From the information given, we find that the cities P, Q, R, S, T are connected as follows:
$\begin{array}{lcr} P \Leftarrow & \Rightarrow R \Leftarrow & \Rightarrow S \\ \Uparrow & \Uparrow & \\ \Downarrow & \Downarrow & \\ Q \Leftarrow & \Rightarrow T & \end{array}$
To go to S back to P, R must be visited twice.