"""simple docstring"""




def      UpperCAmelCase    (		UpperCamelCase__ ):






							"""simple docstring"""





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

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

							return sequence






def      UpperCAmelCase    (		UpperCamelCase__ ):






							"""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(_lowerCamelCase )

							# 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(_lowerCamelCase )

							return sequence


if __name__ == "__main__":
				import doctest

				doctest.testmod()










def 				A				(					_lowerCamelCase  ):





							'''simple docstring'''




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

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

							return sequence






def 				A				(					_lowerCamelCase  ):





							'''simple docstring'''




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

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

							_lowerCAmelCase     :							List[Any]    =    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     :							Optional[int]    =    gray_code_sequence_string(bit_count - 1  )

							_lowerCAmelCase     :							str    =    []

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

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

							return sequence


if __name__ == "__main__":
						import doctest

						doctest.testmod()
