




'''simple docstring'''
def   UpperCamelCase_       (		__SCREAMING_SNAKE_CASE    ):
    """simple docstring"""






    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:
        snake_case_	:      int            =  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   UpperCamelCase_       (		__SCREAMING_SNAKE_CASE    ):
    """simple docstring"""






    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"    )
    snake_case_	:      List[str]            =  1
    for value in series:
        answer *= value
    return pow(__SCREAMING_SNAKE_CASE,						1 / len(__SCREAMING_SNAKE_CASE    )    )


if __name__ == "__main__":
  import doctest

  doctest.testmod()






'''simple docstring'''
def   UpperCamelCase_       (		__SCREAMING_SNAKE_CASE    ):
    """simple docstring"""






    snake_case_	:      Optional[int]            =  len(__SCREAMING_SNAKE_CASE    )

    # Set the gap value to be decreased by a factor of 1.3
    # after each iteration
    snake_case_	:      Optional[int]            =  1.3

    # Continue sorting until the gap is 1
    while gap > 1:
        # Decrease the gap value
        snake_case_	:      Optional[Any]            =  int(gap / shrink    )

        # Sort the elements using insertion sort
        for i in range(__SCREAMING_SNAKE_CASE,						len(__SCREAMING_SNAKE_CASE    )    ):
            snake_case_	:      Any            =  collection[i]
            snake_case_	:      int            =  i
            while j >= gap and collection[j - gap] > temp:
                snake_case_	:      Dict            =  collection[j - gap]
                j -= gap
            snake_case_	:      Optional[int]            =  temp

    return collection


if __name__ == "__main__":
  import doctest

  doctest.testmod()




