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@Pati ******
First off I'd say IF you intend to be here longer than 30 days (the amount of time a visa exempt entry gets you stamped in for) you should at least BUY a single entry tourist visa from the thai consulate in your country BEFORE you wing your way here.
That would stamp you in for 60 days and you could apply for a 30 day extension for 1900baht at the immigration office once you're here.
That does a couple things, FIRST it means you won't have a problem checking in with the air carrier bringing you here because you'll have a valid visa in your passport when you check in. (meaning you won't need to show them proof of onward travel). AND secondly you will get almost 90 days here without having to leave the country.
Good Luck, (y)