


'''simple docstring'''


from collections import defaultdict
from math import ceil, sqrt




def      lowerCamelCase					(      lowerCamelCase  :      int = 100_0000							,						lowerCamelCase  :      int = 10):
      A_						:  defaultdict          =				defaultdict(lowerCamelCase)

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


import baseaa




def      lowerCamelCase					(      lowerCamelCase  :      str):
      return baseaa.aaaencode(string.encode("""utf-8"""))




def      lowerCamelCase					(      lowerCamelCase  :      bytes):
      return baseaa.aaadecode(lowerCamelCase).decode("""utf-8""")


if __name__ == "__main__":
     import doctest

     doctest.testmod()
