
def 		UpperCAmelCase     (      a_		)						->      list:







				"""simple docstring"""



				if bit_count < 0:
								raise ValueError("The given input must be positive"		)

				# get the generated string sequence
				__A       =					gray_code_sequence_string(a_		)
				#
				# convert them to integers
				for i in range(len(a_		)		):
								__A       =					int(sequence[i]						,  2		)

				return sequence


def 		UpperCAmelCase     (      a_		)						->      list:







				"""simple docstring"""



				if bit_count == 0:
								return ["0"]

				if bit_count == 1:
								return ["0", "1"]

				__A       =					1 << bit_count  # defines the length of the sequence
				# 1<< n is equivalent to 2^n

				# recursive answer will generate answer for n-1 bits
				__A       =					gray_code_sequence_string(bit_count - 1		)

				__A       =					[]

				# append 0 to first half of the smaller sequence generated
				for i in range(seq_len // 2		):
								__A       =					"0" + smaller_sequence[i]
								sequence.append(a_		)

				# append 1 to second half ... start from the end of the list
				for i in reversed(range(seq_len // 2		)		):
								__A       =					"1" + smaller_sequence[i]
								sequence.append(a_		)

				return sequence


if __name__ == "__main__":
					import doctest

					doctest.testmod()


from math import isqrt





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

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





def      lowerCamelCase_					(							lowerCamelCase__ = 1_0**8       ):
				lowerCamelCase_         =     calculate_prime_numbers(max_number // 2       )

				lowerCamelCase_         =     0
				lowerCamelCase_         =     0
				lowerCamelCase_         =     len(lowerCamelCase__       ) - 1
				while left <= right:
								while prime_numbers[left] * prime_numbers[right] >= max_number:
												right -= 1
								semiprimes_count += right - left + 1
								left += 1

				return semiprimes_count


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


