





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


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


if __name__ == "__main__":
						import doctest

						doctest.testmod()








def 				SCREAMING_SNAKE_CASE__    (     __a ,			__a ):
	if len(str(__a ) ) == 1 or len(str(__a ) ) == 1:
		return a * b

	snake_case_		:      Dict           =						max(len(str(__a ) ) ,			len(str(__a ) ) )
	snake_case_		:      Tuple           =						ma // 2

	snake_case_    ,snake_case_		:      Tuple           =						divmod(__a ,			10**ma )
	snake_case_    ,snake_case_		:      int           =						divmod(__a ,			10**ma )

	snake_case_		:      str           =						karatsuba(__a ,			__a )
	snake_case_		:      List[str]           =						karatsuba((aa + aa) ,			(ba + ba) )
	snake_case_		:      Optional[Any]           =						karatsuba(__a ,			__a )

	return (z * 10 ** (2 * ma)) + ((y - z - x) * 10 ** (ma)) + (x)


def 				SCREAMING_SNAKE_CASE__    (     ):
	print(karatsuba(1_54_63 ,			2_34_89 ) )


if __name__ == "__main__":
						main()

