There are hotels nearby and affordable too...you cannot go through security to the departure halls, till you are checked in, the airline check in desk will not be open until a few hours to reporting time. but you can descend the escalators to the arrival hall. There are seats there and you will find other passengers sleeping or waiting too. There are also airport staff around at the arrival hall.
better look for hotel nearby. lounges require membership and will close between at least midnight and 5 a.m....
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