"""simple docstring"""






from __future__ import annotations


def      UpperCAmelCase__			(							lowerCAmelCase__	:list[int | str]						)					->       None:
      '''simple docstring'''


      create_state_space_tree(lowerCAmelCase__   ,						[]   ,						0   ,						[0 for i in range(len(lowerCAmelCase__						)						)]						)


def      UpperCAmelCase__			(							lowerCAmelCase__	:list[int | str]   ,						lowerCAmelCase__	:list[int | str]   ,						lowerCAmelCase__	:int   ,						lowerCAmelCase__	:list[int]   ,						)					->       None:
      '''simple docstring'''


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

      for i in range(len(lowerCAmelCase__						)						):
            if not index_used[i]:
                  current_sequence.append(sequence[i]						)
                  lowercase								=      True
                  create_state_space_tree(lowerCAmelCase__   ,						lowerCAmelCase__   ,						index + 1   ,						lowerCAmelCase__						)
                  current_sequence.pop()
                  lowercase								=      False
__lowerCAmelCase       :			list[int | str]   	=[3, 1, 2, 4]
generate_all_permutations(sequence)

__lowerCAmelCase       :			list[int | str]   	=["A", "B", "C"]






generate_all_permutations(sequence_a)




"""simple docstring"""






from math import pow, sqrt


def      UpperCAmelCase__			(							*lowerCAmelCase__	:float						)					->       bool:
      '''simple docstring'''


      lowercase								=      len(lowerCAmelCase__						) > 0 and all(value > 0.0 for value in values						)
      return result


def      UpperCAmelCase__			(							lowerCAmelCase__	:float   ,						lowerCAmelCase__	:float						)					->       float | ValueError:
      '''simple docstring'''


      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      UpperCAmelCase__			(							lowerCAmelCase__	:float   ,						lowerCAmelCase__	:float   ,						lowerCAmelCase__	:float						)					->       float | ValueError:
      '''simple docstring'''


      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      UpperCAmelCase__			(							lowerCAmelCase__	:float   ,						lowerCAmelCase__	:float   ,						lowerCAmelCase__	:float						)					->       float | ValueError:
      '''simple docstring'''


      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      UpperCAmelCase__			(							lowerCAmelCase__	:float   ,						lowerCAmelCase__	:float   ,						lowerCAmelCase__	:float						)					->       float | ValueError:
      '''simple docstring'''


      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      UpperCAmelCase__			(							lowerCAmelCase__	:float   ,						lowerCAmelCase__	:float   ,						lowerCAmelCase__	:float						)					->       float | ValueError:
      '''simple docstring'''


      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."""						)
      )



