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For languages $A$ and $B,$ let the $\text{perfect shuffle}$ of $A$ and $B$ be the language

$\text{{$w| w = a_{1}b_{1} · · · a_{k}b_{k},$ where $a_{1} · · · a_{k} ∈ A$ and $b_{1} · · · b_{k} ∈ B,$  each $a_{i}, b_{i} ∈ Σ$}}.$

Show that the class of regular languages is closed under perfect shuffle.
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