


from collections import defaultdict
from math import ceil, sqrt






def   _lowercase(					__a				:						int = 100_0000    ,     __a				:						int = 10     ):
							a__      =defaultdict(__a     )

							for outer_width in range(3    ,     (t_limit // 4) + 2     ):
														if outer_width * outer_width > t_limit:
																					a__      =max(
																					    ceil(sqrt(outer_width * outer_width - t_limit     )     )    ,     1     )
														else:
																					a__      =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 .testing import (
    are_the_same_tensors,
    execute_subprocess_async,
    require_bnb,
    require_cpu,
    require_cuda,
    require_huggingface_suite,
    require_mps,
    require_multi_gpu,
    require_multi_xpu,
    require_safetensors,
    require_single_gpu,
    require_single_xpu,
    require_torch_min_version,
    require_tpu,
    require_xpu,
    skip,
    slow,
)
from .training import RegressionDataset, RegressionModel, RegressionModelaXPU


from .scripts import test_script, test_sync, test_ops  # isort: skip





