





from collections import defaultdict
from math import ceil, sqrt

def   __snake_case    (       _lowerCAmelCase			:			int = 1000000					,					_lowerCAmelCase			:			int = 10						)			->    int:
   A_       :					defaultdict        =      defaultdict(_lowerCAmelCase						)

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







def   __snake_case    (       _lowerCAmelCase			:			int = 1					,					_lowerCAmelCase			:			int = 1000						)			->    int:
   A_       :					Optional[int]        =      1
   A_       :					int        =      0

   for divide_by_number in range(_lowerCAmelCase					,					digit + 1						):
      A_       :					list[int]        =      []
      A_       :					Union[str, Any]        =      numerator
      for _ in range(1					,					digit + 1						):
         if now_divide in has_been_divided:
            if longest_list_length < len(_lowerCAmelCase						):
               A_       :					Optional[Any]        =      len(_lowerCAmelCase						)
               A_       :					Union[str, Any]        =      divide_by_number
         else:
            has_been_divided.append(_lowerCAmelCase						)
            A_       :					Dict        =      now_divide * 10 % divide_by_number

   return the_digit


# Tests
if __name__ == "__main__":
 import doctest

 doctest.testmod()
