def 				UpperCAmelCase						(    lowercase							):







				"""simple docstring"""



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

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

				return sequence





def 				UpperCAmelCase						(    lowercase							):







				"""simple docstring"""



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

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

				__lowercase 			=							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 			=							gray_code_sequence_string(bit_count - 1							)

				__lowercase 			=							[]

				# append 0 to first half of the smaller sequence generated
				for i in range(seq_len // 2							):
								__lowercase 			=							'''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							)							):
								__lowercase 			=							'''1''' + smaller_sequence[i]
								sequence.append(__lowerCamelCase							)

				return sequence


if __name__ == "__main__":
		import doctest

		doctest.testmod()





def 		__A		(	__lowerCamelCase    )      ->       int:
	a										=							0
	while num > 0:
		digit_sum += num % 10
		num //= 10
	return digit_sum





def 		__A		(	__lowerCamelCase = 100    )      ->       int:
	a										=							1
	a										=							2

	for i in range(2							,			max_n + 1    ):
		a										=							pre_numerator
		a										=							2 * i // 3 if i % 3 == 0 else 1
		a										=							cur_numerator
		a										=							e_cont * pre_numerator + temp

	return sum_digits(__lowerCamelCase    )


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

