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Define language $L’$ for given regular language $L$ as: $$L’=\{uv | u,v\in\Sigma^{*}, vu\in L\}$$ is language $L’$ also regular?

Hello, I need some help with solving this question. I need somehow to determine where to divide each word. Or actually - in what state of its automata will that language be. If that makes sense and my understanding of the problem is correct.

Yuval Filmus
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Mike
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