Yea hats are things. So it's a noun. You were a hat, you buy a hat, you take a hat off your head.
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The Suspension System
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hat nolan sotillo eine freundin
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If you mean by French hat the kind artists typically wear, you
are referring to a beret. A beret is a soft, round, flat-crowned
hat, usually of woven, hand-knitted wool, crocheted cotton, wool
felt, or acrylic fabric.