If I make a reservation for 2 nights at an IC, but I do not arrive at the hotel until after midnight on the first night, does it count as a qualifying night (thus 2 nights' booking crediting as 2 qualifying nights) or does the first night not count as a "night" and I'll end up with just 1 qualifying night?

Alternatively, what time of the night is the cut-off time for it to qualify as a "qualifying night"?

I'm catching a late-night flight that will not get me to the hotel until about 0430 am, so I'm wondering how it will credit.