If the point $P(1,3)$ undergoes the following transformations successively:
$(i)$ Reflection with respect to the line $y=x$.
(ii) Translation through $3$ units along the positive direction of the $X$-axis.
(iii) Rotation through an angle of $\frac{\pi}{6}$ about the origin in the clockwise direction.
Then,the final position of the point $P$ is

• A
  $\left(\frac{6 \sqrt{3}+1}{2}, \frac{\sqrt{3}-6}{2}\right)$
• B
  $\left(\frac{\sqrt{7}}{2}, \frac{-5}{\sqrt{2}}\right)$
• C
  $\left(\frac{6+\sqrt{3}}{2}, \frac{1-6 \sqrt{3}}{2}\right)$
• D
  $\left(\frac{6+\sqrt{3}-1}{2}, \frac{6+\sqrt{3}}{2}\right)$