You can get this "mask" by getting a piece of priority mail from Kafei to be delivered to Madame Aroma. If you check by the Post Office on the third day and show him the letter, he will run off to deliver it. The next time you talk to him, he will tell you that he's fleeing the city to get away from its imminent destruction. He will then give you his hat and leave you in charge.
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While wearing the hat, you can check inside of mailboxes for goodies. The first thing you will find will be a Heart Piece but after that you'll only ever find green rupees.
