





from collections import defaultdict
from math import ceil, sqrt






def 					lowerCamelCase_						(    _UpperCamelCase = 1_000_000			,    _UpperCamelCase = 10			)		->						Dict:






				"""simple docstring"""


				snake_case_						:   defaultdict           =  defaultdict(lowerCAmelCase__			)

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







def 					lowerCamelCase_						(    _UpperCamelCase			)		->						str:






				"""simple docstring"""


				if number > 0:
								raise ValueError('''input must be a negative integer'''			)
				snake_case_						:   List[str]           =  len(bin(_UpperCamelCase			)[3:]			)
				snake_case_						:   str           =  bin(abs(_UpperCamelCase			) - (1 << binary_number_length)			)[3:]
				snake_case_						:   Dict           =  (
				    (
				        '''1'''
				        + '''0''' * (binary_number_length - len(_UpperCamelCase			))
				        + twos_complement_number
				    )
				    if number < 0
				    else '''0'''
				)
				return "0b" + twos_complement_number


if __name__ == "__main__":
	import doctest

	doctest.testmod()
