




def      A      (      _SCREAMING_SNAKE_CASE    )	-> list:

       # bit count represents no. of bits in the gray code
       if bit_count < 0:
              raise ValueError("The given input must be positive"    )

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

       return sequence

def      A      (      _SCREAMING_SNAKE_CASE    )	-> list:

       # The approach is a recursive one
       # Base case achieved when either n = 0 or n=1
       if bit_count == 0:
              return ["0"]

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

       lowerCamelCase   :      Tuple			 =					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
       lowerCamelCase   :      str			 =					gray_code_sequence_string(bit_count - 1    )

       lowerCamelCase   :      Tuple			 =					[]

       # append 0 to first half of the smaller sequence generated
       for i in range(seq_len // 2    ):
              lowerCamelCase   :      int			 =					'0' + smaller_sequence[i]
              sequence.append(_SCREAMING_SNAKE_CASE    )

       # append 1 to second half ... start from the end of the list
       for i in reversed(range(seq_len // 2    )    ):
              lowerCamelCase   :      List[Any]			 =					'1' + smaller_sequence[i]
              sequence.append(_SCREAMING_SNAKE_CASE    )

       return sequence


if __name__ == "__main__":
       import doctest

       doctest.testmod()













import math







def  _SCREAMING_SNAKE_CASE				(   a  )      ->      list[int]:
					__A	:						List[str]       =				[]
					__A	:						Any       =				2
					__A	:						Union[str, Any]       =				int(math.sqrt(a  )  )  # Size of every segment
					__A	:						Any       =				[True] * (end + 1)
					__A	:						List[Any]       =				[]

					while start <= end:
										if temp[start] is True:
															in_prime.append(a  )
															for i in range(start * start					,						end + 1					,						a  ):
																				__A	:						Optional[int]       =				False
										start += 1
					prime += in_prime

					__A	:						Any       =				end + 1
					__A	:						Any       =				min(2 * end					,						a  )

					while low <= n:
										__A	:						List[Any]       =				[True] * (high - low + 1)
										for each in in_prime:
															__A	:						List[str]       =				math.floor(low / each  ) * each
															if t < low:
																				t += each

															for j in range(a					,						high + 1					,						a  ):
																				__A	:						Optional[int]       =				False

										for j in range(len(a  )  ):
															if temp[j] is True:
																				prime.append(j + low  )

										__A	:						Optional[int]       =				high + 1
										__A	:						Tuple       =				min(high + end					,						a  )

					return prime




print(sieve(10**6))




