






def        _a  (     UpperCamelCase_					:				int    ,   UpperCamelCase_					:				int   ) ->   str:
						"""simple docstring"""







						if number < 0 or shift_amount < 0:
												raise ValueError("both inputs must be positive integers"   )

						lowerCAmelCase__       =						str(bin(UpperCamelCase_   )   )
						binary_number += "0" * shift_amount
						return binary_number


def        _a  (     UpperCamelCase_					:				int    ,   UpperCamelCase_					:				int   ) ->   str:
						"""simple docstring"""







						if number < 0 or shift_amount < 0:
												raise ValueError("both inputs must be positive integers"   )

						lowerCAmelCase__       =						str(bin(UpperCamelCase_   )   )[2:]
						if shift_amount >= len(UpperCamelCase_   ):
												return "0b0"
						lowerCAmelCase__       =						binary_number[: len(UpperCamelCase_   ) - shift_amount]
						return "0b" + shifted_binary_number


def        _a  (     UpperCamelCase_					:				int    ,   UpperCamelCase_					:				int   ) ->   str:
						"""simple docstring"""







						if number >= 0:  # Get binary representation of positive number
												lowerCAmelCase__       =						"0" + str(bin(UpperCamelCase_   )   ).strip("-"   )[2:]
						else:  # Get binary (2's complement) representation of negative number
												lowerCAmelCase__       =						len(bin(UpperCamelCase_   )[3:]   )  # Find 2's complement of number
												lowerCAmelCase__       =						bin(abs(UpperCamelCase_   ) - (1 << binary_number_length)   )[3:]
												lowerCAmelCase__       =						(
												    "1" + "0" * (binary_number_length - len(UpperCamelCase_   )) + binary_number
												)

						if shift_amount >= len(UpperCamelCase_   ):
												return "0b" + binary_number[0] * len(UpperCamelCase_   )
						return (
						    "0b"
						    + binary_number[0] * shift_amount
						    + binary_number[: len(UpperCamelCase_   ) - shift_amount]
						)


if __name__ == "__main__":
	import doctest

	doctest.testmod()










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() = }")






