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Suppose $$L=\{wo^n\mid w\in\{a,b\}^*, n_a(w)=n \text{ or} |w|=n\}$$ Can we conclude that $L$ is DCFl?

I think it's DCFL because $$L=\{a^no^n\}\cup \{\{a,b\}^no^n\}$$ Since $$\{a^no^n\}\subseteq \{\{a,b\}^no^n\}$$ We can coclude that $L$ is DCFL. Becuase $$L= \{\{a,b\}^no^n\}$$

But i think my argument, maybe isn't true, anyone can approve my argument or disprove my argument?

ErroR
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