






'''simple docstring'''





from collections import defaultdict
from math import ceil, sqrt





def 	lowerCAmelCase_		(lowercase__						:       int = 1_00_00_00     ,					lowercase__						:       int = 10       )		->    Dict:


				'''simple docstring'''




				lowerCAmelCase__      			=						defaultdict(lowercase__       )

				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(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() = }''')













from __future__ import annotations





def 	lowerCAmelCase_		(lowercase__						:       list[int]       )		->    bool:


				'''simple docstring'''




				return len(set(lowercase__       )       ) == len(lowercase__       )


if __name__ == "__main__":
			import doctest

			doctest.testmod()





