






'''simple docstring'''





def      __A					(     _lowercase ):

					'''simple docstring'''







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

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

					return sequence




def      __A					(     _lowercase ):

					'''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(_lowercase )

					# 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(_lowercase )

					return sequence


if __name__ == "__main__":
				import doctest

				doctest.testmod()











import math




def      __A					(     _lowercase ):

					'''simple docstring'''







					_A								= []
					_A								= 2
					_A								= int(math.sqrt(_lowercase ) )  # Size of every segment
					_A								= [True] * (end + 1)
					_A								= []

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

					_A								= end + 1
					_A								= min(2 * end					,			_lowercase )

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

															for j in range(_lowercase					,			high + 1					,			_lowercase ):
																				_A								= False

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

										_A								= high + 1
										_A								= min(high + end					,			_lowercase )

					return prime


print(sieve(10**6))



