





__lowerCAmelCase     =			{
    "kilogram": 1,
    "gram": pow(10, 3),
    "milligram": pow(10, 6),
    "metric-ton": pow(10, -3),
    "long-ton": 0.0009842073,
    "short-ton": 0.0011023122,
    "pound": 2.2046244202,
    "stone": 0.1574731728,
    "ounce": 35.273990723,
    "carrat": 5_000,
    "atomic-mass-unit": 6.0_22_13_66_52e26,
}

__lowerCAmelCase     =			{
    "kilogram": 1,
    "gram": pow(10, -3),
    "milligram": pow(10, -6),
    "metric-ton": pow(10, 3),
    "long-ton": 1016.04608,
    "short-ton": 907.184,
    "pound": 0.453592,
    "stone": 6.35029,
    "ounce": 0.0283495,
    "carrat": 0.0002,
    "atomic-mass-unit": 1.6_60_54_01_99e-27,
}

def     a						(      _lowercase   :     str ,						_lowercase   :     str ,						_lowercase   :     float       )     ->float:
  if to_type not in KILOGRAM_CHART or from_type not in WEIGHT_TYPE_CHART:
    UpperCamelCase__         =	(
        F"""Invalid 'from_type' or 'to_type' value: {from_type!r}, {to_type!r}\n"""
        F"""Supported values are: {', '.join(_lowercase       )}"""
    )
    raise ValueError(_lowercase       )
  return value * KILOGRAM_CHART[to_type] * WEIGHT_TYPE_CHART[from_type]


if __name__ == "__main__":
    import doctest

    doctest.testmod()












__lowerCAmelCase     =			{
    "0": 1,
    "1": 1,
    "2": 2,
    "3": 6,
    "4": 24,
    "5": 120,
    "6": 720,
    "7": 5_040,
    "8": 40_320,
    "9": 362_880,
}

__lowerCAmelCase     =			{145: 145}

__lowerCAmelCase     =			{
    145: 0,
    169: 3,
    36_301: 3,
    1_454: 3,
    871: 2,
    45_361: 2,
    872: 2,
}

def     a						(      _lowercase   :     int       )     ->int:
		if n in CACHE_SUM_DIGIT_FACTORIALS:
				return CACHE_SUM_DIGIT_FACTORIALS[n]
		UpperCamelCase__         =	sum(DIGIT_FACTORIALS[let] for let in str(_lowercase       )       )
		UpperCamelCase__         =	ret
		return ret

def     a						(      _lowercase   :     int ,						_lowercase   :     set | None = None       )     ->int:
		UpperCamelCase__         =	previous or set()
		if n in CHAIN_LENGTH_CACHE:
				return CHAIN_LENGTH_CACHE[n]
		UpperCamelCase__         =	sum_digit_factorials(_lowercase       )
		if next_number in previous:
				UpperCamelCase__         =	0
				return 0
		else:
				previous.add(_lowercase       )
				UpperCamelCase__         =	1 + chain_length(_lowercase ,						_lowercase       )
				UpperCamelCase__         =	ret
				return ret

def     a						(      _lowercase   :     int = 6_0 ,						_lowercase   :     int = 1_0_0_0_0_0_0       )     ->int:
		return sum(1 for i in range(1 ,						_lowercase       ) if chain_length(_lowercase       ) == num_terms       )


if __name__ == "__main__":
				print(f"""{solution() = }""")





