code: 
  
  
  
  """simple docstring"""
  
  
  
  
  def 		__snake_case		(   SCREAMING_SNAKE_CASE__			:		int		,						SCREAMING_SNAKE_CASE__			:		int       )						->     int:
  
  
  
  
  
       '''simple docstring'''
  
       if a < b:
            return gcd(SCREAMING_SNAKE_CASE__		,						SCREAMING_SNAKE_CASE__       )
       if a % b == 0:
            return b
       return gcd(SCREAMING_SNAKE_CASE__		,						a % b       )
  
  def 		__snake_case		(   SCREAMING_SNAKE_CASE__			:		int		,						SCREAMING_SNAKE_CASE__			:		int		,						SCREAMING_SNAKE_CASE__			:		int       )						->     int:
  
  
  
  
  
       '''simple docstring'''
  
       if y == 0:
            return 1
       _UpperCAmelCase    :			List[str]              =					power(SCREAMING_SNAKE_CASE__		,						y // 2		,						SCREAMING_SNAKE_CASE__       ) % mod
       _UpperCAmelCase    :			List[str]              =					(temp * temp) % mod
       if y % 2 == 1:
            _UpperCAmelCase    :			Union[str, Any]              =					(temp * x) % mod
       return temp
  
  def 		__snake_case		(   SCREAMING_SNAKE_CASE__			:		int       )						->     bool:
  
  
  
  
  
       '''simple docstring'''
  
       _UpperCAmelCase    :			Dict              =					2
       while b < n:
            if gcd(SCREAMING_SNAKE_CASE__		,						SCREAMING_SNAKE_CASE__       ) == 1 and power(SCREAMING_SNAKE_CASE__		,						n - 1		,						SCREAMING_SNAKE_CASE__       ) != 1:
                 return False
            b += 1
       return True
  
  
  if __name__ == "__main__":
   _lowerCAmelCase       :      Any							=							int(input("Enter number: ").strip())
   if is_carmichael_number(number):
    print(F"{number} is a Carmichael Number.")
   else:
    print(F"{number} is not a Carmichael Number.")
  
style_context: 
  
  
  
  """simple docstring"""
  
  
  
  
  _lowerCAmelCase       :      str							=							{
      "0": 1,
      "1": 1,
      "2": 2,
      "3": 6,
      "4": 24,
      "5": 1_20,
      "6": 7_20,
      "7": 50_40,
      "8": 4_03_20,
      "9": 36_28_80,
  }
  
  _lowerCAmelCase       :      Optional[int]							=							{1_45: 1_45}
  
  _lowerCAmelCase       :      int							=							{
      1_45: 0,
      1_69: 3,
      3_63_01: 3,
      14_54: 3,
      8_71: 2,
      4_53_61: 2,
      8_72: 2,
  }
  
  def 		__snake_case		(   SCREAMING_SNAKE_CASE__			:		int       )						->     int:
  
  
  
  
  
       '''simple docstring'''
  
       if n in CACHE_SUM_DIGIT_FACTORIALS:
            return CACHE_SUM_DIGIT_FACTORIALS[n]
       _UpperCAmelCase    :			Dict              =					sum(DIGIT_FACTORIALS[let] for let in str(SCREAMING_SNAKE_CASE__       )       )
       _UpperCAmelCase    :			Any              =					ret
       return ret
  
  def 		__snake_case		(   SCREAMING_SNAKE_CASE__			:		int		,						SCREAMING_SNAKE_CASE__			:		set | None = None       )						->     int:
  
  
  
  
  
       '''simple docstring'''
  
       _UpperCAmelCase    :			Dict              =					previous or set()
       if n in CHAIN_LENGTH_CACHE:
            return CHAIN_LENGTH_CACHE[n]
       _UpperCAmelCase    :			Dict              =					sum_digit_factorials(SCREAMING_SNAKE_CASE__       )
       if next_number in previous:
            _UpperCAmelCase    :			List[str]              =					0
            return 0
       else:
            previous.add(SCREAMING_SNAKE_CASE__       )
            _UpperCAmelCase    :			str              =					1 + chain_length(SCREAMING_SNAKE_CASE__		,						SCREAMING_SNAKE_CASE__       )
            _UpperCAmelCase    :			str              =					ret
            return ret
  
  def 		__snake_case		(   SCREAMING_SNAKE_CASE__			:		int = 60		,						SCREAMING_SNAKE_CASE__			:		int = 1_000_000       )						->     int:
  
  
  
  
  
       '''simple docstring'''
  
       return sum(1 for i in range(1		,						SCREAMING_SNAKE_CASE__       ) if chain_length(SCREAMING_SNAKE_CASE__       ) == num_terms       )
  
  
  if __name__ == "__main__":
   print(F"{solution() = }")
  