






from math import sqrt




def 				A		(					lowercase__  :  int = 100_0000  )		-> int:
	UpperCamelCase__ :int						=      0
	UpperCamelCase__ :int						=      0
	UpperCamelCase__ :int

	while num_cuboids <= limit:
		max_cuboid_size += 1
		for sum_shortest_sides in range(2 ,		2 * max_cuboid_size + 1  ):
			if sqrt(sum_shortest_sides**2 + max_cuboid_size**2  ).is_integer():
				num_cuboids += (
				    min(lowercase__ ,		sum_shortest_sides // 2  )
				    - max(1 ,		sum_shortest_sides - max_cuboid_size  )
				    + 1
				)

	return max_cuboid_size


if __name__ == "__main__":
							print(f'''{solution() = }''')





'''simple docstring'''







import os
import time

import pytest

from datasets.utils.filelock import FileLock, Timeout



def        lowerCamelCase__				(      __lowercase				):
     snake_case			:      List[Any]        =			FileLock(str(tmpdir / """foo.lock"""				)				)
     snake_case			:      str        =			FileLock(str(tmpdir / """foo.lock"""				)				)
     snake_case			:      Any        =			0.01
     with locka.acquire():
          with pytest.raises(__lowercase				):
               snake_case			:      Union[str, Any]        =			time.time()
               locka.acquire(__lowercase				)
               assert time.time() - _start > timeout







def        lowerCamelCase__				(      __lowercase				):
     snake_case			:      List[Any]        =			"""a""" * 1_000 + """.lock"""
     snake_case			:      List[str]        =			FileLock(str(tmpdir / filename				)				)
     assert locka._lock_file.endswith(""".lock"""				)
     assert not locka._lock_file.endswith(__lowercase				)
     assert len(os.path.basename(locka._lock_file				)				) <= 255
     snake_case			:      Any        =			FileLock(tmpdir / filename				)
     with locka.acquire():
          with pytest.raises(__lowercase				):
               locka.acquire(0				)



