'''simple docstring'''

def 			__UpperCamelCase       (   UpperCAmelCase     ):

 # 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
 lowercase__				:    List[Any]  =					gray_code_sequence_string(UpperCAmelCase     )
 #
 # convert them to integers
 for i in range(len(UpperCAmelCase     )     ):
  lowercase__				:    str  =					int(sequence[i]		,     2     )

 return sequence
def 			__UpperCamelCase       (   UpperCAmelCase     ):

 # 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"]

 lowercase__				:    Dict  =					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
 lowercase__				:    Dict  =					gray_code_sequence_string(bit_count - 1     )

 lowercase__				:    Dict  =					[]

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

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

 return sequence


if __name__ == "__main__":
  import doctest

  doctest.testmod()



def     _a					(						lowerCamelCase = 100_0000							):
 lowerCamelCase		:	Any							=      set(range(3,	lowerCamelCase,	2							)							)
 primes.add(2							)
 for p in range(3,	lowerCamelCase,	2							):
  if p not in primes:
   continue
  primes.difference_update(set(range(p * p,	lowerCamelCase,	lowerCamelCase							)							)							)

 lowerCamelCase		:	Any							=      [float(lowerCamelCase							) for n in range(limit + 1							)]

 for p in primes:
  for n in range(lowerCamelCase,	limit + 1,	lowerCamelCase							):
   phi[n] *= 1 - 1 / p

 return int(sum(phi[2:]							)							)


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




