
"""simple docstring"""







def    __lowerCAmelCase    (_UpperCamelCase	,  _UpperCamelCase		):
	if number < 0 or shift_amount < 0:
		raise ValueError('both inputs must be positive integers'		)

	__lowerCAmelCase      :						Dict						      =				str(bin(_UpperCamelCase		)		)
	binary_number += "0" * shift_amount
	return binary_number
def    __lowerCAmelCase    (_UpperCamelCase	,  _UpperCamelCase		):
	if number < 0 or shift_amount < 0:
		raise ValueError('both inputs must be positive integers'		)

	__lowerCAmelCase      :						List[Any]						      =				str(bin(_UpperCamelCase		)		)[2:]
	if shift_amount >= len(_UpperCamelCase		):
		return "0b0"
	__lowerCAmelCase      :						Optional[Any]						      =				binary_number[: len(_UpperCamelCase		) - shift_amount]
	return "0b" + shifted_binary_number
def    __lowerCAmelCase    (_UpperCamelCase	,  _UpperCamelCase		):
	if number >= 0:  # Get binary representation of positive number
		__lowerCAmelCase      :						Optional[Any]						      =				'0' + str(bin(_UpperCamelCase		)		).strip('-'		)[2:]
	else:  # Get binary (2's complement) representation of negative number
		__lowerCAmelCase      :						List[str]						      =				len(bin(_UpperCamelCase		)[3:]		)  # Find 2's complement of number
		__lowerCAmelCase      :						str						      =				bin(abs(_UpperCamelCase		) - (1 << binary_number_length)		)[3:]
		__lowerCAmelCase      :						List[str]						      =				(
		    '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()

"""simple docstring"""







from __future__ import annotations
def    __lowerCAmelCase    (_UpperCamelCase		):
	__lowerCAmelCase      :						List[str]						      =				str(_UpperCamelCase		)
	return len(_UpperCamelCase		) == 9 and set(_UpperCamelCase		) == set('123456789'		)
def    __lowerCAmelCase    ():
	for base_num in range(9999	,  4999	,  -1		):
		__lowerCAmelCase      :						Union[str, Any]						      =				10_0002 * base_num
		if is_9_pandigital(_UpperCamelCase		):
			return candidate

	for base_num in range(333	,  99	,  -1		):
		__lowerCAmelCase      :						Dict						      =				100_2003 * base_num
		if is_9_pandigital(_UpperCamelCase		):
			return candidate

	return None


if __name__ == "__main__":
							print(f'{solution() = }')