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January 16-21, 2011. The largest cruise liner in the world up to date, Royal Caribbean's Allure of the Seas on a 7 day sail in the West Caribbean. Here, warming up before the Aqua Aria, a diving and acrobatics show, a polish trampoline champion Patryk Sawicki, 30 (left) and a high diving champion from Czech Republic, Michal Navratil, 25 (right). Piotr Redlinski for The New York Times.