Let $f(x) = x + \log_e x - x\log_e x$, $x \in (0, \infty)$.

- Column 1 contains information about zeros of $f(x)$, $f'(x)$ and $f''(x)$.
- Column 2 contains information about the limiting behavior of $f(x)$, $f'(x)$ and $f''(x)$ at infinity.
- Column 3 contains information about increasing/decreasing nature of $f(x)$ and $f'(x)$.

\begin{tabular}{|l|l|l|}
\hline
Column 1 & Column 2 & Column 3 \\
\hline
(I) $f(x) = 0$ for some $x \in (1, e^2)$ & (i) $\lim_{x\to\infty} f(x) = 0$ & (P) $f$ is increasing in $(0,1)$ \\
\hline
(II) $f'(x) = 0$ for some $x \in (1, e)$ & (ii) $\lim_{x\to\infty} f(x) = -\infty$ & (Q) $f$ is decreasing in $(e, e^2)$ \\
\hline
(III) $f'(x) = 0$ for some $x \in (0,1)$ & (iii) $\lim_{x\to\infty} f'(x) = -\infty$ & (R) $f'$ is increasing in $(0,1)$ \\
\hline
(IV) $f''(x) = 0$ for some $x \in (1, e)$ & (iv) $\lim_{x\to\infty} f''(x) = 0$ & (S) $f'$ is decreasing in $(e, e^2)$ \\
\hline
\end{tabular}

Which of the following options is the only CORRECT combination?

[A] (I) (ii) (R)

[B] (II) (iii) (S)

[C] (III) (iv) (P)

[D] (IV) (i) (S)