



from collections import defaultdict
from math import ceil, sqrt



def       lowercase       (   SCREAMING_SNAKE_CASE__       :	Optional[int] = 1_000_000				,       SCREAMING_SNAKE_CASE__       :	int = 10				)  ->     int:
	_snake_case    :  Optional[int]					=					defaultdict(a__				)

	for outer_width in range(3				,       (t_limit // 4) + 2				):
		if outer_width * outer_width > t_limit:
			_snake_case    :  str					=					max(
			    ceil(sqrt(outer_width * outer_width - t_limit				)				)				,       1				)
		else:
			_snake_case    :  Tuple					=					1

		hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

		for hole_width in range(a__				,       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() = }''')





from __future__ import annotations

from math import pi

# Define the Reduced Planck Constant ℏ (H bar), speed of light C, value of
# Pi and the function
a__    =	1.0_54_57_18_17E-34  # unit of ℏ : J * s

a__    =	3E8  # unit of c : m * s^-1



def       lowercase       (   SCREAMING_SNAKE_CASE__       :	float				,       SCREAMING_SNAKE_CASE__       :	float				,       SCREAMING_SNAKE_CASE__       :	float				)  ->     dict[str, float]:

 if (force, area, distance).count(0				) != 1:
  raise ValueError("""One and only one argument must be 0"""				)
 if force < 0:
  raise ValueError("""Magnitude of force can not be negative"""				)
 if distance < 0:
  raise ValueError("""Distance can not be negative"""				)
 if area < 0:
  raise ValueError("""Area can not be negative"""				)
 if force == 0:
  _snake_case    :  Union[str, Any]					=					(REDUCED_PLANCK_CONSTANT * SPEED_OF_LIGHT * pi**2 * area) / (
      240 * (distance) ** 4
  )
  return {"force": force}
 elif area == 0:
  _snake_case    :  Optional[Any]					=					(240 * force * (distance) ** 4) / (
      REDUCED_PLANCK_CONSTANT * SPEED_OF_LIGHT * pi**2
  )
  return {"area": area}
 elif distance == 0:
  _snake_case    :  str					=					(
      (REDUCED_PLANCK_CONSTANT * SPEED_OF_LIGHT * pi**2 * area) / (240 * force)
  ) ** (1 / 4)
  return {"distance": distance}
 raise ValueError("""One and only one argument must be 0"""				)


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

  doctest.testmod()
