




from collections import defaultdict
from math import ceil, sqrt







def 			lowerCamelCase_		(       UpperCamelCase__				:      int = 100_0000 ,     UpperCamelCase__				:      int = 10      )     ->       int:





				"""simple docstring"""


				__lowerCamelCase		       =    defaultdict(UpperCamelCase__      )

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

								hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

								for hole_width in range(UpperCamelCase__ ,     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() = }''')








def 			lowerCamelCase_		(       UpperCamelCase__				:      int      )     ->       bool:





				"""simple docstring"""


				return number & 1 == 0


if __name__ == "__main__":
					import doctest

					doctest.testmod()


