





from __future__ import annotations

from typing import Any


def     lowerCamelCase_	(      lowerCAmelCase:	list[Any]				)->		None:
  create_state_space_tree(lowerCAmelCase    ,							[]    ,							0				)


def     lowerCamelCase_	(      lowerCAmelCase:	list[Any]    ,							lowerCAmelCase:	list[Any]    ,							lowerCAmelCase:	int				)->		None:

  if index == len(lowerCAmelCase				):
    print(lowerCAmelCase				)
    return

  create_state_space_tree(lowerCAmelCase    ,							lowerCAmelCase    ,							index + 1				)
  current_subsequence.append(sequence[index]				)
  create_state_space_tree(lowerCAmelCase    ,							lowerCAmelCase    ,							index + 1				)
  current_subsequence.pop()


if __name__ == "__main__":
      lowerCAmelCase_						   =    [3, 1, 2, 4]
      generate_all_subsequences(seq)

      seq.clear()
      seq.extend(["""A""", """B""", """C"""])
      generate_all_subsequences(seq)











def     lowerCamelCase_	(      lowerCAmelCase:	int				)->		list:
  _snake_case   :				List[Any]														=	int(lowerCAmelCase				)
  if n_element < 1:
    _snake_case   :				int														=	ValueError('a should be a positive number'				)
    raise my_error

  _snake_case   :				Union[str, Any]														=	[1]
  _snake_case							,					_snake_case							,					_snake_case   :				Any														=	(0, 0, 0)
  _snake_case   :				str														=	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("""-----------------------------------------------------""")




