There aren't any public showers unfortunately, however you can shower if you are able to get into one of the various lounges offered by the airlines for their business class/first class passengers. Most of the lounges have showers amongst other such comforts. If you are not a first class/Business Class passenger, you can pay for a day pass in order to gain entrance to some lounges. There is also a spa at the airport that allows you to purchase a 30 min package for showers. Unfortunately they arent a 24hr service, the lounges are 24/7.
No, you should shower before headed to the airport! :)
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