


"""simple docstring"""







def 					a__			(				SCREAMING_SNAKE_CASE    :    list[list[int]]				,      SCREAMING_SNAKE_CASE    :    int				,      SCREAMING_SNAKE_CASE    :    int				,      SCREAMING_SNAKE_CASE    :    list[int]				):


  '''simple docstring'''







  if graph[path[curr_ind - 1]][next_ver] == 0:
    return False

  # 2. Validate that next vertex is not already in path
  return not any(vertex == next_ver for vertex in path				)
def 					a__			(				SCREAMING_SNAKE_CASE    :    list[list[int]]				,      SCREAMING_SNAKE_CASE    :    list[int]				,      SCREAMING_SNAKE_CASE    :    int				):


  '''simple docstring'''







  if curr_ind == len(SCREAMING_SNAKE_CASE				):
    # return whether path exists between current and starting vertices
    return graph[path[curr_ind - 1]][path[0]] == 1

  # Recursive Step
  for next_ver in range(0				,      len(SCREAMING_SNAKE_CASE				)				):
    if valid_connection(SCREAMING_SNAKE_CASE				,      SCREAMING_SNAKE_CASE				,      SCREAMING_SNAKE_CASE				,      SCREAMING_SNAKE_CASE				):
      # Insert current vertex  into path as next transition
      lowerCAmelCase     :     int								=							next_ver
      # Validate created path
      if util_hamilton_cycle(SCREAMING_SNAKE_CASE				,      SCREAMING_SNAKE_CASE				,      curr_ind + 1				):
        return True
      # Backtrack
      lowerCAmelCase     :     List[Any]								=							-1
  return False





def 					a__			(				SCREAMING_SNAKE_CASE    :    list[list[int]]				,      SCREAMING_SNAKE_CASE    :    int = 0				):


  '''simple docstring'''







  lowerCAmelCase     :     Optional[Any]								=							[-1] * (len(SCREAMING_SNAKE_CASE				) + 1)
  # initialize start and end of path with starting index
  lowerCAmelCase     :     Union[str, Any]								=							start_index
  # evaluate and if we find answer return path either return empty array
  return path if util_hamilton_cycle(SCREAMING_SNAKE_CASE				,      SCREAMING_SNAKE_CASE				,      1				) else []












lowerCAmelCase_    =				{
    "joule": 1.0,
    "kilojoule": 1_0_0_0,
    "megajoule": 1_0_0_0_0_0_0,
    "gigajoule": 1_0_0_0_0_0_0_0_0_0,
    "wattsecond": 1.0,
    "watthour": 3_6_0_0,
    "kilowatthour": 3_6_0_0_0_0_0,
    "newtonmeter": 1.0,
    "calorie_nutr": 4_1_8_6.8,
    "kilocalorie_nutr": 4_1_8_6_8_0_0.0_0,
    "electronvolt": 1.602_176_634e-19,
    "britishthermalunit_it": 1_0_5_5.0_5_5_8_5,
    "footpound": 1.355_818,
}






def      lowerCamelCase_						(				_UpperCamelCase ,				_UpperCamelCase ,				_UpperCamelCase )		->						float:






				"""simple docstring"""


				if to_type not in ENERGY_CONVERSION or from_type not in ENERGY_CONVERSION:
								snake_case_						:    str				=  (
								    f'''Incorrect \'from_type\' or \'to_type\' value: {from_type!r}, {to_type!r}\n'''
								    f'''Valid values are: {", ".join(_UpperCamelCase )}'''
								)
								raise ValueError(_UpperCamelCase )
				return value * ENERGY_CONVERSION[from_type] / ENERGY_CONVERSION[to_type]


if __name__ == "__main__":
	import doctest

	doctest.testmod()
