






"""simple docstring"""





def      lowerCamelCase__       (							_lowerCamelCase       :		int )      ->				list:
  lowerCamelCase_         =						int(_lowerCamelCase )
  if n_element < 1:
    lowerCamelCase_         =						ValueError('a should be a positive number' )
    raise my_error

  lowerCamelCase_         =						[1]
  lowerCamelCase_     ,	lowerCamelCase_     ,	lowerCamelCase_         =						(0, 0, 0)
  lowerCamelCase_         =						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__":
  _SCREAMING_SNAKE_CASE					:				Tuple					    =						input('''Enter the last number (nth term) of the Hamming Number Series: ''')
  print('''Formula of Hamming Number Series => 2^i * 3^j * 5^k''')
  _SCREAMING_SNAKE_CASE					:				Optional[int]					    =						hamming(int(n))
  print('''-----------------------------------------------------''')
  print(F'''The list with nth numbers is: {hamming_numbers}''')
  print('''-----------------------------------------------------''')












"""simple docstring"""





from math import pow, sqrt







def      lowerCamelCase__       (							*_lowerCamelCase       :		float )      ->				bool:
  lowerCamelCase_         =						len(_lowerCamelCase ) > 0 and all(value > 0.0 for value in values )
  return result







def      lowerCamelCase__       (							_lowerCamelCase       :		float		,				_lowerCamelCase       :		float )      ->				float | ValueError:
  return (
      round(sqrt(molar_mass_a / molar_mass_a )		,				6 )
      if validate(_lowerCamelCase		,				_lowerCamelCase )
      else ValueError('Input Error: Molar mass values must greater than 0.' )
  )







def      lowerCamelCase__       (							_lowerCamelCase       :		float		,				_lowerCamelCase       :		float		,				_lowerCamelCase       :		float )      ->				float | ValueError:
  return (
      round(effusion_rate * sqrt(molar_mass_a / molar_mass_a )		,				6 )
      if validate(_lowerCamelCase		,				_lowerCamelCase		,				_lowerCamelCase )
      else ValueError(
          'Input Error: Molar mass and effusion rate values must greater than 0.' )
  )







def      lowerCamelCase__       (							_lowerCamelCase       :		float		,				_lowerCamelCase       :		float		,				_lowerCamelCase       :		float )      ->				float | ValueError:
  return (
      round(effusion_rate / sqrt(molar_mass_a / molar_mass_a )		,				6 )
      if validate(_lowerCamelCase		,				_lowerCamelCase		,				_lowerCamelCase )
      else ValueError(
          'Input Error: Molar mass and effusion rate values must greater than 0.' )
  )







def      lowerCamelCase__       (							_lowerCamelCase       :		float		,				_lowerCamelCase       :		float		,				_lowerCamelCase       :		float )      ->				float | ValueError:
  return (
      round(molar_mass / pow(effusion_rate_a / effusion_rate_a		,				2 )		,				6 )
      if validate(_lowerCamelCase		,				_lowerCamelCase		,				_lowerCamelCase )
      else ValueError(
          'Input Error: Molar mass and effusion rate values must greater than 0.' )
  )







def      lowerCamelCase__       (							_lowerCamelCase       :		float		,				_lowerCamelCase       :		float		,				_lowerCamelCase       :		float )      ->				float | ValueError:
  return (
      round(pow(effusion_rate_a / effusion_rate_a		,				2 ) / molar_mass		,				6 )
      if validate(_lowerCamelCase		,				_lowerCamelCase		,				_lowerCamelCase )
      else ValueError(
          'Input Error: Molar mass and effusion rate values must greater than 0.' )
  )




