



"""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.")





"""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() = }")
