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You don't need to pick up your checked luggage, just go to the Korean counter in the airport lobby directly after exiting the customs. It only takes 3 minutes to get on the bus and arrive at the hotel.
The hotel will give you meal coupons when you check in, and will tell you when to MORNING CALL tomorrow morning and when to take the bus to the airport. There is a bus every 20 minutes.
Overnight at Incheon Airport.
There is an on-site hotel at the airport, which costs about 6,000 yen per night.
It seems to be on the 4th floor.
Very easy to find.
But it is said that the facilities are not very good.