def   __A		(			_A					):



 """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   __A		(			_A					):



 """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()



def   __A		(			_A = 100_0000					):



 """simple docstring"""


 __a       =  [i - 1 for i in range(limit + 1					)]

 for i in range(2							,				limit + 1					):
  if phi[i] == i - 1:
   for j in range(2 * i							,				limit + 1							,				_A					):
    phi[j] -= phi[j] // i

 return sum(phi[2 : limit + 1]					)


if __name__ == "__main__":
  print(solution())


