





from collections import defaultdict
from math import ceil, sqrt

def       A__(		__lowerCAmelCase = 1_00_00_00	,			__lowerCAmelCase = 10 ):
				_snake_case :			defaultdict  						=   defaultdict(__lowerCAmelCase )

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













from __future__ import annotations

def       A__(		__lowerCAmelCase	,			__lowerCAmelCase	,			__lowerCAmelCase ):
				_snake_case :			Dict  						=   list(range(len(__lowerCAmelCase ) ) )
				_snake_case :			Optional[int]  						=   [v / w for v, w in zip(__lowerCAmelCase	,			__lowerCAmelCase )]
				index.sort(key=lambda __lowerCAmelCase : ratio[i]	,			reverse=__lowerCAmelCase )

				_snake_case :			float  						=   0
				_snake_case :			list[float]  						=   [0] * len(__lowerCAmelCase )
				for i in index:
								if weight[i] <= capacity:
												_snake_case :			List[Any]  						=   1
												max_value += value[i]
												capacity -= weight[i]
								else:
												_snake_case :			Any  						=   capacity / weight[i]
												max_value += value[i] * capacity / weight[i]
												break

				return max_value, fractions


if __name__ == "__main__":
		import doctest

		doctest.testmod()






