A large and merry group of N guys and N girls went to celebrate a birthday in a restaurant. They were randomly seated at a big rotating table by a hurried waiter who quickly took their drink orders. Every girl ordered a wine, and every guys ordered a beer. Bringing the drinks, the waiter brought the right number of beers/wines, but forgot who ordered what and placed the drinks randomly in front of everyone. The party was enraged because more than a half got the wrong drink and demanded to see the manager. The manager appeared and said: "My apologies, but this is not such a big deal. In fact, I can rotate the table without touching the drinks so that more than half of you will get what you ordered." Is the manager's claim correct?