Smallest irreducible periodic Markov chain

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What would be the smallest periodic Markov chain?

We're studying periodic Markov chains in my probability course. I'm just trying to picture the smallest possible one but I can't seem to come up with it.

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$0\to1\to0\to1\to0\to1\to0\to1\to0\to1\to0\to1\to0\to1\to0\to1\to\ldots$ -- Did

From state $0$ you go to state $1$ with probability $1$ and from state $1$ you go to state $0$ with probability $1$. -- Ritz