
from collections import defaultdict
from math import ceil, sqrt

def 				SCREAMING_SNAKE_CASE     (      __UpperCamelCase :						int = 1_00_00_00							,						__UpperCamelCase :						int = 10       ):

				"""simple docstring"""







				A__  :	defaultdict         =							defaultdict(__lowercase       )

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

								hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

								for hole_width in range(__lowercase							,						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() = }""")

import inspect
import os
import unittest

import torch

import accelerate
from accelerate import debug_launcher
from accelerate.test_utils import (
    execute_subprocess_async,
    require_cpu,
    require_huggingface_suite,
    require_multi_gpu,
    require_single_gpu,
)
from accelerate.utils import patch_environment







@require_huggingface_suite
class  UpperCamelCase__		(    unittest.TestCase   ):







	'''simple docstring'''





	def   __snake_case				(			self		):
					A__  :	Dict         =							inspect.getfile(accelerate.test_utils		)
					A__  :	Any         =							os.path.sep.join(
					    mod_file.split(os.path.sep		)[:-1] + ['''scripts''', '''external_deps''', '''test_metrics.py''']		)

					from accelerate.test_utils.scripts.external_deps import test_metrics  # noqa: F401

					A__  :	Tuple         =							test_metrics





	@require_cpu
	def   __snake_case				(			self		):
					debug_launcher(self.test_metrics.main				,       num_processes=1		)





	@require_cpu
	def   __snake_case				(			self		):
					debug_launcher(self.test_metrics.main		)





	@require_single_gpu
	def   __snake_case				(			self		):
					self.test_metrics.main()





	@require_multi_gpu
	def   __snake_case				(			self		):
					print(F"Found {torch.cuda.device_count()} devices."		)
					A__  :	int         =							['''torchrun''', F"--nproc_per_node={torch.cuda.device_count()}", self.test_file_path]
					with patch_environment(omp_num_threads=1		):
									execute_subprocess_async(UpperCamelCase__				,       env=os.environ.copy()		)