






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__)










from collections import defaultdict
from math import ceil, sqrt


def        _a  (     UpperCamelCase_					:				int = 1_000_000    ,   UpperCamelCase_					:				int = 10   ) ->   int:
						"""simple docstring"""







						lowerCAmelCase__       =						defaultdict(UpperCamelCase_   )

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






