__a	 =      {
    """configuration_pegasus_x""": ["""PEGASUS_X_PRETRAINED_CONFIG_ARCHIVE_MAP""", """PegasusXConfig"""],
}

try:
 if not is_torch_available():
  raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
 pass
else:
 __a	 =      [
     """PEGASUS_X_PRETRAINED_MODEL_ARCHIVE_LIST""",
     """PegasusXForConditionalGeneration""",
     """PegasusXModel""",
     """PegasusXPreTrainedModel""",
 ]


if TYPE_CHECKING:
 from .configuration_pegasus_x import PEGASUS_X_PRETRAINED_CONFIG_ARCHIVE_MAP, PegasusXConfig

 try:
  if not is_torch_available():
   raise OptionalDependencyNotAvailable()
 except OptionalDependencyNotAvailable:
  pass
 else:
  from .modeling_pegasus_x import (
      PEGASUS_X_PRETRAINED_MODEL_ARCHIVE_LIST,
      PegasusXForConditionalGeneration,
      PegasusXModel,
      PegasusXPreTrainedModel,
  )


else:
 import sys

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



