



"""simple docstring"""




import math

def 		__snake_case		(   SCREAMING_SNAKE_CASE__			:		Optional[int]       )						->     Optional[Any]:





     '''simple docstring'''

     if 1 < number < 4:
          # 2 and 3 are primes
          return True
     elif number < 2 or number % 2 == 0 or number % 3 == 0:
          # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
          return False

     # All primes number are in format of 6k +/- 1
     for i in range(5		,						int(math.sqrt(SCREAMING_SNAKE_CASE__       ) + 1       )		,						6       ):
          if number % i == 0 or number % (i + 2) == 0:
               return False
     return True

def 		__snake_case		(   SCREAMING_SNAKE_CASE__			:		Dict = 600_851_475_143       )						->     Any:





     '''simple docstring'''

     try:
          _UpperCAmelCase    :			List[str]              =					int(SCREAMING_SNAKE_CASE__       )
     except (TypeError, ValueError):
          raise TypeError("Parameter n must be int or castable to int."       )
     if n <= 0:
          raise ValueError("Parameter n must be greater than or equal to one."       )
     _UpperCAmelCase    :			str              =					0
     if is_prime(SCREAMING_SNAKE_CASE__       ):
          return n
     while n % 2 == 0:
          n //= 2
     if is_prime(SCREAMING_SNAKE_CASE__       ):
          return n
     for i in range(3		,						int(math.sqrt(SCREAMING_SNAKE_CASE__       )       ) + 1		,						2       ):
          if n % i == 0:
               if is_prime(n // i       ):
                    _UpperCAmelCase    :			Union[str, Any]              =					n // i
                    break
               elif is_prime(SCREAMING_SNAKE_CASE__       ):
                    _UpperCAmelCase    :			Dict              =					i
     return max_number


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





"""simple docstring"""




def 		__snake_case		(   SCREAMING_SNAKE_CASE__			:		list       )						->     bool:





     '''simple docstring'''

     if not isinstance(SCREAMING_SNAKE_CASE__		,						SCREAMING_SNAKE_CASE__       ):
          raise ValueError("Input series is not valid, valid series - [1, 2/3, 2]"       )
     if len(SCREAMING_SNAKE_CASE__       ) == 0:
          raise ValueError("Input list must be a non empty list"       )
     if len(SCREAMING_SNAKE_CASE__       ) == 1 and series[0] != 0:
          return True
     _UpperCAmelCase    :			Tuple              =					[]
     _UpperCAmelCase    :			Any              =					len(SCREAMING_SNAKE_CASE__       )
     for i in range(0		,						SCREAMING_SNAKE_CASE__       ):
          if series[i] == 0:
               raise ValueError("Input series cannot have 0 as an element"       )
          rec_series.append(1 / series[i]       )
     _UpperCAmelCase    :			Dict              =					rec_series[1] - rec_series[0]
     for index in range(2		,						SCREAMING_SNAKE_CASE__       ):
          if rec_series[index] - rec_series[index - 1] != common_diff:
               return False
     return True

def 		__snake_case		(   SCREAMING_SNAKE_CASE__			:		list       )						->     float:





     '''simple docstring'''

     if not isinstance(SCREAMING_SNAKE_CASE__		,						SCREAMING_SNAKE_CASE__       ):
          raise ValueError("Input series is not valid, valid series - [2, 4, 6]"       )
     if len(SCREAMING_SNAKE_CASE__       ) == 0:
          raise ValueError("Input list must be a non empty list"       )
     _UpperCAmelCase    :			Any              =					0
     for val in series:
          answer += 1 / val
     return len(SCREAMING_SNAKE_CASE__       ) / answer


if __name__ == "__main__":
 import doctest

 doctest.testmod()
