
"""simple docstring"""





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

		__SCREAMING_SNAKE_CASE            = 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"""				)

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



def 						_lowerCAmelCase				(				UpperCamelCase_  ,				UpperCamelCase_				):
		if number >= 0:  # Get binary representation of positive number
				__SCREAMING_SNAKE_CASE            = """0""" + str(bin(UpperCamelCase_				)				).strip("""-"""				)[2:]
		else:  # Get binary (2's complement) representation of negative number
				__SCREAMING_SNAKE_CASE            = len(bin(UpperCamelCase_				)[3:]				)  # Find 2's complement of number
				__SCREAMING_SNAKE_CASE            = bin(abs(UpperCamelCase_				) - (1 << binary_number_length)				)[3:]
				__SCREAMING_SNAKE_CASE            = (
				    """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 math import isqrt, loga



def 						_lowerCAmelCase				(				UpperCamelCase_				):
		__SCREAMING_SNAKE_CASE            = [True] * max_number
		for i in range(2  ,				isqrt(max_number - 1				) + 1				):
				if is_prime[i]:
						for j in range(i**2  ,				UpperCamelCase_  ,				UpperCamelCase_				):
								__SCREAMING_SNAKE_CASE            = False

		return [i for i in range(2  ,				UpperCamelCase_				) if is_prime[i]]



def 						_lowerCAmelCase				(				UpperCamelCase_ = 80_0800  ,				UpperCamelCase_ = 80_0800				):
		__SCREAMING_SNAKE_CASE            = degree * loga(UpperCamelCase_				)
		__SCREAMING_SNAKE_CASE            = int(UpperCamelCase_				)
		__SCREAMING_SNAKE_CASE            = calculate_prime_numbers(UpperCamelCase_				)

		__SCREAMING_SNAKE_CASE            = 0
		__SCREAMING_SNAKE_CASE            = 0
		__SCREAMING_SNAKE_CASE            = len(UpperCamelCase_				) - 1
		while left < right:
				while (
				    prime_numbers[right] * loga(prime_numbers[left]				)
				    + prime_numbers[left] * loga(prime_numbers[right]				)
				    > upper_bound
				):
						right -= 1
				hybrid_integers_count += right - left
				left += 1

		return hybrid_integers_count


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




