

import itertools


def        _UpperCAmelCase							(	_SCREAMING_SNAKE_CASE       :		int = 1_000_000							):





    """simple docstring"""


    SCREAMING_SNAKE_CASE_						=    [1]

    for i in itertools.count(len(_SCREAMING_SNAKE_CASE							)							):
        SCREAMING_SNAKE_CASE_						=    0
        for j in itertools.count(1							):
            SCREAMING_SNAKE_CASE_						=    -1 if j % 2 == 0 else +1
            SCREAMING_SNAKE_CASE_						=    (j * j * 3 - j) // 2
            if index > i:
                break
            item += partitions[i - index] * sign
            item %= number
            index += j
            if index > i:
                break
            item += partitions[i - index] * sign
            item %= number

        if item == 0:
            return i
        partitions.append(_SCREAMING_SNAKE_CASE							)

    return 0


if __name__ == "__main__":
       import doctest

       doctest.testmod()

       print(F'{solution() = }')





def        _UpperCAmelCase							(	_SCREAMING_SNAKE_CASE       :		list							):





    """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:
        SCREAMING_SNAKE_CASE_						=    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       :		list							):





    """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'							)
    SCREAMING_SNAKE_CASE_						=    1
    for value in series:
        answer *= value
    return pow(_SCREAMING_SNAKE_CASE			, 1 / len(_SCREAMING_SNAKE_CASE							)							)


if __name__ == "__main__":
       import doctest

       doctest.testmod()


