"""

Doctest example from the official Python documentation.

https://docs.python.org/library/doctest.html

"""

def factorial(n):

    """Return the factorial of n, an exact integer >= 0.

    >>> [factorial(n) for n in range(6)]

    [1, 1, 2, 6, 24, 120]

    >>> factorial(30)  # doctest: +ELLIPSIS

    265252859812191058636308480000000...

    >>> factorial(-1)

    Traceback (most recent call last):

        ...

    ValueError: n must be >= 0

    Factorials of floats are OK, but the float must be an exact integer:

    >>> factorial(30.1)

    Traceback (most recent call last):

        ...

    ValueError: n must be exact integer

    >>> factorial(30.0)  # doctest: +ELLIPSIS

    265252859812191058636308480000000...

    It must also not be ridiculously large:

    >>> factorial(1e100)

    Traceback (most recent call last):

        ...

    OverflowError: n too large

    """

    import math

    if not n >= 0:

        raise ValueError("n must be >= 0")

    if math.floor(n) != n:

        raise ValueError("n must be exact integer")

    if n + 1 == n:  # catch a value like 1e300

        raise OverflowError("n too large")

    result = 1

    factor = 2

    while factor <= n:

        result *= factor

        factor += 1

    return result