



from collections import defaultdict
from math import ceil, sqrt

def      lowerCAmelCase_					(  _lowercase    :       int = 100_0000						,       _lowercase    :       int = 10)							->	int:







			"""simple docstring"""
			a__       :						defaultdict							=  defaultdict(_lowercase)

			for outer_width in range(3						,       (t_limit // 4) + 2):
						if outer_width * outer_width > t_limit:
									a__       :						List[Any]							=  max(
									    ceil(sqrt(outer_width * outer_width - t_limit))						,       1)
						else:
									a__       :						str							=  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 os
import sys
from contextlib import contextmanager


# Windows only
if os.name == "nt":
		import ctypes
		import msvcrt  # noqa

		class        snake_case__    (ctypes.Structure		):







								"""simple docstring"""




								__lowerCAmelCase					:Dict      =					[("size", ctypes.c_int), ("visible", ctypes.c_byte)]

def      lowerCAmelCase_					(  )							->	List[Any]:







			"""simple docstring"""
			if os.name == "nt":
						a__       :						int							=  CursorInfo()
						a__       :						Union[str, Any]							=  ctypes.windll.kernelaa.GetStdHandle(-11)
						ctypes.windll.kernelaa.GetConsoleCursorInfo(_lowercase						,       ctypes.byref(_lowercase))
						a__       :						List[str]							=  False
						ctypes.windll.kernelaa.SetConsoleCursorInfo(_lowercase						,       ctypes.byref(_lowercase))
			elif os.name == "posix":
						sys.stdout.write("""\033[?25l""")
						sys.stdout.flush()

def      lowerCAmelCase_					(  )							->	Optional[Any]:







			"""simple docstring"""
			if os.name == "nt":
						a__       :						List[Any]							=  CursorInfo()
						a__       :						Optional[int]							=  ctypes.windll.kernelaa.GetStdHandle(-11)
						ctypes.windll.kernelaa.GetConsoleCursorInfo(_lowercase						,       ctypes.byref(_lowercase))
						a__       :						Dict							=  True
						ctypes.windll.kernelaa.SetConsoleCursorInfo(_lowercase						,       ctypes.byref(_lowercase))
			elif os.name == "posix":
						sys.stdout.write("""\033[?25h""")
						sys.stdout.flush()





@contextmanager
def      lowerCAmelCase_					(  )							->	Any:







			"""simple docstring"""
			try:
						hide_cursor()
						yield
			finally:
						show_cursor()




