Sensible is absolutely right. You can do that on a Visa Waiver.
Now you'd just better hope the guy working on immigration the day you arrive knows the rules as well as you do. Coz if he doesn't, you're going home. Doesn't matter what the rules say - if he thinks you need a Visa, that's all that counts.
Best advice would be to get a Visa anyway if you've got time, even though you don't need one. If you travel without a Visa, don't lie to immigration, but don't offer them any more information than you have to either.
Once you get past immigration, you'll find America is a fantastic place to fly!
Have fun!
FFF
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