

"""simple docstring"""


from collections import defaultdict
from math import ceil, sqrt




def  _lowercase					(    __lowerCAmelCase = 100_0000  ,					__lowerCAmelCase = 10							)       ->				int:
      SCREAMING_SNAKE_CASE__   :      defaultdict      		=	defaultdict(__lowerCAmelCase							)

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

            hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

            for hole_width in range(__lowerCAmelCase  ,					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					(    __lowerCAmelCase							)       ->				int:
      if divisor % 5 == 0 or divisor % 2 == 0:
            return 0
      SCREAMING_SNAKE_CASE__   :      List[Any]      		=	1
      SCREAMING_SNAKE_CASE__   :      int      		=	1
      while repunit:
            SCREAMING_SNAKE_CASE__   :      str      		=	(10 * repunit + 1) % divisor
            repunit_index += 1
      return repunit_index




def  _lowercase					(    __lowerCAmelCase = 100_0000							)       ->				int:
      SCREAMING_SNAKE_CASE__   :      Dict      		=	limit - 1
      if divisor % 2 == 0:
            divisor += 1
      while least_divisible_repunit(__lowerCAmelCase							) <= limit:
            divisor += 2
      return divisor


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




