


def 						__SCREAMING_SNAKE_CASE       (					lowercase_			)		->    list:




						'''simple docstring'''







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

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

						return sequence




def 						__SCREAMING_SNAKE_CASE       (					lowercase_			)		->    list:




						'''simple docstring'''







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

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

						__UpperCAmelCase :       Union[str, 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
						__UpperCAmelCase :       Any  						=  gray_code_sequence_string(bit_count - 1			)

						__UpperCAmelCase :       Optional[Any]  						=  []

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

						# append 1 to second half ... start from the end of the list
						for i in reversed(range(seq_len // 2			)			):
												__UpperCAmelCase :       List[Any]  						=  '''1''' + smaller_sequence[i]
												sequence.append(lowercase_			)

						return sequence


if __name__ == "__main__":
				import doctest

				doctest.testmod()





def 						__SCREAMING_SNAKE_CASE       (					lowercase_			)		->    list:




						'''simple docstring'''







						__UpperCAmelCase :       Optional[Any]  						=  int(lowercase_			)
						if n_element < 1:
												__UpperCAmelCase :       str  						=  ValueError('''a should be a positive number'''			)
												raise my_error

						__UpperCAmelCase :       Any  						=  [1]
						__UpperCAmelCase						,			__UpperCAmelCase						,			__UpperCAmelCase :       Any  						=  (0, 0, 0)
						__UpperCAmelCase :       int  						=  1
						while index < n_element:
												while hamming_list[i] * 2 <= hamming_list[-1]:
																		i += 1
												while hamming_list[j] * 3 <= hamming_list[-1]:
																		j += 1
												while hamming_list[k] * 5 <= hamming_list[-1]:
																		k += 1
												hamming_list.append(
												    min(hamming_list[i] * 2			,					hamming_list[j] * 3			,					hamming_list[k] * 5			)			)
												index += 1
						return hamming_list


if __name__ == "__main__":
				lowerCAmelCase							=						input("""Enter the last number (nth term) of the Hamming Number Series: """)
				print("""Formula of Hamming Number Series => 2^i * 3^j * 5^k""")
				lowerCAmelCase							=						hamming(int(n))
				print("""-----------------------------------------------------""")
				print(F'The list with nth numbers is: {hamming_numbers}')
				print("""-----------------------------------------------------""")

