
"""simple docstring"""




from collections import defaultdict
from math import ceil, sqrt

def lowercase_						(     _snake_case = 1_000_000     ,_snake_case = 10		):
							SCREAMING_SNAKE_CASE__		: defaultdict     =     defaultdict(_snake_case		)

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

														hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

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






"""simple docstring"""




def lowercase_						(     _snake_case		):
							if divisor % 5 == 0 or divisor % 2 == 0:
														return 0
							SCREAMING_SNAKE_CASE__		: List[str]     =     1
							SCREAMING_SNAKE_CASE__		: List[Any]     =     1
							while repunit:
														SCREAMING_SNAKE_CASE__		: Dict     =     (10 * repunit + 1) % divisor
														repunit_index += 1
							return repunit_index

def lowercase_						(     _snake_case = 1_000_000		):
							SCREAMING_SNAKE_CASE__		: int     =     limit - 1
							if divisor % 2 == 0:
														divisor += 1
							while least_divisible_repunit(_snake_case		) <= limit:
														divisor += 2
							return divisor


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




