


"""simple docstring"""





from collections import defaultdict
from math import ceil, sqrt


def    _snake_case  (  _snake_case :	int = 1000000       ,      _snake_case :	int = 10	):
      lowerCAmelCase    :		defaultdict				=      defaultdict(_snake_case	)

      for outer_width in range(3       ,      (t_limit // 4) + 2	):
            if outer_width * outer_width > t_limit:
                  lowerCAmelCase    :		int				=      max(
                      ceil(sqrt(outer_width * outer_width - t_limit	)	)       ,      1	)
            else:
                  lowerCAmelCase    :		Any				=      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"""





import numpy as np


def    _snake_case  (  _snake_case :	np.array	):
      return 1 / (1 + np.exp(-vector	))


if __name__ == "__main__":
 import doctest

 doctest.testmod()


