For a function \({f(n)}=n\times \lg\left(n\right)\) and time \(\text{t}=10^{3}\) \(\mu\text{s}\), calculate the largest size of the problem \(\text{n} \in \mathbb{N}\) that can be solved in \(\text{t}\), assuming that for the algorithm to solve the problem it takes \({f(n)}\) microseconds.

**Details and assumptions**:

\(1\)) Do it \(\color{blue}{\text{without WA}}\)

\(2\)) Inspired from \(\color{tan}{\text{CLRS}}\)

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