






from collections import defaultdict
from math import ceil, sqrt


def        _a  (     UpperCamelCase_					:				int = 1_000_000    ,   UpperCamelCase_					:				int = 10   ) ->   int:
						"""simple docstring"""







						lowerCAmelCase__       =						defaultdict(UpperCamelCase_   )

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

												hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

												for hole_width in range(UpperCamelCase_    ,   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        _a  (     UpperCamelCase_					:				list    ,   UpperCamelCase_					:				list   ) ->   float:
						"""simple docstring"""







						_validate_point(UpperCamelCase_   )
						_validate_point(UpperCamelCase_   )
						if len(UpperCamelCase_   ) != len(UpperCamelCase_   ):
												raise ValueError("Both points must be in the same n-dimensional space"   )

						return float(sum(abs(a - b   ) for a, b in zip(UpperCamelCase_    ,   UpperCamelCase_   )   )   )


def        _a  (     UpperCamelCase_					:				list[float]   ) ->   None:
						"""simple docstring"""







						if point:
												if isinstance(UpperCamelCase_    ,   UpperCamelCase_   ):
																		for item in point:
																								if not isinstance(UpperCamelCase_    ,   (int, float)   ):
																														lowerCAmelCase__       =						(
																														    "Expected a list of numbers as input, found "
																														    F"{type(UpperCamelCase_   ).__name__}"
																														)
																														raise TypeError(UpperCamelCase_   )
												else:
																		lowerCAmelCase__       =						F"Expected a list of numbers as input, found {type(UpperCamelCase_   ).__name__}"
																		raise TypeError(UpperCamelCase_   )
						else:
												raise ValueError("Missing an input"   )


def        _a  (     UpperCamelCase_					:				list    ,   UpperCamelCase_					:				list   ) ->   float:
						"""simple docstring"""







						_validate_point(UpperCamelCase_   )
						_validate_point(UpperCamelCase_   )
						if len(UpperCamelCase_   ) != len(UpperCamelCase_   ):
												raise ValueError("Both points must be in the same n-dimensional space"   )

						return float(sum(abs(x - y   ) for x, y in zip(UpperCamelCase_    ,   UpperCamelCase_   )   )   )


if __name__ == "__main__":
	import doctest

	doctest.testmod()






