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







def 		A_(     A						:		int = 100_0000		,     A						:		int = 10):
							UpperCamelCase   			=     defaultdict(A)

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

														hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

														for hole_width in range(A		,     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_torch_available,
)


lowerCAmelCase					:    Optional[Any]           = {
    'configuration_falcon': ['FALCON_PRETRAINED_CONFIG_ARCHIVE_MAP', 'FalconConfig'],
}

try:
						if not is_torch_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						lowerCAmelCase					:    str           = [
						    'FALCON_PRETRAINED_MODEL_ARCHIVE_LIST',
						    'FalconForCausalLM',
						    'FalconModel',
						    'FalconPreTrainedModel',
						    'FalconForSequenceClassification',
						    'FalconForTokenClassification',
						    'FalconForQuestionAnswering',
						]


if TYPE_CHECKING:
						from .configuration_falcon import FALCON_PRETRAINED_CONFIG_ARCHIVE_MAP, FalconConfig

						try:
												if not is_torch_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_falcon import (
												    FALCON_PRETRAINED_MODEL_ARCHIVE_LIST,
												    FalconForCausalLM,
												    FalconForQuestionAnswering,
												    FalconForSequenceClassification,
												    FalconForTokenClassification,
												    FalconModel,
												    FalconPreTrainedModel,
												)


else:
						import sys

						lowerCAmelCase					:    Tuple           = _LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)




