



"""simple docstring"""
def   A_    (     _lowercase      ):







						'''simple docstring'''


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







						'''simple docstring'''


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


if __name__ == "__main__":
						import doctest

						doctest.testmod()




import sys



def      __lowerCAmelCase    (				snake_case						:     int    ,   snake_case						:     list[int]			)							->				int:
   if not numbers:
      return 0
   if target == 0 and target in numbers:
      return 0
   if not isinstance(snake_case    ,   (list, tuple)			) or not all(
       isinstance(snake_case    ,   snake_case			) for number in numbers			):
      raise ValueError("""numbers must be an iterable of integers"""			)

   __lowerCamelCase:					Union[str, Any]	 =						0
   __lowerCamelCase:					str	 =						sys.maxsize

   while right < len(snake_case			):
      curr_sum += numbers[right]
      while curr_sum >= target and left <= right:
         __lowerCamelCase:					str	 =						min(snake_case    ,   right - left + 1			)
         curr_sum -= numbers[left]
         left += 1
      right += 1

   return 0 if min_len == sys.maxsize else min_len


