Counterexample to show that the interior of union may be larger than the union of interiors

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I know the identity $\operatorname{int}(C \cup D) \supset \operatorname{int}(C) \cup \operatorname{int}(D) $.

I need to find a counterexample showing that equality does not hold in general.

Could you please give me any hint?

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Consider the subsets $(0,1]$ and $(1,3)$ of real line.