





def      SCREAMING_SNAKE_CASE      (   lowerCAmelCase       ):
       if not isinstance(SCREAMING_SNAKE_CASE__     ,							SCREAMING_SNAKE_CASE__       ):
              raise ValueError('''Input series is not valid, valid series - [2, 4, 8]'''       )
       if len(SCREAMING_SNAKE_CASE__       ) == 0:
              raise ValueError('''Input list must be a non empty list'''       )
       if len(SCREAMING_SNAKE_CASE__       ) == 1:
              return True
       try:
              _UpperCamelCase														=    series[1] / series[0]
              for index in range(len(SCREAMING_SNAKE_CASE__       ) - 1       ):
                     if series[index + 1] / series[index] != common_ratio:
                            return False
       except ZeroDivisionError:
              return False
       return True


def      SCREAMING_SNAKE_CASE      (   lowerCAmelCase       ):
       if not isinstance(SCREAMING_SNAKE_CASE__     ,							SCREAMING_SNAKE_CASE__       ):
              raise ValueError('''Input series is not valid, valid series - [2, 4, 8]'''       )
       if len(SCREAMING_SNAKE_CASE__       ) == 0:
              raise ValueError('''Input list must be a non empty list'''       )
       _UpperCamelCase														=    1
       for value in series:
              answer *= value
       return pow(SCREAMING_SNAKE_CASE__     ,							1 / len(SCREAMING_SNAKE_CASE__       )       )


if __name__ == "__main__":
       import doctest

       doctest.testmod()










def 		_UpperCAmelCase							(     SCREAMING_SNAKE_CASE__     :   Union[str, Any]     ,	SCREAMING_SNAKE_CASE__     :   int							):
     if n < 0:
          return 0
     # table[i] represents the number of ways to get to amount i
     __UpperCamelCase       				=[0] * (n + 1)

     # There is exactly 1 way to get to zero(You pick no coins).
     __UpperCamelCase       				=1

     # Pick all coins one by one and update table[] values
     # after the index greater than or equal to the value of the
     # picked coin
     for coin_val in s:
          for j in range(SCREAMING_SNAKE_CASE__     ,	n + 1							):
               table[j] += table[j - coin_val]

     return table[n]


if __name__ == "__main__":
   import doctest

   doctest.testmod()





