


"""simple docstring"""
from math import factorial







def 						_a				(      _SCREAMING_SNAKE_CASE = 20				)    ->				int:
							snake_case_           =		2 * n  # middle entry of odd rows starting at row 3 is the solution for n = 1,
							# 2, 3,...
							snake_case_           =		n // 2

							return int(factorial(_SCREAMING_SNAKE_CASE				) / (factorial(_SCREAMING_SNAKE_CASE				) * factorial(n - k				))				)


if __name__ == "__main__":
				import sys

				if len(sys.argv) == 1:
								print(solution(20))
				else:
								try:
												__SCREAMING_SNAKE_CASE							:    Optional[int]		=    int(sys.argv[1])
												print(solution(n))
								except ValueError:
												print('Invalid entry - please enter a number.')







"""simple docstring"""
def 						_a				(      _SCREAMING_SNAKE_CASE				)    ->				list:

							# 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
							snake_case_           =		gray_code_sequence_string(_SCREAMING_SNAKE_CASE				)
							#
							# convert them to integers
							for i in range(len(_SCREAMING_SNAKE_CASE				)				):
														snake_case_           =		int(sequence[i]				, 2				)

							return sequence







def 						_a				(      _SCREAMING_SNAKE_CASE				)    ->				list:

							# 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"]

							snake_case_           =		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
							snake_case_           =		gray_code_sequence_string(bit_count - 1				)

							snake_case_           =		[]

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

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

							return sequence


if __name__ == "__main__":
				import doctest

				doctest.testmod()



